Average Error: 60.5 → 59.5
Time: 53.8s
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 r1061316 = a;
        double r1061317 = cosh(r1061316);
        double r1061318 = r1061316 * r1061316;
        double r1061319 = fmod(r1061317, r1061318);
        double r1061320 = log1p(r1061316);
        double r1061321 = pow(r1061319, r1061320);
        double r1061322 = acos(r1061321);
        return r1061322;
}
↓
double f(double a) {
        double r1061323 = a;
        double r1061324 = cosh(r1061323);
        double r1061325 = r1061323 * r1061323;
        double r1061326 = fmod(r1061324, r1061325);
        double r1061327 = exp(r1061326);
        double r1061328 = log(r1061327);
        double r1061329 = log1p(r1061323);
        double r1061330 = pow(r1061328, r1061329);
        double r1061331 = acos(r1061330);
        return r1061331;
}

Error

Bits error versus a

Derivation

  1. Initial program 60.5

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

  3. Applied add-log-exp59.5

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

  4. Final simplification59.5

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

Reproduce

herbie shell --seed 2019132 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))