Average Error: 0.1 → 0.1
Time: 4.3s
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 r16165 = b;
        double r16166 = atan2(r16165, r16165);
        double r16167 = sqrt(r16166);
        double r16168 = a;
        double r16169 = r16165 - r16168;
        double r16170 = pow(r16167, r16169);
        double r16171 = sin(r16170);
        return r16171;
}
↓
double f(double a, double b) {
        double r16172 = exp(1.0);
        double r16173 = b;
        double r16174 = atan2(r16173, r16173);
        double r16175 = 0.5;
        double r16176 = a;
        double r16177 = r16173 - r16176;
        double r16178 = r16175 * r16177;
        double r16179 = pow(r16174, r16178);
        double r16180 = sin(r16179);
        double r16181 = log(r16180);
        double r16182 = pow(r16172, r16181);
        return r16182;
}

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 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))