Average Error: 34.4 → 34.5
Time: 15.2s
Precision: 64
\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
↓
\[{\left({\left(\sqrt[3]{\sqrt{e^{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}}\right)}^{\left(\sqrt{5}\right)}\right)}^{\left(\sqrt{5}\right)} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\]
\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)
↓
{\left({\left(\sqrt[3]{\sqrt{e^{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}}\right)}^{\left(\sqrt{5}\right)}\right)}^{\left(\sqrt{5}\right)} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}
double f(double a, double c) {
        double r12949 = c;
        double r12950 = cosh(r12949);
        double r12951 = a;
        double r12952 = log1p(r12951);
        double r12953 = fmod(r12950, r12952);
        return r12953;
}
↓
double f(double a, double c) {
        double r12954 = c;
        double r12955 = cosh(r12954);
        double r12956 = a;
        double r12957 = log1p(r12956);
        double r12958 = fmod(r12955, r12957);
        double r12959 = log(r12958);
        double r12960 = exp(r12959);
        double r12961 = sqrt(r12960);
        double r12962 = cbrt(r12961);
        double r12963 = 5.0;
        double r12964 = sqrt(r12963);
        double r12965 = pow(r12962, r12964);
        double r12966 = pow(r12965, r12964);
        double r12967 = sqrt(r12958);
        double r12968 = cbrt(r12967);
        double r12969 = r12966 * r12968;
        return r12969;
}

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-sqr-sqrt34.5

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

  5. Applied add-cube-cbrt34.5

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

  6. Applied associate-*r*34.5

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

  7. Simplified34.5

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

  9. Applied add-sqr-sqrt34.5

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

  10. Applied pow-unpow34.5

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

  12. Applied add-exp-log34.5

    \[\leadsto {\left({\left(\sqrt[3]{\sqrt{\color{blue}{e^{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}}}\right)}^{\left(\sqrt{5}\right)}\right)}^{\left(\sqrt{5}\right)} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\]

  13. Final simplification34.5

    \[\leadsto {\left({\left(\sqrt[3]{\sqrt{e^{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}}\right)}^{\left(\sqrt{5}\right)}\right)}^{\left(\sqrt{5}\right)} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\]

Reproduce

herbie shell --seed 2020024 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))