Average Error: 0.2 → 0.2
Time: 3.7s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
\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)
double f(double a, double b) {
        double r9187 = b;
        double r9188 = atan2(r9187, r9187);
        double r9189 = sqrt(r9188);
        double r9190 = a;
        double r9191 = r9187 - r9190;
        double r9192 = pow(r9189, r9191);
        double r9193 = sin(r9192);
        return r9193;
}
↓
double f(double a, double b) {
        double r9194 = b;
        double r9195 = atan2(r9194, r9194);
        double r9196 = sqrt(r9195);
        double r9197 = a;
        double r9198 = r9194 - r9197;
        double r9199 = pow(r9196, r9198);
        double r9200 = sin(r9199);
        return r9200;
}

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 0.2

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

  2. Final simplification0.2

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

Reproduce

herbie shell --seed 2020100 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))