Average Error: 0.1 → 0.1
Time: 15.9s
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 r7446 = b;
        double r7447 = atan2(r7446, r7446);
        double r7448 = sqrt(r7447);
        double r7449 = a;
        double r7450 = r7446 - r7449;
        double r7451 = pow(r7448, r7450);
        double r7452 = sin(r7451);
        return r7452;
}
↓
double f(double a, double b) {
        double r7453 = b;
        double r7454 = atan2(r7453, r7453);
        double r7455 = sqrt(r7454);
        double r7456 = a;
        double r7457 = r7453 - r7456;
        double r7458 = pow(r7455, r7457);
        double r7459 = sin(r7458);
        double r7460 = sqrt(r7459);
        double r7461 = r7460 * r7460;
        return r7461;
}

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 2020044 
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))