Average Error: 0.1 → 0.1
Time: 15.2s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)} \cdot {\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)} \cdot {\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)}\right)
double f(double a, double b) {
        double r28002 = b;
        double r28003 = atan2(r28002, r28002);
        double r28004 = sqrt(r28003);
        double r28005 = a;
        double r28006 = r28002 - r28005;
        double r28007 = pow(r28004, r28006);
        double r28008 = sin(r28007);
        return r28008;
}
↓
double f(double a, double b) {
        double r28009 = b;
        double r28010 = atan2(r28009, r28009);
        double r28011 = cbrt(r28010);
        double r28012 = a;
        double r28013 = r28009 - r28012;
        double r28014 = 0.5;
        double r28015 = r28013 * r28014;
        double r28016 = pow(r28011, r28015);
        double r28017 = r28011 * r28011;
        double r28018 = pow(r28017, r28015);
        double r28019 = r28016 * r28018;
        double r28020 = sin(r28019);
        return r28020;
}

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 pow1/20.1

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

  4. Applied pow-pow0.1

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

  5. Simplified0.1

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

  7. Applied add-cube-cbrt0.1

    \[\leadsto \sin \left({\color{blue}{\left(\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right) \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}}^{\left(\frac{b - a}{2}\right)}\right)\]

  8. Applied unpow-prod-down0.1

    \[\leadsto \sin \color{blue}{\left({\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{b - a}{2}\right)} \cdot {\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{b - a}{2}\right)}\right)}\]

  9. Simplified0.1

    \[\leadsto \sin \left(\color{blue}{{\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)}} \cdot {\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{b - a}{2}\right)}\right)\]

  10. Simplified0.1

    \[\leadsto \sin \left({\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)} \cdot \color{blue}{{\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)}}\right)\]

  11. Final simplification0.1

    \[\leadsto \sin \left({\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)} \cdot {\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)}\right)\]

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))