Average Error: 34.7 → 34.8
Time: 31.4s
Precision: 64
\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
↓
\[\left(\left(\frac{1}{2} \cdot {c}^{2} + \left(\left(\frac{1}{24} \cdot {\left(\sqrt[3]{c} \cdot \left({\left(\sqrt[3]{\sqrt[3]{c}}\right)}^{2} \cdot \sqrt[3]{\sqrt[3]{c}}\right)\right)}^{4}\right) \cdot {\left(\sqrt[3]{c}\right)}^{4} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)
↓
\left(\left(\frac{1}{2} \cdot {c}^{2} + \left(\left(\frac{1}{24} \cdot {\left(\sqrt[3]{c} \cdot \left({\left(\sqrt[3]{\sqrt[3]{c}}\right)}^{2} \cdot \sqrt[3]{\sqrt[3]{c}}\right)\right)}^{4}\right) \cdot {\left(\sqrt[3]{c}\right)}^{4} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)
double f(double a, double c) {
        double r26498 = c;
        double r26499 = cosh(r26498);
        double r26500 = a;
        double r26501 = log1p(r26500);
        double r26502 = fmod(r26499, r26501);
        return r26502;
}
↓
double f(double a, double c) {
        double r26503 = 0.5;
        double r26504 = c;
        double r26505 = 2.0;
        double r26506 = pow(r26504, r26505);
        double r26507 = r26503 * r26506;
        double r26508 = 0.041666666666666664;
        double r26509 = cbrt(r26504);
        double r26510 = cbrt(r26509);
        double r26511 = pow(r26510, r26505);
        double r26512 = r26511 * r26510;
        double r26513 = r26509 * r26512;
        double r26514 = 4.0;
        double r26515 = pow(r26513, r26514);
        double r26516 = r26508 * r26515;
        double r26517 = pow(r26509, r26514);
        double r26518 = r26516 * r26517;
        double r26519 = 1.0;
        double r26520 = r26518 + r26519;
        double r26521 = r26507 + r26520;
        double r26522 = a;
        double r26523 = log1p(r26522);
        double r26524 = fmod(r26521, r26523);
        return r26524;
}

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 34.7

    \[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

  2. Taylor expanded around 0 34.8

    \[\leadsto \left(\color{blue}{\left(\frac{1}{2} \cdot {c}^{2} + \left(\frac{1}{24} \cdot {c}^{4} + 1\right)\right)} \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
  3. Using strategy rm

  4. Applied add-cube-cbrt34.8

    \[\leadsto \left(\left(\frac{1}{2} \cdot {c}^{2} + \left(\frac{1}{24} \cdot {\color{blue}{\left(\left(\sqrt[3]{c} \cdot \sqrt[3]{c}\right) \cdot \sqrt[3]{c}\right)}}^{4} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

  5. Applied unpow-prod-down34.8

    \[\leadsto \left(\left(\frac{1}{2} \cdot {c}^{2} + \left(\frac{1}{24} \cdot \color{blue}{\left({\left(\sqrt[3]{c} \cdot \sqrt[3]{c}\right)}^{4} \cdot {\left(\sqrt[3]{c}\right)}^{4}\right)} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

  6. Applied associate-*r*34.8

    \[\leadsto \left(\left(\frac{1}{2} \cdot {c}^{2} + \left(\color{blue}{\left(\frac{1}{24} \cdot {\left(\sqrt[3]{c} \cdot \sqrt[3]{c}\right)}^{4}\right) \cdot {\left(\sqrt[3]{c}\right)}^{4}} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
  7. Using strategy rm

  8. Applied add-cube-cbrt34.8

    \[\leadsto \left(\left(\frac{1}{2} \cdot {c}^{2} + \left(\left(\frac{1}{24} \cdot {\left(\sqrt[3]{c} \cdot \color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{c}} \cdot \sqrt[3]{\sqrt[3]{c}}\right) \cdot \sqrt[3]{\sqrt[3]{c}}\right)}\right)}^{4}\right) \cdot {\left(\sqrt[3]{c}\right)}^{4} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

  9. Simplified34.8

    \[\leadsto \left(\left(\frac{1}{2} \cdot {c}^{2} + \left(\left(\frac{1}{24} \cdot {\left(\sqrt[3]{c} \cdot \left(\color{blue}{{\left(\sqrt[3]{\sqrt[3]{c}}\right)}^{2}} \cdot \sqrt[3]{\sqrt[3]{c}}\right)\right)}^{4}\right) \cdot {\left(\sqrt[3]{c}\right)}^{4} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

  10. Final simplification34.8

    \[\leadsto \left(\left(\frac{1}{2} \cdot {c}^{2} + \left(\left(\frac{1}{24} \cdot {\left(\sqrt[3]{c} \cdot \left({\left(\sqrt[3]{\sqrt[3]{c}}\right)}^{2} \cdot \sqrt[3]{\sqrt[3]{c}}\right)\right)}^{4}\right) \cdot {\left(\sqrt[3]{c}\right)}^{4} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

Reproduce

herbie shell --seed 2019195 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))