Average Error: 61.1 → 60.3
Time: 57.3s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\cos^{-1} \left({\left(\log \left(\sqrt{e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right) + \log \left(\sqrt{e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)
↓
\cos^{-1} \left({\left(\log \left(\sqrt{e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right) + \log \left(\sqrt{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 r18337 = a;
        double r18338 = cosh(r18337);
        double r18339 = r18337 * r18337;
        double r18340 = fmod(r18338, r18339);
        double r18341 = log1p(r18337);
        double r18342 = pow(r18340, r18341);
        double r18343 = acos(r18342);
        return r18343;
}
↓
double f(double a) {
        double r18344 = a;
        double r18345 = cosh(r18344);
        double r18346 = r18344 * r18344;
        double r18347 = fmod(r18345, r18346);
        double r18348 = exp(r18347);
        double r18349 = sqrt(r18348);
        double r18350 = log(r18349);
        double r18351 = r18350 + r18350;
        double r18352 = log1p(r18344);
        double r18353 = pow(r18351, r18352);
        double r18354 = acos(r18353);
        return r18354;
}

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 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 add-sqr-sqrt60.3

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

  6. Applied log-prod60.3

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

  7. Final simplification60.3

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

Reproduce

herbie shell --seed 2019322 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))