Average Error: 0.1 → 0.1
Time: 14.9s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\left({\left(\sqrt[3]{b}\right)}^{3} - a\right) \cdot \frac{1}{2}\right)} \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\left(\left(-a\right) + a\right) \cdot \frac{1}{2}\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\left({\left(\sqrt[3]{b}\right)}^{3} - a\right) \cdot \frac{1}{2}\right)} \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\left(\left(-a\right) + a\right) \cdot \frac{1}{2}\right)}\right)
double f(double a, double b) {
        double r17655 = b;
        double r17656 = atan2(r17655, r17655);
        double r17657 = sqrt(r17656);
        double r17658 = a;
        double r17659 = r17655 - r17658;
        double r17660 = pow(r17657, r17659);
        double r17661 = sin(r17660);
        return r17661;
}
↓
double f(double a, double b) {
        double r17662 = b;
        double r17663 = atan2(r17662, r17662);
        double r17664 = cbrt(r17662);
        double r17665 = 3.0;
        double r17666 = pow(r17664, r17665);
        double r17667 = a;
        double r17668 = r17666 - r17667;
        double r17669 = 0.5;
        double r17670 = r17668 * r17669;
        double r17671 = pow(r17663, r17670);
        double r17672 = -r17667;
        double r17673 = r17672 + r17667;
        double r17674 = r17673 * r17669;
        double r17675 = pow(r17663, r17674);
        double r17676 = r17671 * r17675;
        double r17677 = sin(r17676);
        return r17677;
}

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. Using strategy rm

  6. Applied add-cube-cbrt0.1

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

  7. Applied add-cube-cbrt0.1

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

  8. Applied prod-diff0.1

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

  9. Applied distribute-lft-in0.1

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

  10. Applied unpow-prod-up11.3

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

  11. Simplified11.3

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

  12. Simplified0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2019195 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))