Average Error: 0.1 → 0.1
Time: 3.9s
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 r3772 = b;
        double r3773 = atan2(r3772, r3772);
        double r3774 = sqrt(r3773);
        double r3775 = a;
        double r3776 = r3772 - r3775;
        double r3777 = pow(r3774, r3776);
        double r3778 = sin(r3777);
        return r3778;
}
↓
double f(double a, double b) {
        double r3779 = b;
        double r3780 = atan2(r3779, r3779);
        double r3781 = sqrt(r3780);
        double r3782 = exp(r3781);
        double r3783 = log(r3782);
        double r3784 = a;
        double r3785 = r3779 - r3784;
        double r3786 = pow(r3783, r3785);
        double r3787 = sin(r3786);
        return r3787;
}

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 2020060 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))