my output is not simplified to one number

Hi guys,

I need help with this issue please.

my output are not simplified at all. For example on of the outputs is

>> P(1)

ans =

(3931879*sin(exp(1) - 2))/4000000 - (1862469*sin(exp(2) - 2))/80000000 + (45497457*sin(exp(1/3) - 2))/40000000 - (18734247*sin(exp(2/3) - 2))/16000000 - (8607627*sin(exp(4/3) - 2))/16000000 + (6776217*sin(exp(5/3) - 2))/40000000 - (35386911*sin(1))/80000000

This all in on line i should has a one number instead of all this long expression

Best,

Answer 1

[Walter Roberson]

vpa(P(1))

if you want to evaluate to a symbolic number with some number of decimal places.

double(P(1))

if you want to evaluate to a double precision floating point number.

[Abdulaziz]

Thank you Mr Walter your answers always the best

I appreciate your advice.

Answer 2

[Geoff]

Looks like you want:

A .* sin(exp(B) - 2) ./ C;

Where:

A = [3931879, -1862469, 45497457, -18734247, ...];
B = [1, 2, 1/3, 2/3, ...];
C = [4, 80, 40, 16, ...] * 1e6;

[edit]

Oh, I think you mean you want:

>> eval(P(1))

ans =

    -0.8428

[Abdulaziz]

Tank you

[Walter Roberson]

You should never eval() a symbolic expression. Symbolic expressions are in a language that is not MATLAB.

Answer 3

[m sh]

Thank you. It was helpful for me.

Answer 4

[muhammad kaleem]

simplify 2+5-4+10^10+7^2

6

Answer 5

[Tomi Asli]

Hi,

I have a similar problem, however the accepted answer will not work:

solving for x at an intersection of a linear function with a 4th order polynomial function

>> syms a b c d e m t x 
>> eqn = t+m*x == a+b*x+c*x^2+d*x^3+e*x^4
>> fforx = solve(eqn, x, "MaxDegree", 4)

results in the expected output.

with the parameters for the variables

 t = -120.07208, m = -0.80227, a = 0.77755, b = 0.00161, c = 1.46526E-6, d = 7.15449E-8, e = 2.88799E-10

the second solution of fforx gives an expected value of -150.2553.

However the precedure to get this value is a two step procedure:

 >> fforx (2)
 
ans =
 
(3*6^(1/2)*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))*(3*3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2) + 2*(c/e - (3*d^2)/(8*e^2))^3 + 27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 72*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2) - 12*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))*((c/e - (3*d^2)/(8*e^2))^2 + 9*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(2/3) - 6*(c/e - (3*d^2)/(8*e^2))*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(1/3) + (12*(a - t))/e - (9*d^4)/(64*e^4) - (3*d*(b - m))/e^2 + (3*c*d^2)/(4*e^3))^(1/2) - 9*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(2/3)*((c/e - (3*d^2)/(8*e^2))^2 + 9*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(2/3) - 6*(c/e - (3*d^2)/(8*e^2))*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(1/3) + (12*(a - t))/e - (9*d^4)/(64*e^4) - (3*d*(b - m))/e^2 + (3*c*d^2)/(4*e^3))^(1/2) - (c/e - (3*d^2)/(8*e^2))^2*((c/e - (3*d^2)/(8*e^2))^2 + 9*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(2/3) - 6*(c/e - (3*d^2)/(8*e^2))*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(1/3) + (12*(a - t))/e - (9*d^4)/(64*e^4) - (3*d*(b - m))/e^2 + (3*c*d^2)/(4*e^3))^(1/2) - 12*(c/e - (3*d^2)/(8*e^2))*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(1/3)*((c/e - (3*d^2)/(8*e^2))^2 + 9*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(2/3) - 6*(c/e - (3*d^2)/(8*e^2))*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(1/3) + (12*(a - t))/e - (9*d^4)/(64*e^4) - (3*d*(b - m))/e^2 + (3*c*d^2)/(4*e^3))^(1/2))^(1/2)/(6*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(1/6)*((c/e - (3*d^2)/(8*e^2))^2 + 9*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(2/3) - 6*(c/e - (3*d^2)/(8*e^2))*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(1/3) + (12*(a - t))/e - (9*d^4)/(64*e^4) - (3*d*(b - m))/e^2 + (3*c*d^2)/(4*e^3))^(1/4)) - d/(4*e) - ((c/e - (3*d^2)/(8*e^2))^2 + 9*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(2/3) - 6*(c/e - (3*d^2)/(8*e^2))*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(1/3) + (12*(a - t))/e - (9*d^4)/(64*e^4) - (3*d*(b - m))/e^2 + (3*c*d^2)/(4*e^3))^(1/2)/(6*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(1/6))
 
