Average Error: 0.1 → 0.1
Time: 4.6s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot e^{\log \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot e^{\log \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)}\right)
double f(double a, double b) {
        double r20888 = b;
        double r20889 = atan2(r20888, r20888);
        double r20890 = sqrt(r20889);
        double r20891 = a;
        double r20892 = r20888 - r20891;
        double r20893 = pow(r20890, r20892);
        double r20894 = sin(r20893);
        return r20894;
}
↓
double f(double a, double b) {
        double r20895 = b;
        double r20896 = atan2(r20895, r20895);
        double r20897 = sqrt(r20896);
        double r20898 = sqrt(r20897);
        double r20899 = a;
        double r20900 = r20895 - r20899;
        double r20901 = pow(r20898, r20900);
        double r20902 = log(r20901);
        double r20903 = exp(r20902);
        double r20904 = r20901 * r20903;
        double r20905 = sin(r20904);
        return r20905;
}

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-sqr-sqrt0.1

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

  4. Applied sqrt-prod0.1

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

  5. Applied unpow-prod-down0.1

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

  7. Applied add-exp-log0.1

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

  8. Applied pow-exp0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020056 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))