Average Error: 0.1 → 0.1
Time: 4.6s
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 r17217 = b;
        double r17218 = atan2(r17217, r17217);
        double r17219 = sqrt(r17218);
        double r17220 = a;
        double r17221 = r17217 - r17220;
        double r17222 = pow(r17219, r17221);
        double r17223 = sin(r17222);
        return r17223;
}
↓
double f(double a, double b) {
        double r17224 = exp(1.0);
        double r17225 = b;
        double r17226 = atan2(r17225, r17225);
        double r17227 = 0.5;
        double r17228 = a;
        double r17229 = r17225 - r17228;
        double r17230 = r17227 * r17229;
        double r17231 = pow(r17226, r17230);
        double r17232 = sin(r17231);
        double r17233 = log(r17232);
        double r17234 = pow(r17224, r17233);
        return r17234;
}

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 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))