Random Jason Timeout Test 012

Average Error: 60.4 → 59.2

Time: 44.6s

Precision: 64

• could not determine a ground truth for program body

  1. a = 3.5462679030988947e+276

Math

\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\]

↓

\[\sqrt{\frac{\pi}{2} - \sin^{-1} \left({\left(\log \left(e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right) \cdot \sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}^{\left(\log_* (1 + a)\right)}\right)} \cdot \sqrt{\frac{\pi}{2} - \sin^{-1} \left({\left(\log \left(e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right) \cdot \sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}^{\left(\log_* (1 + a)\right)}\right)}\]

C

double f(double a) {
        double r300041 = a;
        double r300042 = cosh(r300041);
        double r300043 = r300041 * r300041;
        double r300044 = fmod(r300042, r300043);
        double r300045 = log1p(r300041);
        double r300046 = pow(r300044, r300045);
        double r300047 = acos(r300046);
        return r300047;
}

↓

double f(double a) {
        double r300048 = atan2(1.0, 0.0);
        double r300049 = 2.0;
        double r300050 = r300048 / r300049;
        double r300051 = a;
        double r300052 = cosh(r300051);
        double r300053 = r300051 * r300051;
        double r300054 = fmod(r300052, r300053);
        double r300055 = sqrt(r300054);
        double r300056 = exp(r300055);
        double r300057 = log(r300056);
        double r300058 = r300057 * r300055;
        double r300059 = log1p(r300051);
        double r300060 = pow(r300058, r300059);
        double r300061 = asin(r300060);
        double r300062 = r300050 - r300061;
        double r300063 = sqrt(r300062);
        double r300064 = r300063 * r300063;
        return r300064;
}

Error

Bits error versus a

Derivation

1. Initial program 60.4

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

3. Applied add-log-exp 59.5

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

5. Applied add-sqr-sqrt 59.5

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

6. Applied exp-prod 59.5

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

7. Applied log-pow 59.2

   \[\leadsto \cos^{-1} \left({\color{blue}{\left(\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)} \cdot \log \left(e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right)\right)}}^{\left(\log_* (1 + a)\right)}\right)\]
8. Using strategy rm

9. Applied acos-asin 59.2

   \[\leadsto \color{blue}{\frac{\pi}{2} - \sin^{-1} \left({\left(\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)} \cdot \log \left(e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right)\right)}^{\left(\log_* (1 + a)\right)}\right)}\]
10. Using strategy rm

11. Applied add-sqr-sqrt 59.2

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

12. Final simplification 59.2

    \[\leadsto \sqrt{\frac{\pi}{2} - \sin^{-1} \left({\left(\log \left(e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right) \cdot \sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}^{\left(\log_* (1 + a)\right)}\right)} \cdot \sqrt{\frac{\pi}{2} - \sin^{-1} \left({\left(\log \left(e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right) \cdot \sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}^{\left(\log_* (1 + a)\right)}\right)}\]

Reproduce

herbie shell --seed 2019119 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))