Average Error: 0.1 → 0.1
Time: 21.0s
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 r1520087 = b;
        double r1520088 = atan2(r1520087, r1520087);
        double r1520089 = sqrt(r1520088);
        double r1520090 = a;
        double r1520091 = r1520087 - r1520090;
        double r1520092 = pow(r1520089, r1520091);
        double r1520093 = sin(r1520092);
        return r1520093;
}
↓
double f(double a, double b) {
        double r1520094 = b;
        double r1520095 = atan2(r1520094, r1520094);
        double r1520096 = cbrt(r1520095);
        double r1520097 = a;
        double r1520098 = r1520094 - r1520097;
        double r1520099 = 2.0;
        double r1520100 = r1520098 / r1520099;
        double r1520101 = pow(r1520096, r1520100);
        double r1520102 = fabs(r1520096);
        double r1520103 = pow(r1520102, r1520098);
        double r1520104 = r1520101 * r1520103;
        double r1520105 = sin(r1520104);
        return r1520105;
}

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 
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  (sin (pow (sqrt (atan2 b b)) (- b a))))