Average Error: 33.6 → 33.6
Time: 16.8s
Precision: 64
\[\left|\left(\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right) \bmod a\right)\right|\]
↓
\[\left|\left(\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right) \bmod a\right)\right|\]
\left|\left(\left(\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(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right) \bmod a\right)\right|
double f(double a) {
        double r4589 = a;
        double r4590 = expm1(r4589);
        double r4591 = sin(r4590);
        double r4592 = expm1(r4591);
        double r4593 = atan(r4589);
        double r4594 = atan2(r4592, r4593);
        double r4595 = fmod(r4594, r4589);
        double r4596 = fabs(r4595);
        return r4596;
}
↓
double f(double a) {
        double r4597 = a;
        double r4598 = expm1(r4597);
        double r4599 = sin(r4598);
        double r4600 = expm1(r4599);
        double r4601 = atan(r4597);
        double r4602 = atan2(r4600, r4601);
        double r4603 = fmod(r4602, r4597);
        double r4604 = fabs(r4603);
        return r4604;
}

Error

Bits error versus a

Derivation

  1. Initial program 33.6

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

  2. Final simplification33.6

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

Reproduce

herbie shell --seed 2020047 
(FPCore (a)
  :name "Random Jason Timeout Test 006"
  :precision binary64
  (fabs (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))