Average Error: 0.1 → 0.2
Time: 5.2s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sqrt{\sin \left(e^{\left(2 \cdot \left(b - a\right)\right) \cdot \log \left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}\right)} \cdot \sqrt{\sin \left(e^{\left(2 \cdot \left(b - a\right)\right) \cdot \log \left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}\right)}\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sqrt{\sin \left(e^{\left(2 \cdot \left(b - a\right)\right) \cdot \log \left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}\right)} \cdot \sqrt{\sin \left(e^{\left(2 \cdot \left(b - a\right)\right) \cdot \log \left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}\right)}
double f(double a, double b) {
        double r7285 = b;
        double r7286 = atan2(r7285, r7285);
        double r7287 = sqrt(r7286);
        double r7288 = a;
        double r7289 = r7285 - r7288;
        double r7290 = pow(r7287, r7289);
        double r7291 = sin(r7290);
        return r7291;
}
↓
double f(double a, double b) {
        double r7292 = 2.0;
        double r7293 = b;
        double r7294 = a;
        double r7295 = r7293 - r7294;
        double r7296 = r7292 * r7295;
        double r7297 = atan2(r7293, r7293);
        double r7298 = sqrt(r7297);
        double r7299 = sqrt(r7298);
        double r7300 = log(r7299);
        double r7301 = r7296 * r7300;
        double r7302 = exp(r7301);
        double r7303 = sin(r7302);
        double r7304 = sqrt(r7303);
        double r7305 = r7304 * r7304;
        return r7305;
}

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-sqr-sqrt0.1

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

  4. Applied sqrt-prod0.1

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

  5. Applied unpow-prod-down0.1

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

  7. Applied add-cbrt-cube0.1

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

  8. Simplified0.1

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

  10. Applied add-exp-log0.1

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

  11. Applied add-exp-log0.1

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

  12. Applied pow-exp0.1

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

  13. Applied prod-exp0.1

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

  14. Simplified0.1

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

  16. Applied add-sqr-sqrt0.2

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

  17. Final simplification0.2

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

Reproduce

herbie shell --seed 2020047 
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))