Average Error: 34.3 → 33.8
Time: 36.3s
Precision: 64
\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
↓
\[\left(\sqrt[3]{\left(\left(\sqrt[3]{\frac{{\left(\sqrt{e^{c} + e^{-c}}\right)}^{3}}{4}} \cdot \frac{\sqrt{e^{-c} + e^{c}}}{\sqrt[3]{2}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\left(\left(\sqrt[3]{\frac{{\left(\sqrt{e^{c} + e^{-c}}\right)}^{3}}{4}} \cdot \frac{\sqrt{e^{-c} + e^{c}}}{\sqrt[3]{2}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\left(\left(\sqrt[3]{\frac{{\left(\sqrt{e^{c} + e^{-c}}\right)}^{3}}{4}} \cdot \frac{\sqrt{e^{-c} + e^{c}}}{\sqrt[3]{2}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\]
\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)
↓
\left(\sqrt[3]{\left(\left(\sqrt[3]{\frac{{\left(\sqrt{e^{c} + e^{-c}}\right)}^{3}}{4}} \cdot \frac{\sqrt{e^{-c} + e^{c}}}{\sqrt[3]{2}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\left(\left(\sqrt[3]{\frac{{\left(\sqrt{e^{c} + e^{-c}}\right)}^{3}}{4}} \cdot \frac{\sqrt{e^{-c} + e^{c}}}{\sqrt[3]{2}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\left(\left(\sqrt[3]{\frac{{\left(\sqrt{e^{c} + e^{-c}}\right)}^{3}}{4}} \cdot \frac{\sqrt{e^{-c} + e^{c}}}{\sqrt[3]{2}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}
double f(double a, double c) {
        double r20631 = c;
        double r20632 = cosh(r20631);
        double r20633 = a;
        double r20634 = log1p(r20633);
        double r20635 = fmod(r20632, r20634);
        return r20635;
}
↓
double f(double a, double c) {
        double r20636 = c;
        double r20637 = exp(r20636);
        double r20638 = -r20636;
        double r20639 = exp(r20638);
        double r20640 = r20637 + r20639;
        double r20641 = sqrt(r20640);
        double r20642 = 3.0;
        double r20643 = pow(r20641, r20642);
        double r20644 = 4.0;
        double r20645 = r20643 / r20644;
        double r20646 = cbrt(r20645);
        double r20647 = r20639 + r20637;
        double r20648 = sqrt(r20647);
        double r20649 = 2.0;
        double r20650 = cbrt(r20649);
        double r20651 = r20648 / r20650;
        double r20652 = r20646 * r20651;
        double r20653 = a;
        double r20654 = log1p(r20653);
        double r20655 = fmod(r20652, r20654);
        double r20656 = cbrt(r20655);
        double r20657 = r20656 * r20656;
        double r20658 = r20657 * r20656;
        return r20658;
}

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 34.3

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

  3. Applied add-cbrt-cube34.3

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

  4. Simplified34.3

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

  6. Applied cosh-def34.3

    \[\leadsto \left(\left(\sqrt[3]{{\color{blue}{\left(\frac{e^{c} + e^{-c}}{2}\right)}}^{3}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

  7. Simplified34.3

    \[\leadsto \left(\left(\sqrt[3]{{\left(\frac{\color{blue}{e^{-c} + e^{c}}}{2}\right)}^{3}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
  8. Using strategy rm

  9. Applied add-cube-cbrt34.7

    \[\leadsto \left(\left(\sqrt[3]{{\left(\frac{e^{-c} + e^{c}}{\color{blue}{\left(\sqrt[3]{2} \cdot \sqrt[3]{2}\right) \cdot \sqrt[3]{2}}}\right)}^{3}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

