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;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 59.5

    \[\frac{\cos^{-1} \left(x + 1\right)}{2}\]
  2. Using strategy rm
  3. Applied add-cbrt-cube59.5

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