Average Error: 61.2 → 60.3
Time: 27.2s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\left(\sqrt[3]{\frac{\pi}{2} - \sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)} \cdot \sqrt[3]{\frac{\pi}{2} - \sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right) \cdot \sqrt[3]{\frac{\pi}{2} - \sin^{-1} \left({\left(2 \cdot \log \left(\sqrt[3]{e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right) + \log \left(\sqrt[3]{e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\]
\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)
↓
\left(\sqrt[3]{\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 \sqrt[3]{\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)}\right) \cdot \sqrt[3]{\frac{\pi}{2} - \sin^{-1} \left({\left(2 \cdot \log \left(\sqrt[3]{e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right) + \log \left(\sqrt[3]{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 r3258 = a;
        double r3259 = cosh(r3258);
        double r3260 = r3258 * r3258;
        double r3261 = fmod(r3259, r3260);
        double r3262 = log1p(r3258);
        double r3263 = pow(r3261, r3262);
        double r3264 = acos(r3263);
        return r3264;
}
↓
double f(double a) {
        double r3265 = atan2(1.0, 0.0);
        double r3266 = 2.0;
        double r3267 = r3265 / r3266;
        double r3268 = a;
        double r3269 = cosh(r3268);
        double r3270 = r3268 * r3268;
        double r3271 = fmod(r3269, r3270);
        double r3272 = exp(r3271);
        double r3273 = log(r3272);
        double r3274 = log1p(r3268);
        double r3275 = pow(r3273, r3274);
        double r3276 = asin(r3275);
        double r3277 = r3267 - r3276;
        double r3278 = cbrt(r3277);
        double r3279 = r3278 * r3278;
        double r3280 = cbrt(r3272);
        double r3281 = log(r3280);
        double r3282 = r3266 * r3281;
        double r3283 = r3282 + r3281;
        double r3284 = pow(r3283, r3274);
        double r3285 = asin(r3284);
        double r3286 = r3267 - r3285;
        double r3287 = cbrt(r3286);
        double r3288 = r3279 * r3287;
        return r3288;
}

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-exp60.2

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

  5. Applied acos-asin60.2

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

  7. Applied add-cube-cbrt60.2

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

  9. Applied add-cube-cbrt60.3

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

  10. Applied log-prod60.3

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

  11. Simplified60.3

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

  12. Final simplification60.3

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

Reproduce

herbie shell --seed 2020021 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))