Average Error: 0.1 → 0.2
Time: 21.2s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left(\log \left(\sqrt{e^{{\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}}}\right) + \log \left(\sqrt{e^{{\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}}}\right)\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left(\log \left(\sqrt{e^{{\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}}}\right) + \log \left(\sqrt{e^{{\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}}}\right)\right)
double f(double a, double b) {
        double r2253194 = b;
        double r2253195 = atan2(r2253194, r2253194);
        double r2253196 = sqrt(r2253195);
        double r2253197 = a;
        double r2253198 = r2253194 - r2253197;
        double r2253199 = pow(r2253196, r2253198);
        double r2253200 = sin(r2253199);
        return r2253200;
}
↓
double f(double a, double b) {
        double r2253201 = b;
        double r2253202 = atan2(r2253201, r2253201);
        double r2253203 = sqrt(r2253202);
        double r2253204 = a;
        double r2253205 = r2253201 - r2253204;
        double r2253206 = pow(r2253203, r2253205);
        double r2253207 = exp(r2253206);
        double r2253208 = sqrt(r2253207);
        double r2253209 = log(r2253208);
        double r2253210 = r2253209 + r2253209;
        double r2253211 = sin(r2253210);
        return r2253211;
}

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 add-sqr-sqrt0.2

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

  6. Applied log-prod0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019192 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))