Random Jason Timeout Test 012

Average Error: 60.4 → 59.4

Time: 59.1s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.6831471702984413e+19

Math

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

↓

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

C

double f(double a) {
        double r1366294 = a;
        double r1366295 = cosh(r1366294);
        double r1366296 = r1366294 * r1366294;
        double r1366297 = fmod(r1366295, r1366296);
        double r1366298 = log1p(r1366294);
        double r1366299 = pow(r1366297, r1366298);
        double r1366300 = acos(r1366299);
        return r1366300;
}

↓

double f(double a) {
        double r1366301 = a;
        double r1366302 = cosh(r1366301);
        double r1366303 = r1366301 * r1366301;
        double r1366304 = fmod(r1366302, r1366303);
        double r1366305 = exp(r1366304);
        double r1366306 = log(r1366305);
        double r1366307 = log1p(r1366301);
        double r1366308 = pow(r1366306, r1366307);
        double r1366309 = acos(r1366308);
        double r1366310 = cbrt(r1366309);
        double r1366311 = r1366310 * r1366310;
        double r1366312 = r1366310 * r1366311;
        return r1366312;
}

Error

Bits error versus a

Derivation

1. Initial program 60.4

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

3. Applied add-log-exp 59.4

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

5. Applied add-cube-cbrt 59.4

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

6. Final simplification 59.4

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

Reproduce

herbie shell --seed 2019138 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))