Random Jason Timeout Test 012

Average Error: 60.6 → 59.6

Time: 53.8s

Precision: 64

• could not determine a ground truth for program body

  1. a = 9.786110833240265e+222

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 r1363302 = a;
        double r1363303 = cosh(r1363302);
        double r1363304 = r1363302 * r1363302;
        double r1363305 = fmod(r1363303, r1363304);
        double r1363306 = log1p(r1363302);
        double r1363307 = pow(r1363305, r1363306);
        double r1363308 = acos(r1363307);
        return r1363308;
}

↓

double f(double a) {
        double r1363309 = a;
        double r1363310 = cosh(r1363309);
        double r1363311 = r1363309 * r1363309;
        double r1363312 = fmod(r1363310, r1363311);
        double r1363313 = exp(r1363312);
        double r1363314 = log(r1363313);
        double r1363315 = log1p(r1363309);
        double r1363316 = pow(r1363314, r1363315);
        double r1363317 = acos(r1363316);
        double r1363318 = cbrt(r1363317);
        double r1363319 = r1363318 * r1363318;
        double r1363320 = r1363318 * r1363319;
        return r1363320;
}

Error

Bits error versus a

Derivation

1. Initial program 60.6

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

3. Applied add-log-exp 59.6

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

5. Applied add-cube-cbrt 59.6

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

6. Final simplification 59.6

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

Reproduce

herbie shell --seed 2019133 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))