Average Error: 0.1 → 0.1
Time: 20.8s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\frac{b - a}{2}}{2}\right)} \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\frac{b - a}{2}}{2}\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\frac{b - a}{2}}{2}\right)} \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\frac{b - a}{2}}{2}\right)}\right)
double f(double a, double b) {
        double r2821427 = b;
        double r2821428 = atan2(r2821427, r2821427);
        double r2821429 = sqrt(r2821428);
        double r2821430 = a;
        double r2821431 = r2821427 - r2821430;
        double r2821432 = pow(r2821429, r2821431);
        double r2821433 = sin(r2821432);
        return r2821433;
}
↓
double f(double a, double b) {
        double r2821434 = b;
        double r2821435 = atan2(r2821434, r2821434);
        double r2821436 = a;
        double r2821437 = r2821434 - r2821436;
        double r2821438 = 2.0;
        double r2821439 = r2821437 / r2821438;
        double r2821440 = r2821439 / r2821438;
        double r2821441 = pow(r2821435, r2821440);
        double r2821442 = r2821441 * r2821441;
        double r2821443 = sin(r2821442);
        return r2821443;
}

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. Using strategy rm

  3. Applied sqrt-pow20.1

    \[\leadsto \sin \color{blue}{\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{b - a}{2}\right)}\right)}\]
  4. Using strategy rm

  5. Applied sqr-pow0.1

    \[\leadsto \sin \color{blue}{\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\frac{b - a}{2}}{2}\right)} \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\frac{b - a}{2}}{2}\right)}\right)}\]

  6. Final simplification0.1

    \[\leadsto \sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\frac{b - a}{2}}{2}\right)} \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\frac{b - a}{2}}{2}\right)}\right)\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))