Average Error: 34.4 → 34.3
Time: 39.7s
Precision: 64
\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
↓
\[\left(\left(\left(\sqrt{\frac{1}{2}} \cdot \sqrt{e^{c} + e^{-c}}\right) \cdot \sqrt[3]{\sqrt{{\left(\cosh c\right)}^{3}}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)
↓
\left(\left(\left(\sqrt{\frac{1}{2}} \cdot \sqrt{e^{c} + e^{-c}}\right) \cdot \sqrt[3]{\sqrt{{\left(\cosh c\right)}^{3}}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)
double f(double a, double c) {
        double r20476 = c;
        double r20477 = cosh(r20476);
        double r20478 = a;
        double r20479 = log1p(r20478);
        double r20480 = fmod(r20477, r20479);
        return r20480;
}
↓
double f(double a, double c) {
        double r20481 = 0.5;
        double r20482 = sqrt(r20481);
        double r20483 = c;
        double r20484 = exp(r20483);
        double r20485 = -r20483;
        double r20486 = exp(r20485);
        double r20487 = r20484 + r20486;
        double r20488 = sqrt(r20487);
        double r20489 = r20482 * r20488;
        double r20490 = cosh(r20483);
        double r20491 = 3.0;
        double r20492 = pow(r20490, r20491);
        double r20493 = sqrt(r20492);
        double r20494 = cbrt(r20493);
        double r20495 = r20489 * r20494;
        double r20496 = a;
        double r20497 = log1p(r20496);
        double r20498 = fmod(r20495, r20497);
        return r20498;
}

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 34.4

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

  3. Applied add-cbrt-cube34.4

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

  4. Simplified34.4

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

  6. Applied add-sqr-sqrt34.4

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

  7. Applied cbrt-prod34.4

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

  8. Taylor expanded around inf 34.3

    \[\leadsto \left(\left(\color{blue}{\left(\sqrt{e^{c} + e^{-c}} \cdot \sqrt{\frac{1}{2}}\right)} \cdot \sqrt[3]{\sqrt{{\left(\cosh c\right)}^{3}}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

  9. Simplified34.3

    \[\leadsto \left(\left(\color{blue}{\left(\sqrt{\frac{1}{2}} \cdot \sqrt{e^{c} + e^{-c}}\right)} \cdot \sqrt[3]{\sqrt{{\left(\cosh c\right)}^{3}}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

  10. Final simplification34.3

    \[\leadsto \left(\left(\left(\sqrt{\frac{1}{2}} \cdot \sqrt{e^{c} + e^{-c}}\right) \cdot \sqrt[3]{\sqrt{{\left(\cosh c\right)}^{3}}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

Reproduce

herbie shell --seed 2019303 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))