Average Error: 0.1 → 0.1
Time: 18.9s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot {\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}\right)}\right)}^{\left(\frac{\sqrt[3]{\left(b + a\right) \cdot \left(b - a\right)}}{\sqrt[3]{b + a}}\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot {\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}\right)}\right)}^{\left(\frac{\sqrt[3]{\left(b + a\right) \cdot \left(b - a\right)}}{\sqrt[3]{b + a}}\right)}\right)
double f(double a, double b) {
        double r1600802 = b;
        double r1600803 = atan2(r1600802, r1600802);
        double r1600804 = sqrt(r1600803);
        double r1600805 = a;
        double r1600806 = r1600802 - r1600805;
        double r1600807 = pow(r1600804, r1600806);
        double r1600808 = sin(r1600807);
        return r1600808;
}
↓
double f(double a, double b) {
        double r1600809 = b;
        double r1600810 = atan2(r1600809, r1600809);
        double r1600811 = sqrt(r1600810);
        double r1600812 = sqrt(r1600811);
        double r1600813 = a;
        double r1600814 = r1600809 - r1600813;
        double r1600815 = pow(r1600812, r1600814);
        double r1600816 = cbrt(r1600814);
        double r1600817 = r1600816 * r1600816;
        double r1600818 = pow(r1600812, r1600817);
        double r1600819 = r1600809 + r1600813;
        double r1600820 = r1600819 * r1600814;
        double r1600821 = cbrt(r1600820);
        double r1600822 = cbrt(r1600819);
        double r1600823 = r1600821 / r1600822;
        double r1600824 = pow(r1600818, r1600823);
        double r1600825 = r1600815 * r1600824;
        double r1600826 = sin(r1600825);
        return r1600826;
}

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 flip--3.9

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

  11. Applied cbrt-div3.9

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

  12. Simplified0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2019171 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))