Average Error: 0.1 → 0.1
Time: 3.3s
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 r675 = b;
        double r676 = atan2(r675, r675);
        double r677 = sqrt(r676);
        double r678 = a;
        double r679 = r675 - r678;
        double r680 = pow(r677, r679);
        double r681 = sin(r680);
        return r681;
}
↓
double f(double a, double b) {
        double r682 = b;
        double r683 = atan2(r682, r682);
        double r684 = sqrt(r683);
        double r685 = a;
        double r686 = r682 - r685;
        double r687 = pow(r684, r686);
        double r688 = sin(r687);
        return r688;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020083 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))