Average Error: 61.1 → 59.3
Time: 49.8s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\frac{\pi}{2} - \sqrt{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)} \cdot \sqrt{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\]
\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)
↓
\frac{\pi}{2} - \sqrt{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)} \cdot \sqrt{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}
double f(double a) {
        double r13354 = a;
        double r13355 = cosh(r13354);
        double r13356 = r13354 * r13354;
        double r13357 = fmod(r13355, r13356);
        double r13358 = log1p(r13354);
        double r13359 = pow(r13357, r13358);
        double r13360 = acos(r13359);
        return r13360;
}
↓
double f(double a) {
        double r13361 = atan2(1.0, 0.0);
        double r13362 = 2.0;
        double r13363 = r13361 / r13362;
        double r13364 = a;
        double r13365 = cosh(r13364);
        double r13366 = r13364 * r13364;
        double r13367 = fmod(r13365, r13366);
        double r13368 = log1p(r13364);
        double r13369 = pow(r13367, r13368);
        double r13370 = asin(r13369);
        double r13371 = sqrt(r13370);
        double r13372 = r13371 * r13371;
        double r13373 = r13363 - r13372;
        return r13373;
}

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 acos-asin61.1

    \[\leadsto \color{blue}{\frac{\pi}{2} - \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\]
  4. Using strategy rm

  5. Applied add-sqr-sqrt59.3

    \[\leadsto \frac{\pi}{2} - \color{blue}{\sqrt{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)} \cdot \sqrt{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\]

  6. Final simplification59.3

    \[\leadsto \frac{\pi}{2} - \sqrt{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)} \cdot \sqrt{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\]

Reproduce

herbie shell --seed 2019347 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))