Average Error: 0.1 → 0.1
Time: 22.4s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{b - a}{2}\right)} \cdot {\left(\left|\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right|\right)}^{\left(b - a\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{b - a}{2}\right)} \cdot {\left(\left|\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right|\right)}^{\left(b - a\right)}\right)
double f(double a, double b) {
        double r1375290 = b;
        double r1375291 = atan2(r1375290, r1375290);
        double r1375292 = sqrt(r1375291);
        double r1375293 = a;
        double r1375294 = r1375290 - r1375293;
        double r1375295 = pow(r1375292, r1375294);
        double r1375296 = sin(r1375295);
        return r1375296;
}
↓
double f(double a, double b) {
        double r1375297 = b;
        double r1375298 = atan2(r1375297, r1375297);
        double r1375299 = cbrt(r1375298);
        double r1375300 = a;
        double r1375301 = r1375297 - r1375300;
        double r1375302 = 2.0;
        double r1375303 = r1375301 / r1375302;
        double r1375304 = pow(r1375299, r1375303);
        double r1375305 = fabs(r1375299);
        double r1375306 = pow(r1375305, r1375301);
        double r1375307 = r1375304 * r1375306;
        double r1375308 = sin(r1375307);
        return r1375308;
}

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-cube-cbrt0.1

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

  4. Applied sqrt-prod0.1

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

  5. Applied unpow-prod-down0.1

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

  6. Simplified0.1

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

  8. Applied pow10.1

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

  9. Applied sqrt-pow10.1

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

  10. Applied pow-pow0.1

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

  11. Simplified0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  (sin (pow (sqrt (atan2 b b)) (- b a))))