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;
}

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

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

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