Average Error: 0.2 → 0.2
Time: 13.3s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\mathsf{expm1}\left(\mathsf{log1p}\left(\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\right)\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\mathsf{expm1}\left(\mathsf{log1p}\left(\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\right)\right)
double f(double a, double b) {
        double r5597 = b;
        double r5598 = atan2(r5597, r5597);
        double r5599 = sqrt(r5598);
        double r5600 = a;
        double r5601 = r5597 - r5600;
        double r5602 = pow(r5599, r5601);
        double r5603 = sin(r5602);
        return r5603;
}
↓
double f(double a, double b) {
        double r5604 = b;
        double r5605 = atan2(r5604, r5604);
        double r5606 = sqrt(r5605);
        double r5607 = a;
        double r5608 = r5604 - r5607;
        double r5609 = pow(r5606, r5608);
        double r5610 = sin(r5609);
        double r5611 = log1p(r5610);
        double r5612 = expm1(r5611);
        return r5612;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
  2. Using strategy rm

  3. Applied expm1-log1p-u0.2

    \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\right)\right)}\]

  4. Final simplification0.2

    \[\leadsto \mathsf{expm1}\left(\mathsf{log1p}\left(\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\right)\right)\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))