Average Error: 0.1 → 0.2
Time: 5.0s
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 r11821 = b;
        double r11822 = atan2(r11821, r11821);
        double r11823 = sqrt(r11822);
        double r11824 = a;
        double r11825 = r11821 - r11824;
        double r11826 = pow(r11823, r11825);
        double r11827 = sin(r11826);
        return r11827;
}
↓
double f(double a, double b) {
        double r11828 = 2.0;
        double r11829 = b;
        double r11830 = a;
        double r11831 = r11829 - r11830;
        double r11832 = r11828 * r11831;
        double r11833 = atan2(r11829, r11829);
        double r11834 = sqrt(r11833);
        double r11835 = sqrt(r11834);
        double r11836 = log(r11835);
        double r11837 = r11832 * r11836;
        double r11838 = exp(r11837);
        double r11839 = sin(r11838);
        double r11840 = sqrt(r11839);
        double r11841 = r11840 * r11840;
        return r11841;
}

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 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))