Average Error: 0.3 → 0.4
Time: 15.0s
Precision: 64
\[\frac{a}{-\cos^{-1} a}\]
↓
\[\frac{\sqrt[3]{\sqrt[3]{\frac{1}{\left(\cos^{-1} a \cdot \cos^{-1} a\right) \cdot \left(-\cos^{-1} a\right)}} \cdot \sqrt[3]{\frac{1}{\left(\cos^{-1} a \cdot \cos^{-1} a\right) \cdot \left(-\cos^{-1} a\right)}}}}{\frac{\frac{1}{a}}{\sqrt[3]{\sqrt[3]{\frac{1}{\left(\cos^{-1} a \cdot \cos^{-1} a\right) \cdot \left(-\cos^{-1} a\right)}}}}}\]
\frac{a}{-\cos^{-1} a}
↓
\frac{\sqrt[3]{\sqrt[3]{\frac{1}{\left(\cos^{-1} a \cdot \cos^{-1} a\right) \cdot \left(-\cos^{-1} a\right)}} \cdot \sqrt[3]{\frac{1}{\left(\cos^{-1} a \cdot \cos^{-1} a\right) \cdot \left(-\cos^{-1} a\right)}}}}{\frac{\frac{1}{a}}{\sqrt[3]{\sqrt[3]{\frac{1}{\left(\cos^{-1} a \cdot \cos^{-1} a\right) \cdot \left(-\cos^{-1} a\right)}}}}}
double f(double a) {
        double r4858898 = a;
        double r4858899 = acos(r4858898);
        double r4858900 = -r4858899;
        double r4858901 = r4858898 / r4858900;
        return r4858901;
}
↓
double f(double a) {
        double r4858902 = 1.0;
        double r4858903 = a;
        double r4858904 = acos(r4858903);
        double r4858905 = r4858904 * r4858904;
        double r4858906 = -r4858904;
        double r4858907 = r4858905 * r4858906;
        double r4858908 = r4858902 / r4858907;
        double r4858909 = cbrt(r4858908);
        double r4858910 = r4858909 * r4858909;
        double r4858911 = cbrt(r4858910);
        double r4858912 = r4858902 / r4858903;
        double r4858913 = cbrt(r4858909);
        double r4858914 = r4858912 / r4858913;
        double r4858915 = r4858911 / r4858914;
        return r4858915;
}

Error

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

    \[\frac{a}{-\cos^{-1} a}\]
  2. Using strategy rm

  3. Applied clear-num0.4

    \[\leadsto \color{blue}{\frac{1}{\frac{-\cos^{-1} a}{a}}}\]
  4. Using strategy rm

  5. Applied div-inv0.4

    \[\leadsto \frac{1}{\color{blue}{\left(-\cos^{-1} a\right) \cdot \frac{1}{a}}}\]

  6. Applied associate-/r*0.4

    \[\leadsto \color{blue}{\frac{\frac{1}{-\cos^{-1} a}}{\frac{1}{a}}}\]
  7. Using strategy rm

  8. Applied add-cbrt-cube0.7

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

  9. Applied add-cbrt-cube0.7

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

  10. Applied cbrt-undiv0.7

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

  11. Simplified0.7

    \[\leadsto \frac{\sqrt[3]{\color{blue}{\frac{1}{-\left(\cos^{-1} a \cdot \cos^{-1} a\right) \cdot \cos^{-1} a}}}}{\frac{1}{a}}\]
  12. Using strategy rm

  13. Applied add-cube-cbrt0.7

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

  14. Applied cbrt-prod0.5

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

  15. Applied associate-/l*0.4

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

  16. Final simplification0.4

    \[\leadsto \frac{\sqrt[3]{\sqrt[3]{\frac{1}{\left(\cos^{-1} a \cdot \cos^{-1} a\right) \cdot \left(-\cos^{-1} a\right)}} \cdot \sqrt[3]{\frac{1}{\left(\cos^{-1} a \cdot \cos^{-1} a\right) \cdot \left(-\cos^{-1} a\right)}}}}{\frac{\frac{1}{a}}{\sqrt[3]{\sqrt[3]{\frac{1}{\left(\cos^{-1} a \cdot \cos^{-1} a\right) \cdot \left(-\cos^{-1} a\right)}}}}}\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 001"
  (/ a (- (acos a))))