Average Error: 0.1 → 0.1
Time: 4.5s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)}^{1}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)}^{1}\right)
double f(double a, double b) {
        double r5281 = b;
        double r5282 = atan2(r5281, r5281);
        double r5283 = sqrt(r5282);
        double r5284 = a;
        double r5285 = r5281 - r5284;
        double r5286 = pow(r5283, r5285);
        double r5287 = sin(r5286);
        return r5287;
}
↓
double f(double a, double b) {
        double r5288 = b;
        double r5289 = atan2(r5288, r5288);
        double r5290 = sqrt(r5289);
        double r5291 = a;
        double r5292 = r5288 - r5291;
        double r5293 = pow(r5290, r5292);
        double r5294 = 1.0;
        double r5295 = pow(r5293, r5294);
        double r5296 = sin(r5295);
        return r5296;
}

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 pow10.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))