Average Error: 61.3 → 60.5
Time: 36.7s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\cos^{-1} \left({\left(\sqrt[3]{{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{3}}\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
\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(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{3}}\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)
double f(double a) {
        double r8288 = a;
        double r8289 = cosh(r8288);
        double r8290 = r8288 * r8288;
        double r8291 = fmod(r8289, r8290);
        double r8292 = log1p(r8288);
        double r8293 = pow(r8291, r8292);
        double r8294 = acos(r8293);
        return r8294;
}
↓
double f(double a) {
        double r8295 = a;
        double r8296 = cosh(r8295);
        double r8297 = r8295 * r8295;
        double r8298 = fmod(r8296, r8297);
        double r8299 = 3.0;
        double r8300 = pow(r8298, r8299);
        double r8301 = cbrt(r8300);
        double r8302 = log1p(r8295);
        double r8303 = pow(r8301, r8302);
        double r8304 = acos(r8303);
        return r8304;
}

Error

Bits error versus a

Derivation

  1. Initial program 61.3

    \[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
  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-cbrt-cube60.3

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

  6. Simplified60.5

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

  7. Final simplification60.5

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

Reproduce

herbie shell --seed 2020045 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))