Average Error: 34.2 → 34.2
Time: 13.7s
Precision: 64
\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
↓
\[\sqrt{e^{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt{\left(\left(\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot \sqrt[3]{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\]
\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)
↓
\sqrt{e^{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt{\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)}
double f(double a, double c) {
        double r17188 = c;
        double r17189 = cosh(r17188);
        double r17190 = a;
        double r17191 = log1p(r17190);
        double r17192 = fmod(r17189, r17191);
        return r17192;
}
↓
double f(double a, double c) {
        double r17193 = c;
        double r17194 = cosh(r17193);
        double r17195 = a;
        double r17196 = log1p(r17195);
        double r17197 = fmod(r17194, r17196);
        double r17198 = log(r17197);
        double r17199 = exp(r17198);
        double r17200 = sqrt(r17199);
        double r17201 = cbrt(r17194);
        double r17202 = r17201 * r17201;
        double r17203 = r17202 * r17201;
        double r17204 = fmod(r17203, r17196);
        double r17205 = sqrt(r17204);
        double r17206 = r17200 * r17205;
        return r17206;
}

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-sqr-sqrt34.2

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

  5. Applied add-cube-cbrt34.2

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

  7. Applied add-exp-log34.2

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

  8. Final simplification34.2

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

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))