Average Error: 61.2 → 60.3
Time: 26.7s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\cos^{-1} \left(\left(\sqrt[3]{{\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}} \cdot \sqrt[3]{{\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}}\right) \cdot \sqrt[3]{{\left(1 \cdot \left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}}\right)\]
\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(\sqrt[3]{{\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)}} \cdot \sqrt[3]{{\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]{{\left(1 \cdot \left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}}\right)
double f(double a) {
        double r5219 = a;
        double r5220 = cosh(r5219);
        double r5221 = r5219 * r5219;
        double r5222 = fmod(r5220, r5221);
        double r5223 = log1p(r5219);
        double r5224 = pow(r5222, r5223);
        double r5225 = acos(r5224);
        return r5225;
}
↓
double f(double a) {
        double r5226 = a;
        double r5227 = cosh(r5226);
        double r5228 = r5226 * r5226;
        double r5229 = fmod(r5227, r5228);
        double r5230 = exp(r5229);
        double r5231 = log(r5230);
        double r5232 = log1p(r5226);
        double r5233 = pow(r5231, r5232);
        double r5234 = cbrt(r5233);
        double r5235 = r5234 * r5234;
        double r5236 = 1.0;
        double r5237 = r5236 * r5229;
        double r5238 = pow(r5237, r5232);
        double r5239 = cbrt(r5238);
        double r5240 = r5235 * r5239;
        double r5241 = acos(r5240);
        return r5241;
}

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 add-cube-cbrt60.3

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

  7. Applied pow160.3

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

  8. Applied log-pow60.3

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

  9. Simplified60.3

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

  10. Final simplification60.3

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

Reproduce

herbie shell --seed 2020003 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))