Average Error: 0.1 → 0.1
Time: 20.4s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{b - a}{2}\right)} \cdot {\left(\left|\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right|\right)}^{\left(b - a\right)}\right)\]
\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(\frac{b - a}{2}\right)} \cdot {\left(\left|\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right|\right)}^{\left(b - a\right)}\right)
double f(double a, double b) {
        double r3032351 = b;
        double r3032352 = atan2(r3032351, r3032351);
        double r3032353 = sqrt(r3032352);
        double r3032354 = a;
        double r3032355 = r3032351 - r3032354;
        double r3032356 = pow(r3032353, r3032355);
        double r3032357 = sin(r3032356);
        return r3032357;
}
↓
double f(double a, double b) {
        double r3032358 = b;
        double r3032359 = atan2(r3032358, r3032358);
        double r3032360 = cbrt(r3032359);
        double r3032361 = a;
        double r3032362 = r3032358 - r3032361;
        double r3032363 = 2.0;
        double r3032364 = r3032362 / r3032363;
        double r3032365 = pow(r3032360, r3032364);
        double r3032366 = fabs(r3032360);
        double r3032367 = pow(r3032366, r3032362);
        double r3032368 = r3032365 * r3032367;
        double r3032369 = sin(r3032368);
        return r3032369;
}

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 add-cube-cbrt0.1

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

  4. Applied sqrt-prod0.1

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

  5. Applied unpow-prod-down0.1

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

  6. Simplified0.1

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

  8. Applied pow10.1

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

  9. Applied sqrt-pow10.1

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

  10. Applied pow-pow0.1

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

  11. Simplified0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019164 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))