Random Jason Timeout Test 006

Average Error: 34.0 → 34.0

Time: 42.7s

Precision: 64

• could not determine a ground truth for program body

  1. a = 4.608700736709935e+77

Math

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

↓

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

C

double f(double a) {
        double r348383 = a;
        double r348384 = expm1(r348383);
        double r348385 = sin(r348384);
        double r348386 = expm1(r348385);
        double r348387 = atan(r348383);
        double r348388 = atan2(r348386, r348387);
        double r348389 = fmod(r348388, r348383);
        double r348390 = fabs(r348389);
        return r348390;
}

↓

double f(double a) {
        double r348391 = a;
        double r348392 = expm1(r348391);
        double r348393 = sin(r348392);
        double r348394 = expm1(r348393);
        double r348395 = cbrt(r348394);
        double r348396 = r348395 * r348395;
        double r348397 = cbrt(r348395);
        double r348398 = r348397 * r348397;
        double r348399 = cbrt(r348397);
        double r348400 = r348399 * r348399;
        double r348401 = r348400 * r348399;
        double r348402 = r348398 * r348401;
        double r348403 = r348396 * r348402;
        double r348404 = atan(r348391);
        double r348405 = atan2(r348403, r348404);
        double r348406 = fmod(r348405, r348391);
        double r348407 = cbrt(r348406);
        double r348408 = r348395 * r348396;
        double r348409 = atan2(r348408, r348404);
        double r348410 = fmod(r348409, r348391);
        double r348411 = cbrt(r348410);
        double r348412 = r348411 * r348411;
        double r348413 = r348407 * r348412;
        double r348414 = fabs(r348413);
        return r348414;
}

Error

Bits error versus a

Derivation

1. Initial program 34.0

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

3. Applied add-cube-cbrt 34.1

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

5. Applied add-cube-cbrt 34.1

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

7. Applied add-cube-cbrt 34.1

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

9. Applied add-cube-cbrt 34.0

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

10. Final simplification 34.0

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

Reproduce

herbie shell --seed 2019154 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 006"
  (fabs (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))