Average Error: 0.1 → 0.1
Time: 26.6s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left(\left(\sqrt{{\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}} \cdot \sqrt{e^{\left(b - a\right) \cdot \left(\log \left(\tan^{-1}_* \frac{b}{b}\right) \cdot \frac{1}{4}\right)}}\right) \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left(\left(\sqrt{{\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}} \cdot \sqrt{e^{\left(b - a\right) \cdot \left(\log \left(\tan^{-1}_* \frac{b}{b}\right) \cdot \frac{1}{4}\right)}}\right) \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)
double f(double a, double b) {
        double r1313719 = b;
        double r1313720 = atan2(r1313719, r1313719);
        double r1313721 = sqrt(r1313720);
        double r1313722 = a;
        double r1313723 = r1313719 - r1313722;
        double r1313724 = pow(r1313721, r1313723);
        double r1313725 = sin(r1313724);
        return r1313725;
}
↓
double f(double a, double b) {
        double r1313726 = b;
        double r1313727 = atan2(r1313726, r1313726);
        double r1313728 = sqrt(r1313727);
        double r1313729 = sqrt(r1313728);
        double r1313730 = a;
        double r1313731 = r1313726 - r1313730;
        double r1313732 = pow(r1313729, r1313731);
        double r1313733 = sqrt(r1313732);
        double r1313734 = log(r1313727);
        double r1313735 = 0.25;
        double r1313736 = r1313734 * r1313735;
        double r1313737 = r1313731 * r1313736;
        double r1313738 = exp(r1313737);
        double r1313739 = sqrt(r1313738);
        double r1313740 = r1313733 * r1313739;
        double r1313741 = r1313740 * r1313732;
        double r1313742 = sin(r1313741);
        return r1313742;
}

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-sqr-sqrt0.1

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

  8. Taylor expanded around inf 0.1

    \[\leadsto \sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot \left(\sqrt{{\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}} \cdot \color{blue}{\sqrt{{\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\frac{1}{4}}\right)}^{\left(b - a\right)}}}\right)\right)\]

  9. Simplified0.1

    \[\leadsto \sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot \left(\sqrt{{\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}} \cdot \color{blue}{\sqrt{e^{\left(\frac{1}{4} \cdot \log \left(\tan^{-1}_* \frac{b}{b}\right)\right) \cdot \left(b - a\right)}}}\right)\right)\]

  10. Final simplification0.1

    \[\leadsto \sin \left(\left(\sqrt{{\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}} \cdot \sqrt{e^{\left(b - a\right) \cdot \left(\log \left(\tan^{-1}_* \frac{b}{b}\right) \cdot \frac{1}{4}\right)}}\right) \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]

Reproduce

herbie shell --seed 2019146 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))