Random Jason Timeout Test 012

Average Error: 61.1 → 59.3

Time: 27.2s

Precision: 64

• could not determine a ground truth for program body

  1. a = 6.044374590537398e+170

Math

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

↓

\[\frac{\mathsf{fma}\left(-1, {\left(\sqrt[3]{\sin^{-1} \left({\left(e^{\log \left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)}^{6}, \frac{\pi \cdot \pi}{4}\right)}{\mathsf{fma}\left(\frac{1}{2}, \pi, \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}\]

C

double f(double a) {
        double r6052 = a;
        double r6053 = cosh(r6052);
        double r6054 = r6052 * r6052;
        double r6055 = fmod(r6053, r6054);
        double r6056 = log1p(r6052);
        double r6057 = pow(r6055, r6056);
        double r6058 = acos(r6057);
        return r6058;
}

↓

double f(double a) {
        double r6059 = 1.0;
        double r6060 = -r6059;
        double r6061 = a;
        double r6062 = cosh(r6061);
        double r6063 = r6061 * r6061;
        double r6064 = fmod(r6062, r6063);
        double r6065 = log(r6064);
        double r6066 = exp(r6065);
        double r6067 = log1p(r6061);
        double r6068 = pow(r6066, r6067);
        double r6069 = asin(r6068);
        double r6070 = cbrt(r6069);
        double r6071 = 6.0;
        double r6072 = pow(r6070, r6071);
        double r6073 = atan2(1.0, 0.0);
        double r6074 = r6073 * r6073;
        double r6075 = 4.0;
        double r6076 = r6074 / r6075;
        double r6077 = fma(r6060, r6072, r6076);
        double r6078 = 0.5;
        double r6079 = 2.0;
        double r6080 = pow(r6061, r6079);
        double r6081 = fmod(r6062, r6080);
        double r6082 = pow(r6081, r6067);
        double r6083 = asin(r6082);
        double r6084 = fma(r6078, r6073, r6083);
        double r6085 = r6077 / r6084;
        return r6085;
}

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-exp 60.2

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

5. Applied acos-asin 60.2

   \[\leadsto \color{blue}{\frac{\pi}{2} - \sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\]
6. Using strategy rm

7. Applied flip-- 60.2

   \[\leadsto \color{blue}{\frac{\frac{\pi}{2} \cdot \frac{\pi}{2} - \sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \cdot \sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}{\frac{\pi}{2} + \sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\]

8. Simplified 60.2

   \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-1, {\left(\sqrt[3]{\sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)}^{6}, \frac{\pi \cdot \pi}{4}\right)}}{\frac{\pi}{2} + \sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\]

9. Simplified 60.2

   \[\leadsto \frac{\mathsf{fma}\left(-1, {\left(\sqrt[3]{\sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)}^{6}, \frac{\pi \cdot \pi}{4}\right)}{\color{blue}{\mathsf{fma}\left(\frac{1}{2}, \pi, \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}}\]
10. Using strategy rm

11. Applied add-exp-log 60.2

    \[\leadsto \frac{\mathsf{fma}\left(-1, {\left(\sqrt[3]{\sin^{-1} \left({\color{blue}{\left(e^{\log \left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}\right)}}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)}^{6}, \frac{\pi \cdot \pi}{4}\right)}{\mathsf{fma}\left(\frac{1}{2}, \pi, \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}\]

12. Simplified 59.3

    \[\leadsto \frac{\mathsf{fma}\left(-1, {\left(\sqrt[3]{\sin^{-1} \left({\left(e^{\color{blue}{\log \left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)}^{6}, \frac{\pi \cdot \pi}{4}\right)}{\mathsf{fma}\left(\frac{1}{2}, \pi, \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}\]

13. Final simplification 59.3

    \[\leadsto \frac{\mathsf{fma}\left(-1, {\left(\sqrt[3]{\sin^{-1} \left({\left(e^{\log \left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)}^{6}, \frac{\pi \cdot \pi}{4}\right)}{\mathsf{fma}\left(\frac{1}{2}, \pi, \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}\]

Reproduce

herbie shell --seed 2020024 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))