Average Error: 61.2 → 60.3
Time: 53.9s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)
↓
\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)
double f(double a) {
        double r20373 = a;
        double r20374 = cosh(r20373);
        double r20375 = r20373 * r20373;
        double r20376 = fmod(r20374, r20375);
        double r20377 = log1p(r20373);
        double r20378 = pow(r20376, r20377);
        double r20379 = acos(r20378);
        return r20379;
}
↓
double f(double a) {
        double r20380 = a;
        double r20381 = cosh(r20380);
        double r20382 = r20380 * r20380;
        double r20383 = fmod(r20381, r20382);
        double r20384 = exp(r20383);
        double r20385 = log(r20384);
        double r20386 = log1p(r20380);
        double r20387 = pow(r20385, r20386);
        double r20388 = acos(r20387);
        return r20388;
}

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-exp60.3

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

  4. Final simplification60.3

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

Reproduce

herbie shell --seed 2019304 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))