Average Error: 61.2 → 59.5
Time: 33.2s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\frac{\mathsf{fma}\left(\pi \cdot \pi, \frac{1}{4}, \left(-1\right) \cdot {\left(\sqrt[3]{\sin^{-1} \left({\left(\left(\sqrt[3]{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)} \cdot \sqrt[3]{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right) \cdot \sqrt[3]{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)}^{6}\right)}{\mathsf{fma}\left(\pi, \frac{1}{2}, \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}\]
\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)
↓
\frac{\mathsf{fma}\left(\pi \cdot \pi, \frac{1}{4}, \left(-1\right) \cdot {\left(\sqrt[3]{\sin^{-1} \left({\left(\left(\sqrt[3]{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)} \cdot \sqrt[3]{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right) \cdot \sqrt[3]{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)}^{6}\right)}{\mathsf{fma}\left(\pi, \frac{1}{2}, \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}
double f(double a) {
        double r64 = a;
        double r65 = cosh(r64);
        double r66 = r64 * r64;
        double r67 = fmod(r65, r66);
        double r68 = log1p(r64);
        double r69 = pow(r67, r68);
        double r70 = acos(r69);
        return r70;
}
↓
double f(double a) {
        double r71 = atan2(1.0, 0.0);
        double r72 = r71 * r71;
        double r73 = 0.25;
        double r74 = 1.0;
        double r75 = -r74;
        double r76 = a;
        double r77 = cosh(r76);
        double r78 = r76 * r76;
        double r79 = fmod(r77, r78);
        double r80 = cbrt(r79);
        double r81 = r80 * r80;
        double r82 = r81 * r80;
        double r83 = log1p(r76);
        double r84 = pow(r82, r83);
        double r85 = asin(r84);
        double r86 = cbrt(r85);
        double r87 = 6.0;
        double r88 = pow(r86, r87);
        double r89 = r75 * r88;
        double r90 = fma(r72, r73, r89);
        double r91 = 0.5;
        double r92 = 2.0;
        double r93 = pow(r76, r92);
        double r94 = fmod(r77, r93);
        double r95 = pow(r94, r83);
        double r96 = asin(r95);
        double r97 = fma(r71, r91, r96);
        double r98 = r90 / r97;
        return r98;
}

Error

Bits error versus a

Derivation

  1. Initial program 61.2

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

  5. Applied acos-asin60.3

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

  7. Applied flip--60.3

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

  8. Simplified60.3

    \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\pi \cdot \pi, \frac{1}{4}, \left(-1\right) \cdot {\left(\sqrt[3]{\sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)}^{6}\right)}}{\frac{\pi}{2} + \sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\]

  9. Simplified60.3

    \[\leadsto \frac{\mathsf{fma}\left(\pi \cdot \pi, \frac{1}{4}, \left(-1\right) \cdot {\left(\sqrt[3]{\sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)}^{6}\right)}{\color{blue}{\mathsf{fma}\left(\pi, \frac{1}{2}, \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}}\]
  10. Using strategy rm

  11. Applied add-cube-cbrt60.3

    \[\leadsto \frac{\mathsf{fma}\left(\pi \cdot \pi, \frac{1}{4}, \left(-1\right) \cdot {\left(\sqrt[3]{\sin^{-1} \left({\color{blue}{\left(\left(\sqrt[3]{\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)} \cdot \sqrt[3]{\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}\right) \cdot \sqrt[3]{\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}\right)}}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)}^{6}\right)}{\mathsf{fma}\left(\pi, \frac{1}{2}, \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}\]

  12. Simplified60.3

    \[\leadsto \frac{\mathsf{fma}\left(\pi \cdot \pi, \frac{1}{4}, \left(-1\right) \cdot {\left(\sqrt[3]{\sin^{-1} \left({\left(\color{blue}{\left(\sqrt[3]{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)} \cdot \sqrt[3]{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)} \cdot \sqrt[3]{\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)}^{6}\right)}{\mathsf{fma}\left(\pi, \frac{1}{2}, \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}\]

  13. Simplified59.5

    \[\leadsto \frac{\mathsf{fma}\left(\pi \cdot \pi, \frac{1}{4}, \left(-1\right) \cdot {\left(\sqrt[3]{\sin^{-1} \left({\left(\left(\sqrt[3]{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)} \cdot \sqrt[3]{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right) \cdot \color{blue}{\sqrt[3]{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)}^{6}\right)}{\mathsf{fma}\left(\pi, \frac{1}{2}, \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}\]

  14. Final simplification59.5

    \[\leadsto \frac{\mathsf{fma}\left(\pi \cdot \pi, \frac{1}{4}, \left(-1\right) \cdot {\left(\sqrt[3]{\sin^{-1} \left({\left(\left(\sqrt[3]{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)} \cdot \sqrt[3]{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right) \cdot \sqrt[3]{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)}^{6}\right)}{\mathsf{fma}\left(\pi, \frac{1}{2}, \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}\]

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))