Average Error: 61.1 → 60.1
Time: 52.6s
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 r968282 = a;
        double r968283 = cosh(r968282);
        double r968284 = r968282 * r968282;
        double r968285 = fmod(r968283, r968284);
        double r968286 = log1p(r968282);
        double r968287 = pow(r968285, r968286);
        double r968288 = acos(r968287);
        return r968288;
}
↓
double f(double a) {
        double r968289 = a;
        double r968290 = cosh(r968289);
        double r968291 = r968289 * r968289;
        double r968292 = fmod(r968290, r968291);
        double r968293 = exp(r968292);
        double r968294 = log(r968293);
        double r968295 = log1p(r968289);
        double r968296 = pow(r968294, r968295);
        double r968297 = acos(r968296);
        return r968297;
}

Error

Bits error versus a

Derivation

  1. Initial program 61.1

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

  3. Applied add-log-exp60.1

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

  4. Final simplification60.1

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

Reproduce

herbie shell --seed 2019172 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))