Average Error: 34.2 → 34.2
Time: 18.2s
Precision: 64
\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
↓
\[\left(\sqrt[3]{\left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\left(\left(\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot \sqrt[3]{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot e^{\frac{1}{3} \cdot \log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\]
\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)
↓
\left(\sqrt[3]{\left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\left(\left(\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot \sqrt[3]{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot e^{\frac{1}{3} \cdot \log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}
double f(double a, double c) {
        double r28630 = c;
        double r28631 = cosh(r28630);
        double r28632 = a;
        double r28633 = log1p(r28632);
        double r28634 = fmod(r28631, r28633);
        return r28634;
}
↓
double f(double a, double c) {
        double r28635 = c;
        double r28636 = cosh(r28635);
        double r28637 = a;
        double r28638 = log1p(r28637);
        double r28639 = fmod(r28636, r28638);
        double r28640 = cbrt(r28639);
        double r28641 = r28640 * r28640;
        double r28642 = r28641 * r28640;
        double r28643 = cbrt(r28642);
        double r28644 = cbrt(r28636);
        double r28645 = r28644 * r28644;
        double r28646 = r28645 * r28644;
        double r28647 = fmod(r28646, r28638);
        double r28648 = cbrt(r28647);
        double r28649 = r28643 * r28648;
        double r28650 = 0.3333333333333333;
        double r28651 = log(r28639);
        double r28652 = r28650 * r28651;
        double r28653 = exp(r28652);
        double r28654 = r28649 * r28653;
        return r28654;
}

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 34.2

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

  3. Applied add-cube-cbrt34.2

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

  5. Applied add-cube-cbrt34.2

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

  7. Applied add-exp-log34.2

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

  8. Simplified34.2

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

  10. Applied add-cube-cbrt34.2

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

  11. Simplified34.2

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

  12. Simplified34.2

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

  13. Final simplification34.2

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

Reproduce

herbie shell --seed 2019318 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))