Average Error: 0.1 → 0.1
Time: 19.9s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot e^{\log \left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right) \cdot \left(b - a\right)}\right)\]
\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(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right) \cdot \left(b - a\right)}\right)
double f(double a, double b) {
        double r24874 = b;
        double r24875 = atan2(r24874, r24874);
        double r24876 = sqrt(r24875);
        double r24877 = a;
        double r24878 = r24874 - r24877;
        double r24879 = pow(r24876, r24878);
        double r24880 = sin(r24879);
        return r24880;
}
↓
double f(double a, double b) {
        double r24881 = b;
        double r24882 = atan2(r24881, r24881);
        double r24883 = sqrt(r24882);
        double r24884 = sqrt(r24883);
        double r24885 = a;
        double r24886 = r24881 - r24885;
        double r24887 = pow(r24884, r24886);
        double r24888 = log(r24884);
        double r24889 = r24888 * r24886;
        double r24890 = exp(r24889);
        double r24891 = r24887 * r24890;
        double r24892 = sin(r24891);
        return r24892;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019347 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))