Average Error: 0.1 → 0.1
Time: 26.7s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sqrt{\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)} \cdot \sqrt{\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)}\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sqrt{\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)} \cdot \sqrt{\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)}
double f(double a, double b) {
        double r22259 = b;
        double r22260 = atan2(r22259, r22259);
        double r22261 = sqrt(r22260);
        double r22262 = a;
        double r22263 = r22259 - r22262;
        double r22264 = pow(r22261, r22263);
        double r22265 = sin(r22264);
        return r22265;
}
↓
double f(double a, double b) {
        double r22266 = b;
        double r22267 = atan2(r22266, r22266);
        double r22268 = sqrt(r22267);
        double r22269 = a;
        double r22270 = r22266 - r22269;
        double r22271 = pow(r22268, r22270);
        double r22272 = sin(r22271);
        double r22273 = sqrt(r22272);
        double r22274 = r22273 * r22273;
        return r22274;
}

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 add-sqr-sqrt0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019306 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))