  10. Applied add-sqr-sqrt34.1

    \[\leadsto \left(\left(\sqrt[3]{{\left(\frac{\color{blue}{\sqrt{e^{-c} + e^{c}} \cdot \sqrt{e^{-c} + e^{c}}}}{\left(\sqrt[3]{2} \cdot \sqrt[3]{2}\right) \cdot \sqrt[3]{2}}\right)}^{3}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

  11. Applied times-frac34.8

    \[\leadsto \left(\left(\sqrt[3]{{\color{blue}{\left(\frac{\sqrt{e^{-c} + e^{c}}}{\sqrt[3]{2} \cdot \sqrt[3]{2}} \cdot \frac{\sqrt{e^{-c} + e^{c}}}{\sqrt[3]{2}}\right)}}^{3}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

  12. Applied unpow-prod-down34.7

    \[\leadsto \left(\left(\sqrt[3]{\color{blue}{{\left(\frac{\sqrt{e^{-c} + e^{c}}}{\sqrt[3]{2} \cdot \sqrt[3]{2}}\right)}^{3} \cdot {\left(\frac{\sqrt{e^{-c} + e^{c}}}{\sqrt[3]{2}}\right)}^{3}}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

  13. Applied cbrt-prod34.7

    \[\leadsto \left(\color{blue}{\left(\sqrt[3]{{\left(\frac{\sqrt{e^{-c} + e^{c}}}{\sqrt[3]{2} \cdot \sqrt[3]{2}}\right)}^{3}} \cdot \sqrt[3]{{\left(\frac{\sqrt{e^{-c} + e^{c}}}{\sqrt[3]{2}}\right)}^{3}}\right)} \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

  14. Simplified34.1

    \[\leadsto \left(\left(\color{blue}{\sqrt[3]{\frac{{\left(\sqrt{e^{c} + e^{-c}}\right)}^{3}}{4}}} \cdot \sqrt[3]{{\left(\frac{\sqrt{e^{-c} + e^{c}}}{\sqrt[3]{2}}\right)}^{3}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

  15. Simplified34.1

    \[\leadsto \left(\left(\sqrt[3]{\frac{{\left(\sqrt{e^{c} + e^{-c}}\right)}^{3}}{4}} \cdot \color{blue}{\frac{\sqrt{e^{-c} + e^{c}}}{\sqrt[3]{2}}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
  16. Using strategy rm

  17. Applied add-cube-cbrt33.8

    \[\leadsto \color{blue}{\left(\sqrt[3]{\left(\left(\sqrt[3]{\frac{{\left(\sqrt{e^{c} + e^{-c}}\right)}^{3}}{4}} \cdot \frac{\sqrt{e^{-c} + e^{c}}}{\sqrt[3]{2}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\left(\left(\sqrt[3]{\frac{{\left(\sqrt{e^{c} + e^{-c}}\right)}^{3}}{4}} \cdot \frac{\sqrt{e^{-c} + e^{c}}}{\sqrt[3]{2}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\left(\left(\sqrt[3]{\frac{{\left(\sqrt{e^{c} + e^{-c}}\right)}^{3}}{4}} \cdot \frac{\sqrt{e^{-c} + e^{c}}}{\sqrt[3]{2}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\]

  18. Final simplification33.8

    \[\leadsto \left(\sqrt[3]{\left(\left(\sqrt[3]{\frac{{\left(\sqrt{e^{c} + e^{-c}}\right)}^{3}}{4}} \cdot \frac{\sqrt{e^{-c} + e^{c}}}{\sqrt[3]{2}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\left(\left(\sqrt[3]{\frac{{\left(\sqrt{e^{c} + e^{-c}}\right)}^{3}}{4}} \cdot \frac{\sqrt{e^{-c} + e^{c}}}{\sqrt[3]{2}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\left(\left(\sqrt[3]{\frac{{\left(\sqrt{e^{c} + e^{-c}}\right)}^{3}}{4}} \cdot \frac{\sqrt{e^{-c} + e^{c}}}{\sqrt[3]{2}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\]

Reproduce

herbie shell --seed 2019325 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))