Average Error: 0.1 → 0.8
Time: 6.9s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}\right)}\right)}^{\left(e^{\log \left(\sqrt[3]{b - a}\right)}\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}\right)}\right)}^{\left(e^{\log \left(\sqrt[3]{b - a}\right)}\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)
double f(double a, double b) {
        double r31852 = b;
        double r31853 = atan2(r31852, r31852);
        double r31854 = sqrt(r31853);
        double r31855 = a;
        double r31856 = r31852 - r31855;
        double r31857 = pow(r31854, r31856);
        double r31858 = sin(r31857);
        return r31858;
}
↓
double f(double a, double b) {
        double r31859 = b;
        double r31860 = atan2(r31859, r31859);
        double r31861 = sqrt(r31860);
        double r31862 = sqrt(r31861);
        double r31863 = a;
        double r31864 = r31859 - r31863;
        double r31865 = cbrt(r31864);
        double r31866 = r31865 * r31865;
        double r31867 = pow(r31862, r31866);
        double r31868 = log(r31865);
        double r31869 = exp(r31868);
        double r31870 = pow(r31867, r31869);
        double r31871 = pow(r31862, r31864);
        double r31872 = r31870 * r31871;
        double r31873 = sin(r31872);
        return r31873;
}

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-cube-cbrt0.1

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

  8. Applied pow-unpow0.1

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

  10. Applied add-exp-log0.8

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

  11. Final simplification0.8

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

Reproduce

herbie shell --seed 2019322 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))