Average Error: 0.1 → 0.1
Time: 3.9s
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 r13716 = b;
        double r13717 = atan2(r13716, r13716);
        double r13718 = sqrt(r13717);
        double r13719 = a;
        double r13720 = r13716 - r13719;
        double r13721 = pow(r13718, r13720);
        double r13722 = sin(r13721);
        return r13722;
}
↓
double f(double a, double b) {
        double r13723 = b;
        double r13724 = atan2(r13723, r13723);
        double r13725 = sqrt(r13724);
        double r13726 = a;
        double r13727 = r13723 - r13726;
        double r13728 = pow(r13725, r13727);
        double r13729 = sin(r13728);
        return r13729;
}

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 2020034 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))