Average Error: 61.2 → 60.3
Time: 35.9s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\log \left(e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)\]
\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)
↓
\log \left(e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)
double f(double a) {
        double r6555 = a;
        double r6556 = cosh(r6555);
        double r6557 = r6555 * r6555;
        double r6558 = fmod(r6556, r6557);
        double r6559 = log1p(r6555);
        double r6560 = pow(r6558, r6559);
        double r6561 = acos(r6560);
        return r6561;
}
↓
double f(double a) {
        double r6562 = a;
        double r6563 = cosh(r6562);
        double r6564 = r6562 * r6562;
        double r6565 = fmod(r6563, r6564);
        double r6566 = exp(r6565);
        double r6567 = log(r6566);
        double r6568 = log1p(r6562);
        double r6569 = pow(r6567, r6568);
        double r6570 = acos(r6569);
        double r6571 = exp(r6570);
        double r6572 = log(r6571);
        return r6572;
}

Error

Bits error versus a

Derivation

  1. Initial program 61.2

    \[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
  2. Using strategy rm

  3. Applied add-log-exp61.2

    \[\leadsto \color{blue}{\log \left(e^{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)}\]
  4. Using strategy rm

  5. Applied add-log-exp60.3

    \[\leadsto \log \left(e^{\cos^{-1} \left({\color{blue}{\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)\]

  6. Final simplification60.3

    \[\leadsto \log \left(e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))