Average Error: 34.0 → 34.0
Time: 30.8s
Precision: 64
\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
↓
\[\left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right) \cdot {\left({\left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)}^{\left(\sqrt{\frac{4}{3}}\right)}\right)}^{\left(\sqrt{\frac{4}{3}}\right)}\]
\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)
↓
\left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right) \cdot {\left({\left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)}^{\left(\sqrt{\frac{4}{3}}\right)}\right)}^{\left(\sqrt{\frac{4}{3}}\right)}
double f(double a, double c) {
        double r15537 = c;
        double r15538 = cosh(r15537);
        double r15539 = a;
        double r15540 = log1p(r15539);
        double r15541 = fmod(r15538, r15540);
        return r15541;
}
↓
double f(double a, double c) {
        double r15542 = c;
        double r15543 = cosh(r15542);
        double r15544 = a;
        double r15545 = log1p(r15544);
        double r15546 = fmod(r15543, r15545);
        double r15547 = sqrt(r15546);
        double r15548 = cbrt(r15547);
        double r15549 = r15548 * r15548;
        double r15550 = 1.3333333333333333;
        double r15551 = sqrt(r15550);
        double r15552 = pow(r15547, r15551);
        double r15553 = pow(r15552, r15551);
        double r15554 = r15549 * r15553;
        return r15554;
}

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 34.0

    \[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt34.0

    \[\leadsto \color{blue}{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt34.0

    \[\leadsto \sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \color{blue}{\left(\left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right) \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)}\]

  6. Applied add-cube-cbrt34.1

    \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right) \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)} \cdot \left(\left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right) \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)\]

  7. Applied swap-sqr34.1

    \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right) \cdot \left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)\right) \cdot \left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)}\]

  8. Simplified34.1

    \[\leadsto \color{blue}{{\left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)}^{\left(3 + 1\right)}} \cdot \left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)\]
  9. Using strategy rm

  10. Applied pow1/334.0

    \[\leadsto {\color{blue}{\left({\left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)}^{\frac{1}{3}}\right)}}^{\left(3 + 1\right)} \cdot \left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)\]

  11. Applied pow-pow34.0

    \[\leadsto \color{blue}{{\left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)}^{\left(\frac{1}{3} \cdot \left(3 + 1\right)\right)}} \cdot \left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)\]

  12. Simplified34.0

    \[\leadsto {\left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)}^{\color{blue}{\frac{4}{3}}} \cdot \left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)\]
  13. Using strategy rm

  14. Applied add-sqr-sqrt34.0

    \[\leadsto {\left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)}^{\color{blue}{\left(\sqrt{\frac{4}{3}} \cdot \sqrt{\frac{4}{3}}\right)}} \cdot \left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)\]

  15. Applied pow-unpow34.0

    \[\leadsto \color{blue}{{\left({\left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)}^{\left(\sqrt{\frac{4}{3}}\right)}\right)}^{\left(\sqrt{\frac{4}{3}}\right)}} \cdot \left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)\]

  16. Final simplification34.0

    \[\leadsto \left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right) \cdot {\left({\left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)}^{\left(\sqrt{\frac{4}{3}}\right)}\right)}^{\left(\sqrt{\frac{4}{3}}\right)}\]

Reproduce

herbie shell --seed 2019196 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))