Average Error: 0.1 → 0.1
Time: 28.3s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sqrt{\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)} \cdot \sqrt{\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)}\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sqrt{\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)} \cdot \sqrt{\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)}
double f(double a, double b) {
        double r21688 = b;
        double r21689 = atan2(r21688, r21688);
        double r21690 = sqrt(r21689);
        double r21691 = a;
        double r21692 = r21688 - r21691;
        double r21693 = pow(r21690, r21692);
        double r21694 = sin(r21693);
        return r21694;
}
↓
double f(double a, double b) {
        double r21695 = b;
        double r21696 = atan2(r21695, r21695);
        double r21697 = sqrt(r21696);
        double r21698 = a;
        double r21699 = r21695 - r21698;
        double r21700 = pow(r21697, r21699);
        double r21701 = sin(r21700);
        double r21702 = sqrt(r21701);
        double r21703 = r21702 * r21702;
        return r21703;
}

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

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))