Average Error: 0.1 → 0.1
Time: 20.2s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left(\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\frac{b - a}{2}\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\frac{b - a}{2}\right)}\right) \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left(\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\frac{b - a}{2}\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\frac{b - a}{2}\right)}\right) \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)
double f(double a, double b) {
        double r1070292 = b;
        double r1070293 = atan2(r1070292, r1070292);
        double r1070294 = sqrt(r1070293);
        double r1070295 = a;
        double r1070296 = r1070292 - r1070295;
        double r1070297 = pow(r1070294, r1070296);
        double r1070298 = sin(r1070297);
        return r1070298;
}
↓
double f(double a, double b) {
        double r1070299 = b;
        double r1070300 = atan2(r1070299, r1070299);
        double r1070301 = sqrt(r1070300);
        double r1070302 = sqrt(r1070301);
        double r1070303 = a;
        double r1070304 = r1070299 - r1070303;
        double r1070305 = 2.0;
        double r1070306 = r1070304 / r1070305;
        double r1070307 = pow(r1070302, r1070306);
        double r1070308 = r1070307 * r1070307;
        double r1070309 = pow(r1070302, r1070304);
        double r1070310 = r1070308 * r1070309;
        double r1070311 = sin(r1070310);
        return r1070311;
}

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-sqr-sqrt0.1

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

  4. Applied sqrt-prod0.1

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

  5. Applied unpow-prod-down0.1

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

  7. Applied sqr-pow0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019153 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))