Average Error: 60.4 → 59.3
Time: 49.4s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\sqrt[3]{\left(\mathsf{log1p}\left(a\right) \cdot \mathsf{log1p}\left(a\right)\right) \cdot \mathsf{log1p}\left(a\right)}\right)}\right)\]
\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(\sqrt[3]{\left(\mathsf{log1p}\left(a\right) \cdot \mathsf{log1p}\left(a\right)\right) \cdot \mathsf{log1p}\left(a\right)}\right)}\right)
double f(double a) {
        double r926411 = a;
        double r926412 = cosh(r926411);
        double r926413 = r926411 * r926411;
        double r926414 = fmod(r926412, r926413);
        double r926415 = log1p(r926411);
        double r926416 = pow(r926414, r926415);
        double r926417 = acos(r926416);
        return r926417;
}
↓
double f(double a) {
        double r926418 = a;
        double r926419 = cosh(r926418);
        double r926420 = r926418 * r926418;
        double r926421 = fmod(r926419, r926420);
        double r926422 = exp(r926421);
        double r926423 = log(r926422);
        double r926424 = log1p(r926418);
        double r926425 = r926424 * r926424;
        double r926426 = r926425 * r926424;
        double r926427 = cbrt(r926426);
        double r926428 = pow(r926423, r926427);
        double r926429 = acos(r926428);
        return r926429;
}

Error

Bits error versus a

Derivation

  1. Initial program 60.4

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

  5. Applied add-cbrt-cube59.3

    \[\leadsto \cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\color{blue}{\left(\sqrt[3]{\left(\mathsf{log1p}\left(a\right) \cdot \mathsf{log1p}\left(a\right)\right) \cdot \mathsf{log1p}\left(a\right)}\right)}}\right)\]

  6. Final simplification59.3

    \[\leadsto \cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\sqrt[3]{\left(\mathsf{log1p}\left(a\right) \cdot \mathsf{log1p}\left(a\right)\right) \cdot \mathsf{log1p}\left(a\right)}\right)}\right)\]

Reproduce

herbie shell --seed 2019137 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))