Average Error: 33.8 → 33.8
Time: 38.0s
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 r1141611 = a;
        double r1141612 = expm1(r1141611);
        double r1141613 = sin(r1141612);
        double r1141614 = expm1(r1141613);
        double r1141615 = atan(r1141611);
        double r1141616 = atan2(r1141614, r1141615);
        double r1141617 = fmod(r1141616, r1141611);
        double r1141618 = fabs(r1141617);
        return r1141618;
}
↓
double f(double a) {
        double r1141619 = a;
        double r1141620 = expm1(r1141619);
        double r1141621 = sin(r1141620);
        double r1141622 = expm1(r1141621);
        double r1141623 = atan(r1141619);
        double r1141624 = atan2(r1141622, r1141623);
        double r1141625 = fmod(r1141624, r1141619);
        double r1141626 = fabs(r1141625);
        return r1141626;
}

Error

Bits error versus a

Derivation

  1. Initial program 33.8

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

  2. Final simplification33.8

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

Reproduce

herbie shell --seed 2019171 
(FPCore (a)
  :name "Random Jason Timeout Test 006"
  (fabs (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))