Average Error: 59.5 → 59.5
Time: 14.5s
Precision: 64
$\frac{\cos^{-1} \left(x + 1\right)}{2}$
$\frac{\sqrt[3]{\cos^{-1} \left(x + 1\right) \cdot \cos^{-1} \left(x + 1\right)} \cdot \sqrt[3]{\cos^{-1} \left(x + 1\right)}}{2}$
\frac{\cos^{-1} \left(x + 1\right)}{2}
\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)}}{2}
double f(double x) {
double r38801604 = x;
double r38801605 = 1.0;
double r38801606 = r38801604 + r38801605;
double r38801607 = acos(r38801606);
double r38801608 = 2.0;
double r38801609 = r38801607 / r38801608;
return r38801609;
}

double f(double x) {
double r38801610 = x;
double r38801611 = 1.0;
double r38801612 = r38801610 + r38801611;
double r38801613 = acos(r38801612);
double r38801614 = r38801613 * r38801613;
double r38801615 = cbrt(r38801614);
double r38801616 = cbrt(r38801613);
double r38801617 = r38801615 * r38801616;
double r38801618 = 2.0;
double r38801619 = r38801617 / r38801618;
return r38801619;
}

# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 59.5

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

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

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

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

# Reproduce

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