Average Error: 0.1 → 0.1
Time: 18.6s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{\sqrt[3]{2} \cdot \sqrt[3]{2}}\right)}\right)}^{\left(\frac{b - a}{\sqrt[3]{2}}\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{\sqrt[3]{2} \cdot \sqrt[3]{2}}\right)}\right)}^{\left(\frac{b - a}{\sqrt[3]{2}}\right)}\right)
double f(double a, double b) {
        double r1195882 = b;
        double r1195883 = atan2(r1195882, r1195882);
        double r1195884 = sqrt(r1195883);
        double r1195885 = a;
        double r1195886 = r1195882 - r1195885;
        double r1195887 = pow(r1195884, r1195886);
        double r1195888 = sin(r1195887);
        return r1195888;
}
↓
double f(double a, double b) {
        double r1195889 = b;
        double r1195890 = atan2(r1195889, r1195889);
        double r1195891 = 1.0;
        double r1195892 = 2.0;
        double r1195893 = cbrt(r1195892);
        double r1195894 = r1195893 * r1195893;
        double r1195895 = r1195891 / r1195894;
        double r1195896 = pow(r1195890, r1195895);
        double r1195897 = a;
        double r1195898 = r1195889 - r1195897;
        double r1195899 = r1195898 / r1195893;
        double r1195900 = pow(r1195896, r1195899);
        double r1195901 = sin(r1195900);
        return r1195901;
}

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 pow10.1

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

  4. Applied sqrt-pow10.1

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

  5. Applied pow-pow0.1

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

  6. Simplified0.1

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

  8. Applied add-cube-cbrt0.1

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

  9. Applied *-un-lft-identity0.1

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

  10. Applied times-frac0.1

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

  11. Applied pow-unpow0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  (sin (pow (sqrt (atan2 b b)) (- b a))))