Average Error: 0.1 → 0.1
Time: 4.8s
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 r6801 = b;
        double r6802 = atan2(r6801, r6801);
        double r6803 = sqrt(r6802);
        double r6804 = a;
        double r6805 = r6801 - r6804;
        double r6806 = pow(r6803, r6805);
        double r6807 = sin(r6806);
        return r6807;
}
↓
double f(double a, double b) {
        double r6808 = exp(1.0);
        double r6809 = b;
        double r6810 = atan2(r6809, r6809);
        double r6811 = 0.5;
        double r6812 = a;
        double r6813 = r6809 - r6812;
        double r6814 = r6811 * r6813;
        double r6815 = pow(r6810, r6814);
        double r6816 = sin(r6815);
        double r6817 = log(r6816);
        double r6818 = pow(r6808, r6817);
        return r6818;
}

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 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))