Average Error: 0.1 → 0.1
Time: 3.5s
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 r3686 = b;
        double r3687 = atan2(r3686, r3686);
        double r3688 = sqrt(r3687);
        double r3689 = a;
        double r3690 = r3686 - r3689;
        double r3691 = pow(r3688, r3690);
        double r3692 = sin(r3691);
        return r3692;
}
↓
double f(double a, double b) {
        double r3693 = b;
        double r3694 = atan2(r3693, r3693);
        double r3695 = sqrt(r3694);
        double r3696 = exp(r3695);
        double r3697 = log(r3696);
        double r3698 = a;
        double r3699 = r3693 - r3698;
        double r3700 = pow(r3697, r3699);
        double r3701 = sin(r3700);
        return r3701;
}

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 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))