Average Error: 34.1 → 34.1
Time: 28.7s
Precision: 64
\[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
↓
\[{e}^{\left(\log \left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)\right)} \cdot {e}^{\left(\log \left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)\right)}\]
\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)
↓
{e}^{\left(\log \left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)\right)} \cdot {e}^{\left(\log \left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)\right)}
double f(double a, double c) {
        double r133983 = c;
        double r133984 = cosh(r133983);
        double r133985 = a;
        double r133986 = log1p(r133985);
        double r133987 = fmod(r133984, r133986);
        return r133987;
}
↓
double f(double a, double c) {
        double r133988 = exp(1.0);
        double r133989 = c;
        double r133990 = cosh(r133989);
        double r133991 = a;
        double r133992 = log1p(r133991);
        double r133993 = fmod(r133990, r133992);
        double r133994 = sqrt(r133993);
        double r133995 = log(r133994);
        double r133996 = pow(r133988, r133995);
        double r133997 = r133996 * r133996;
        return r133997;
}

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 34.1

    \[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
  2. Using strategy rm

  3. Applied add-exp-log34.1

    \[\leadsto \color{blue}{e^{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity34.1

    \[\leadsto e^{\color{blue}{1 \cdot \log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}}\]

  6. Applied exp-prod34.1

    \[\leadsto \color{blue}{{\left(e^{1}\right)}^{\left(\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\right)}}\]

  7. Simplified34.1

    \[\leadsto {\color{blue}{e}}^{\left(\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\right)}\]
  8. Using strategy rm

  9. Applied add-sqr-sqrt34.1

    \[\leadsto {e}^{\left(\log \color{blue}{\left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)}\right)}\]

  10. Applied log-prod34.1

    \[\leadsto {e}^{\color{blue}{\left(\log \left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right) + \log \left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)\right)}}\]

  11. Applied unpow-prod-up34.1

    \[\leadsto \color{blue}{{e}^{\left(\log \left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)\right)} \cdot {e}^{\left(\log \left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)\right)}}\]

  12. Final simplification34.1

    \[\leadsto {e}^{\left(\log \left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)\right)} \cdot {e}^{\left(\log \left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)\right)}\]

Reproduce

herbie shell --seed 2019119 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))