Average Error: 59.5 → 59.5
Time: 15.7s
Precision: 64
$\frac{\frac{\cos^{-1} \left(x + 1\right)}{1}}{2}$
$\frac{\frac{\sqrt[3]{\cos^{-1} \left(x + 1\right) \cdot \cos^{-1} \left(x + 1\right)} \cdot \sqrt[3]{\cos^{-1} \left(x + 1\right)}}{1}}{2}$
\frac{\frac{\cos^{-1} \left(x + 1\right)}{1}}{2}
\frac{\frac{\sqrt[3]{\cos^{-1} \left(x + 1\right) \cdot \cos^{-1} \left(x + 1\right)} \cdot \sqrt[3]{\cos^{-1} \left(x + 1\right)}}{1}}{2}
double f(double x) {
double r38390453 = x;
double r38390454 = 1.0;
double r38390455 = r38390453 + r38390454;
double r38390456 = acos(r38390455);
double r38390457 = r38390456 / r38390454;
double r38390458 = 2.0;
double r38390459 = r38390457 / r38390458;
return r38390459;
}


double f(double x) {
double r38390460 = x;
double r38390461 = 1.0;
double r38390462 = r38390460 + r38390461;
double r38390463 = acos(r38390462);
double r38390464 = r38390463 * r38390463;
double r38390465 = cbrt(r38390464);
double r38390466 = cbrt(r38390463);
double r38390467 = r38390465 * r38390466;
double r38390468 = r38390467 / r38390461;
double r38390469 = 2.0;
double r38390470 = r38390468 / r38390469;
return r38390470;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 59.5

$\frac{\frac{\cos^{-1} \left(x + 1\right)}{1}}{2}$
2. Using strategy rm

$\leadsto \frac{\frac{\color{blue}{\sqrt[3]{\left(\cos^{-1} \left(x + 1\right) \cdot \cos^{-1} \left(x + 1\right)\right) \cdot \cos^{-1} \left(x + 1\right)}}}{1}}{2}$
4. Using strategy rm
5. Applied cbrt-prod59.5

$\leadsto \frac{\frac{\color{blue}{\sqrt[3]{\cos^{-1} \left(x + 1\right) \cdot \cos^{-1} \left(x + 1\right)} \cdot \sqrt[3]{\cos^{-1} \left(x + 1\right)}}}{1}}{2}$
6. Final simplification59.5

$\leadsto \frac{\frac{\sqrt[3]{\cos^{-1} \left(x + 1\right) \cdot \cos^{-1} \left(x + 1\right)} \cdot \sqrt[3]{\cos^{-1} \left(x + 1\right)}}{1}}{2}$

# Reproduce

herbie shell --seed 1
(FPCore (x)
:name "acos(x+1)/1/2"
(/ (/ (acos (+ x 1.0)) 1.0) 2.0))