Average Error: 0.1 → 0.2
Time: 6.2s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}}{1}\right)}\right)}^{\left(\frac{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{b - a}\right)\right)}{2}\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}}{1}\right)}\right)}^{\left(\frac{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{b - a}\right)\right)}{2}\right)}\right)
double f(double a, double b) {
        double r15685 = b;
        double r15686 = atan2(r15685, r15685);
        double r15687 = sqrt(r15686);
        double r15688 = a;
        double r15689 = r15685 - r15688;
        double r15690 = pow(r15687, r15689);
        double r15691 = sin(r15690);
        return r15691;
}
↓
double f(double a, double b) {
        double r15692 = b;
        double r15693 = atan2(r15692, r15692);
        double r15694 = a;
        double r15695 = r15692 - r15694;
        double r15696 = cbrt(r15695);
        double r15697 = r15696 * r15696;
        double r15698 = 1.0;
        double r15699 = r15697 / r15698;
        double r15700 = pow(r15693, r15699);
        double r15701 = log1p(r15696);
        double r15702 = expm1(r15701);
        double r15703 = 2.0;
        double r15704 = r15702 / r15703;
        double r15705 = pow(r15700, r15704);
        double r15706 = sin(r15705);
        return r15706;
}

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 *-un-lft-identity0.1

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

  8. Applied add-cube-cbrt0.1

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

  9. Applied times-frac0.1

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

  10. Applied pow-unpow0.1

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

  12. Applied expm1-log1p-u0.2

    \[\leadsto \sin \left({\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}}{1}\right)}\right)}^{\left(\frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{b - a}\right)\right)}}{2}\right)}\right)\]

  13. Final simplification0.2

    \[\leadsto \sin \left({\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}}{1}\right)}\right)}^{\left(\frac{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{b - a}\right)\right)}{2}\right)}\right)\]

Reproduce

herbie shell --seed 2020081 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))