Average Error: 0.1 → 0.1
Time: 16.0s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)} \cdot {\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)} \cdot {\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)}\right)
double f(double a, double b) {
        double r17600 = b;
        double r17601 = atan2(r17600, r17600);
        double r17602 = sqrt(r17601);
        double r17603 = a;
        double r17604 = r17600 - r17603;
        double r17605 = pow(r17602, r17604);
        double r17606 = sin(r17605);
        return r17606;
}
↓
double f(double a, double b) {
        double r17607 = b;
        double r17608 = atan2(r17607, r17607);
        double r17609 = cbrt(r17608);
        double r17610 = a;
        double r17611 = r17607 - r17610;
        double r17612 = 0.5;
        double r17613 = r17611 * r17612;
        double r17614 = pow(r17609, r17613);
        double r17615 = r17609 * r17609;
        double r17616 = pow(r17615, r17613);
        double r17617 = r17614 * r17616;
        double r17618 = sin(r17617);
        return r17618;
}

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 0.1

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

  3. Applied pow1/20.1

    \[\leadsto \sin \left({\color{blue}{\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\frac{1}{2}}\right)}}^{\left(b - a\right)}\right)\]

  4. Applied pow-pow0.1

    \[\leadsto \sin \color{blue}{\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{2} \cdot \left(b - a\right)\right)}\right)}\]

  5. Simplified0.1

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

  7. Applied add-cube-cbrt0.1

    \[\leadsto \sin \left({\color{blue}{\left(\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right) \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}}^{\left(\frac{b - a}{2}\right)}\right)\]

  8. Applied unpow-prod-down0.1

    \[\leadsto \sin \color{blue}{\left({\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{b - a}{2}\right)} \cdot {\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{b - a}{2}\right)}\right)}\]

  9. Simplified0.1

    \[\leadsto \sin \left(\color{blue}{{\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)}} \cdot {\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{b - a}{2}\right)}\right)\]

  10. Simplified0.1

    \[\leadsto \sin \left({\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)} \cdot \color{blue}{{\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)}}\right)\]

  11. Final simplification0.1

    \[\leadsto \sin \left({\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)} \cdot {\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)}\right)\]

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  (sin (pow (sqrt (atan2 b b)) (- b a))))