Random Jason Timeout Test 012

Average Error: 60.4 → 59.2

Time: 1.0m

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 r1431042 = a;
        double r1431043 = cosh(r1431042);
        double r1431044 = r1431042 * r1431042;
        double r1431045 = fmod(r1431043, r1431044);
        double r1431046 = log1p(r1431042);
        double r1431047 = pow(r1431045, r1431046);
        double r1431048 = acos(r1431047);
        return r1431048;
}

↓

double f(double a) {
        double r1431049 = atan2(1.0, 0.0);
        double r1431050 = 2.0;
        double r1431051 = r1431049 / r1431050;
        double r1431052 = a;
        double r1431053 = cosh(r1431052);
        double r1431054 = r1431052 * r1431052;
        double r1431055 = fmod(r1431053, r1431054);
        double r1431056 = sqrt(r1431055);
        double r1431057 = exp(r1431056);
        double r1431058 = log(r1431057);
        double r1431059 = r1431058 * r1431056;
        double r1431060 = log1p(r1431052);
        double r1431061 = pow(r1431059, r1431060);
        double r1431062 = asin(r1431061);
        double r1431063 = r1431051 - r1431062;
        double r1431064 = sqrt(r1431063);
        double r1431065 = r1431064 * r1431064;
        return r1431065;
}

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