Random Jason Timeout Test 006

Average Error: 33.4 → 33.5

Time: 46.0s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.5073988265699047e+58

Math

\[\left|\left(\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right) \bmod a\right)\right|\]

↓

\[\left|\left(\left(\log \left(e^{\tan^{-1}_* \frac{\mathsf{expm1}\left(e^{\log \left({\left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)}^{6}\right)} \cdot \sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}\right)}{\tan^{-1} a}}\right)\right) \bmod a\right)\right|\]

C

double f(double a) {
        double r28268 = a;
        double r28269 = expm1(r28268);
        double r28270 = sin(r28269);
        double r28271 = expm1(r28270);
        double r28272 = atan(r28268);
        double r28273 = atan2(r28271, r28272);
        double r28274 = fmod(r28273, r28268);
        double r28275 = fabs(r28274);
        return r28275;
}

↓

double f(double a) {
        double r28276 = a;
        double r28277 = expm1(r28276);
        double r28278 = sin(r28277);
        double r28279 = cbrt(r28278);
        double r28280 = cbrt(r28279);
        double r28281 = 6.0;
        double r28282 = pow(r28280, r28281);
        double r28283 = log(r28282);
        double r28284 = exp(r28283);
        double r28285 = r28284 * r28279;
        double r28286 = expm1(r28285);
        double r28287 = atan(r28276);
        double r28288 = atan2(r28286, r28287);
        double r28289 = exp(r28288);
        double r28290 = log(r28289);
        double r28291 = fmod(r28290, r28276);
        double r28292 = fabs(r28291);
        return r28292;
}

Error

Bits error versus a

Derivation

1. Initial program 33.4

   \[\left|\left(\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right) \bmod a\right)\right|\]
2. Using strategy rm

3. Applied add-log-exp 33.4

   \[\leadsto \left|\left(\color{blue}{\left(\log \left(e^{\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}}\right)\right)} \bmod a\right)\right|\]
4. Using strategy rm

5. Applied add-cube-cbrt 33.5

   \[\leadsto \left|\left(\left(\log \left(e^{\tan^{-1}_* \frac{\mathsf{expm1}\left(\color{blue}{\left(\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)} \cdot \sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}\right) \cdot \sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)}{\tan^{-1} a}}\right)\right) \bmod a\right)\right|\]
6. Using strategy rm

7. Applied add-cube-cbrt 33.5

   \[\leadsto \left|\left(\left(\log \left(e^{\tan^{-1}_* \frac{\mathsf{expm1}\left(\left(\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)} \cdot \color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}} \cdot \sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right) \cdot \sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)}\right) \cdot \sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}\right)}{\tan^{-1} a}}\right)\right) \bmod a\right)\right|\]

8. Applied associate-*r* 33.5

   \[\leadsto \left|\left(\left(\log \left(e^{\tan^{-1}_* \frac{\mathsf{expm1}\left(\color{blue}{\left(\left(\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)} \cdot \left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}} \cdot \sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)\right) \cdot \sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)} \cdot \sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}\right)}{\tan^{-1} a}}\right)\right) \bmod a\right)\right|\]

9. Simplified 33.5

   \[\leadsto \left|\left(\left(\log \left(e^{\tan^{-1}_* \frac{\mathsf{expm1}\left(\left(\color{blue}{\left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}} \cdot {\left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)}^{\left(3 + 1\right)}\right)} \cdot \sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right) \cdot \sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}\right)}{\tan^{-1} a}}\right)\right) \bmod a\right)\right|\]
10. Using strategy rm

11. Applied add-exp-log 59.5

    \[\leadsto \left|\left(\left(\log \left(e^{\tan^{-1}_* \frac{\mathsf{expm1}\left(\left(\left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}} \cdot {\left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)}^{\left(3 + 1\right)}\right) \cdot \color{blue}{e^{\log \left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)}}\right) \cdot \sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}\right)}{\tan^{-1} a}}\right)\right) \bmod a\right)\right|\]

12. Applied add-exp-log 59.5

    \[\leadsto \left|\left(\left(\log \left(e^{\tan^{-1}_* \frac{\mathsf{expm1}\left(\left(\left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}} \cdot {\color{blue}{\left(e^{\log \left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)}\right)}}^{\left(3 + 1\right)}\right) \cdot e^{\log \left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)}\right) \cdot \sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}\right)}{\tan^{-1} a}}\right)\right) \bmod a\right)\right|\]

13. Applied pow-exp 59.5

    \[\leadsto \left|\left(\left(\log \left(e^{\tan^{-1}_* \frac{\mathsf{expm1}\left(\left(\left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}} \cdot \color{blue}{e^{\log \left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right) \cdot \left(3 + 1\right)}}\right) \cdot e^{\log \left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)}\right) \cdot \sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}\right)}{\tan^{-1} a}}\right)\right) \bmod a\right)\right|\]

14. Applied add-exp-log 59.5

    \[\leadsto \left|\left(\left(\log \left(e^{\tan^{-1}_* \frac{\mathsf{expm1}\left(\left(\left(\color{blue}{e^{\log \left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)}} \cdot e^{\log \left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right) \cdot \left(3 + 1\right)}\right) \cdot e^{\log \left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)}\right) \cdot \sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}\right)}{\tan^{-1} a}}\right)\right) \bmod a\right)\right|\]

15. Applied prod-exp 59.6

    \[\leadsto \left|\left(\left(\log \left(e^{\tan^{-1}_* \frac{\mathsf{expm1}\left(\left(\color{blue}{e^{\log \left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right) + \log \left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right) \cdot \left(3 + 1\right)}} \cdot e^{\log \left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)}\right) \cdot \sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}\right)}{\tan^{-1} a}}\right)\right) \bmod a\right)\right|\]

16. Applied prod-exp 59.5

    \[\leadsto \left|\left(\left(\log \left(e^{\tan^{-1}_* \frac{\mathsf{expm1}\left(\color{blue}{e^{\left(\log \left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right) + \log \left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right) \cdot \left(3 + 1\right)\right) + \log \left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)}} \cdot \sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}\right)}{\tan^{-1} a}}\right)\right) \bmod a\right)\right|\]

17. Simplified 33.5

    \[\leadsto \left|\left(\left(\log \left(e^{\tan^{-1}_* \frac{\mathsf{expm1}\left(e^{\color{blue}{\log \left({\left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)}^{6}\right)}} \cdot \sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}\right)}{\tan^{-1} a}}\right)\right) \bmod a\right)\right|\]

18. Final simplification 33.5

    \[\leadsto \left|\left(\left(\log \left(e^{\tan^{-1}_* \frac{\mathsf{expm1}\left(e^{\log \left({\left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)}^{6}\right)} \cdot \sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}\right)}{\tan^{-1} a}}\right)\right) \bmod a\right)\right|\]

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 006"
  :precision binary64
  (fabs (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))