Average Error: 0.1 → 0.1
Time: 4.5s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[{e}^{\left(\log \left(\sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{2} \cdot \left(b - a\right)\right)}\right)\right)\right)}\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
{e}^{\left(\log \left(\sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{2} \cdot \left(b - a\right)\right)}\right)\right)\right)}
double f(double a, double b) {
        double r6367 = b;
        double r6368 = atan2(r6367, r6367);
        double r6369 = sqrt(r6368);
        double r6370 = a;
        double r6371 = r6367 - r6370;
        double r6372 = pow(r6369, r6371);
        double r6373 = sin(r6372);
        return r6373;
}
↓
double f(double a, double b) {
        double r6374 = exp(1.0);
        double r6375 = b;
        double r6376 = atan2(r6375, r6375);
        double r6377 = 0.5;
        double r6378 = a;
        double r6379 = r6375 - r6378;
        double r6380 = r6377 * r6379;
        double r6381 = pow(r6376, r6380);
        double r6382 = sin(r6381);
        double r6383 = log(r6382);
        double r6384 = pow(r6374, r6383);
        return r6384;
}

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 pow1/20.1

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

  4. Applied pow-pow0.1

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

  6. Applied add-exp-log0.1

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

  8. Applied pow10.1

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

  9. Applied log-pow0.1

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

  10. Applied exp-prod0.1

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

  11. Simplified0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019356 
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))