>> (3*6^(1/2)*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))*(3*3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2) + 2*(c/e - (3*d^2)/(8*e^2))^3 + 27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 72*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2) - 12*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))*((c/e - (3*d^2)/(8*e^2))^2 + 9*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(2/3) - 6*(c/e - (3*d^2)/(8*e^2))*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(1/3) + (12*(a - t))/e - (9*d^4)/(64*e^4) - (3*d*(b - m))/e^2 + (3*c*d^2)/(4*e^3))^(1/2) - 9*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(2/3)*((c/e - (3*d^2)/(8*e^2))^2 + 9*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(2/3) - 6*(c/e - (3*d^2)/(8*e^2))*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(1/3) + (12*(a - t))/e - (9*d^4)/(64*e^4) - (3*d*(b - m))/e^2 + (3*c*d^2)/(4*e^3))^(1/2) - (c/e - (3*d^2)/(8*e^2))^2*((c/e - (3*d^2)/(8*e^2))^2 + 9*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(2/3) - 6*(c/e - (3*d^2)/(8*e^2))*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(1/3) + (12*(a - t))/e - (9*d^4)/(64*e^4) - (3*d*(b - m))/e^2 + (3*c*d^2)/(4*e^3))^(1/2) - 12*(c/e - (3*d^2)/(8*e^2))*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(1/3)*((c/e - (3*d^2)/(8*e^2))^2 + 9*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(2/3) - 6*(c/e - (3*d^2)/(8*e^2))*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(1/3) + (12*(a - t))/e - (9*d^4)/(64*e^4) - (3*d*(b - m))/e^2 + (3*c*d^2)/(4*e^3))^(1/2))^(1/2)/(6*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(1/6)*((c/e - (3*d^2)/(8*e^2))^2 + 9*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(2/3) - 6*(c/e - (3*d^2)/(8*e^2))*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(1/3) + (12*(a - t))/e - (9*d^4)/(64*e^4) - (3*d*(b - m))/e^2 + (3*c*d^2)/(4*e^3))^(1/4)) - d/(4*e) - ((c/e - (3*d^2)/(8*e^2))^2 + 9*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(2/3) - 6*(c/e - (3*d^2)/(8*e^2))*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(1/3) + (12*(a - t))/e - (9*d^4)/(64*e^4) - (3*d*(b - m))/e^2 + (3*c*d^2)/(4*e^3))^(1/2)/(6*((3^(1/2)*(27*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^4 + 128*(c/e - (3*d^2)/(8*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^2 - 256*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3))^3 + 4*(c/e - (3*d^2)/(8*e^2))^3*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2 - 16*(c/e - (3*d^2)/(8*e^2))^4*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)) - 144*(c/e - (3*d^2)/(8*e^2))*((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))^(1/2))/18 + (c/e - (3*d^2)/(8*e^2))^3/27 + ((b - m)/e + d^3/(8*e^3) - (c*d)/(2*e^2))^2/2 - (4*(c/e - (3*d^2)/(8*e^2))*((a - t)/e - (3*d^4)/(256*e^4) - (d*(b - m))/(4*e^2) + (c*d^2)/(16*e^3)))/3)^(1/6))

ans =

 -150.2553

how do I avoid this? Is there a way to directly compute the number? vpa and double will not work..

The output as a rather long expression in the first time prevents further calculations as I want to use the rather long partial derivations of these expression to make an error calculation. The long outputs then result in that the output exceeds the maximum line length for the command window display, which leads to an early end...

A direct computation of the values instead of the output of these expressions would help here I think...

[Walter Roberson]

Use subs()

[Tomi Asli]

Thank you very much!

using subs() and vpa() together, no matter which one first, gave the solution!

Answer 6

[HIMANSHU GAUTAM]

I think this is quiet relevent thread to post my question. Although I have asked same question elsewhere. I am solving an integral equation but command window just prints the expression, rather it should print numerical result.

height = 2.5; % in units of meter.
a=5; % considering square room of area 20*20 meter^2.
area=4*a^2;
psi_FOV = 30*pi/180;
psi_half = 60*pi/180; 
m = -log10(2)/log10(cos(psi_half));
alpha = (m+1)*height^(m+1)/(2*pi);
K = alpha^2;
N = (1e-20)/K;
r_fov_anlytical = height*tan(psi_FOV);
d_fov_anlytical = height/cos(psi_FOV);
beta = (m+3);
height = 2.5;
% lambdaaxis=  .05:.01:1;
% avgSINR=zeros(1,length(lambdaaxis));
% for lambdaIdx=1:length(lambdaaxis)
    syms x y z;
   
     ons= (vpaintegral(vpaintegral(exp(-2.*pi.*.05.*vpaintegral((z - z.*exp ((-y.*N.*(sin( psi_FOV )).^4)./((x.^2+height^2 ).^(-beta))) ...
         .*exp ((-y.*( z.^2+ height.^2) .^( - beta))./(( x.^2+height.^2).^(-beta)))),z,x,r_fov_anlytical)) ...
         .*exp(- .05.*pi.*(x).^2).*(2.*pi).*.05.*x,y,0,inf),x,0,r_fov_anlytical))   
    
%      lambdaIdx

Command window output:

     
ons =
 
vpaintegral(vpaintegral((x*pi*exp(-(pi*vpaintegral(z - z*exp(-(y*(x^2 + 25/4)^4)/(z^2 + 25/4)^4)*exp(-(3358452346175993*y*(x^2 + 25/4)^4)/21267647932558653966460912964485513216), z, x, (5*3^(1/2))/6))/10)*exp(-(pi*x^2)/20))/10, y, 0, Inf), x, 0, (5*3^(1/2))/6)
 

I tried to use double,vpa, subs, but nothing worked.

[Walter Roberson]

What that tells you is that vpaintegral() does not think that the expression converges.

I have had a different software package analyzing the integral for the last couple of days. It has not been able to find a way to reduce the number of integrals. That is, one might hope that using some transformation that a closed form solution could be found for one of the integrals, reducing it to two integrals; the software package was not able to find anything like that.

It did find that with some transformations it was able to find an explicit expansion for some sub-expressions, which is a technique that can sometimes make it easier to integrate -- but the resulting expression then involves the integral of sin() of a long polynomial, and using the techniques to expand out sin of summations, is taking a quite long time.

[Walter Roberson]

I noticed you deleted your Question. I had not responded there because I did not have any results for you as yet, but I was working on it.

[HIMANSHU GAUTAM]

Yes, I deleted it because someone commented that I shouln't post multiple question. Although I have asked new question covering all the aspect of that question. Thank you for the reply. It would help me if you can share your findings, here or at the new question, that I asked.