Average Error: 61.3 → 60.3
Time: 53.3s
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 r16455 = a;
        double r16456 = cosh(r16455);
        double r16457 = r16455 * r16455;
        double r16458 = fmod(r16456, r16457);
        double r16459 = log1p(r16455);
        double r16460 = pow(r16458, r16459);
        double r16461 = acos(r16460);
        return r16461;
}
↓
double f(double a) {
        double r16462 = a;
        double r16463 = cosh(r16462);
        double r16464 = r16462 * r16462;
        double r16465 = fmod(r16463, r16464);
        double r16466 = exp(r16465);
        double r16467 = log(r16466);
        double r16468 = log1p(r16462);
        double r16469 = pow(r16467, r16468);
        double r16470 = acos(r16469);
        return r16470;
}

Error

Bits error versus a

Derivation

  1. Initial program 61.3

    \[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
  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 2019323 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))