Average Error: 0.1 → 0.1
Time: 4.2s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{b - a}{2}\right)} \cdot {\left(\left|\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right| \cdot \sqrt{\sqrt[3]{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\frac{b - a}{2}\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{b - a}{2}\right)} \cdot {\left(\left|\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right| \cdot \sqrt{\sqrt[3]{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\frac{b - a}{2}\right)}\right)
double f(double a, double b) {
        double r18962 = b;
        double r18963 = atan2(r18962, r18962);
        double r18964 = sqrt(r18963);
        double r18965 = a;
        double r18966 = r18962 - r18965;
        double r18967 = pow(r18964, r18966);
        double r18968 = sin(r18967);
        return r18968;
}
↓
double f(double a, double b) {
        double r18969 = b;
        double r18970 = atan2(r18969, r18969);
        double r18971 = sqrt(r18970);
        double r18972 = a;
        double r18973 = r18969 - r18972;
        double r18974 = 2.0;
        double r18975 = r18973 / r18974;
        double r18976 = pow(r18971, r18975);
        double r18977 = cbrt(r18970);
        double r18978 = fabs(r18977);
        double r18979 = sqrt(r18977);
        double r18980 = r18978 * r18979;
        double r18981 = pow(r18980, r18975);
        double r18982 = r18976 * r18981;
        double r18983 = sin(r18982);
        return r18983;
}

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 sqr-pow0.1

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

  5. Applied add-cube-cbrt0.1

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

  6. Applied sqrt-prod0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019354 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))