Average Error: 0.1 → 0.2
Time: 27.8s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left(\log \left(e^{{\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{b - a}{2}\right)} \cdot {\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{b - a}{2}\right)}}\right)\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left(\log \left(e^{{\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{b - a}{2}\right)} \cdot {\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{b - a}{2}\right)}}\right)\right)
double f(double a, double b) {
        double r18275 = b;
        double r18276 = atan2(r18275, r18275);
        double r18277 = sqrt(r18276);
        double r18278 = a;
        double r18279 = r18275 - r18278;
        double r18280 = pow(r18277, r18279);
        double r18281 = sin(r18280);
        return r18281;
}
↓
double f(double a, double b) {
        double r18282 = b;
        double r18283 = atan2(r18282, r18282);
        double r18284 = sqrt(r18283);
        double r18285 = a;
        double r18286 = r18282 - r18285;
        double r18287 = 2.0;
        double r18288 = r18286 / r18287;
        double r18289 = pow(r18284, r18288);
        double r18290 = r18289 * r18289;
        double r18291 = exp(r18290);
        double r18292 = log(r18291);
        double r18293 = sin(r18292);
        return r18293;
}

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-log-exp0.2

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

  5. Applied sqr-pow0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019235 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))