Average Error: 33.5 → 33.5
Time: 16.7s
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 r8794 = a;
        double r8795 = expm1(r8794);
        double r8796 = sin(r8795);
        double r8797 = expm1(r8796);
        double r8798 = atan(r8794);
        double r8799 = atan2(r8797, r8798);
        double r8800 = fmod(r8799, r8794);
        double r8801 = fabs(r8800);
        return r8801;
}
↓
double f(double a) {
        double r8802 = a;
        double r8803 = expm1(r8802);
        double r8804 = sin(r8803);
        double r8805 = expm1(r8804);
        double r8806 = atan(r8802);
        double r8807 = atan2(r8805, r8806);
        double r8808 = fmod(r8807, r8802);
        double r8809 = fabs(r8808);
        return r8809;
}

Error

Bits error versus a

Derivation

  1. Initial program 33.5

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

  2. Final simplification33.5

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

Reproduce

herbie shell --seed 2020060 
(FPCore (a)
  :name "Random Jason Timeout Test 006"
  :precision binary64
  (fabs (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))