Average Error: 0.1 → 0.1
Time: 2.7s
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 r18147 = b;
        double r18148 = atan2(r18147, r18147);
        double r18149 = sqrt(r18148);
        double r18150 = a;
        double r18151 = r18147 - r18150;
        double r18152 = pow(r18149, r18151);
        double r18153 = sin(r18152);
        return r18153;
}
↓
double f(double a, double b) {
        double r18154 = b;
        double r18155 = atan2(r18154, r18154);
        double r18156 = sqrt(r18155);
        double r18157 = a;
        double r18158 = r18154 - r18157;
        double r18159 = pow(r18156, r18158);
        double r18160 = sin(r18159);
        return r18160;
}

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))))