Average Error: 0.1 → 0.1
Time: 3.2s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\log \left(e^{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)\right)}^{\left(b - a\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left(\log \left(e^{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)\right)}^{\left(b - a\right)}\right)
double f(double a, double b) {
        double r11959 = b;
        double r11960 = atan2(r11959, r11959);
        double r11961 = sqrt(r11960);
        double r11962 = a;
        double r11963 = r11959 - r11962;
        double r11964 = pow(r11961, r11963);
        double r11965 = sin(r11964);
        return r11965;
}
↓
double f(double a, double b) {
        double r11966 = b;
        double r11967 = atan2(r11966, r11966);
        double r11968 = sqrt(r11967);
        double r11969 = exp(r11968);
        double r11970 = log(r11969);
        double r11971 = a;
        double r11972 = r11966 - r11971;
        double r11973 = pow(r11970, r11972);
        double r11974 = sin(r11973);
        return r11974;
}

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-log-exp0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020021 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))