Average Error: 0.1 → 0.9
Time: 5.2s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}}{1}\right)}\right)}^{\left(\frac{{\left(b - a\right)}^{\frac{1}{3}}}{2}\right)}\right)\]
\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{{\left(b - a\right)}^{\frac{1}{3}}}{2}\right)}\right)
double f(double a, double b) {
        double r9377 = b;
        double r9378 = atan2(r9377, r9377);
        double r9379 = sqrt(r9378);
        double r9380 = a;
        double r9381 = r9377 - r9380;
        double r9382 = pow(r9379, r9381);
        double r9383 = sin(r9382);
        return r9383;
}
↓
double f(double a, double b) {
        double r9384 = b;
        double r9385 = atan2(r9384, r9384);
        double r9386 = a;
        double r9387 = r9384 - r9386;
        double r9388 = cbrt(r9387);
        double r9389 = r9388 * r9388;
        double r9390 = 1.0;
        double r9391 = r9389 / r9390;
        double r9392 = pow(r9385, r9391);
        double r9393 = 0.3333333333333333;
        double r9394 = pow(r9387, r9393);
        double r9395 = 2.0;
        double r9396 = r9394 / r9395;
        double r9397 = pow(r9392, r9396);
        double r9398 = sin(r9397);
        return r9398;
}

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 pow1/30.9

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

  13. Final simplification0.9

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

Reproduce

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