Average Error: 0.1 → 0.1
Time: 2.8s
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 r18139 = b;
        double r18140 = atan2(r18139, r18139);
        double r18141 = sqrt(r18140);
        double r18142 = a;
        double r18143 = r18139 - r18142;
        double r18144 = pow(r18141, r18143);
        double r18145 = sin(r18144);
        return r18145;
}
↓
double f(double a, double b) {
        double r18146 = b;
        double r18147 = atan2(r18146, r18146);
        double r18148 = sqrt(r18147);
        double r18149 = a;
        double r18150 = r18146 - r18149;
        double r18151 = pow(r18148, r18150);
        double r18152 = sin(r18151);
        return r18152;
}

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 2019353 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))