Average Error: 0.1 → 0.1
Time: 5.4s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[e^{\log \left(\sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(2 \cdot \left(b - a\right)\right)}\right)\right)}\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
e^{\log \left(\sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(2 \cdot \left(b - a\right)\right)}\right)\right)}
double f(double a, double b) {
        double r7354 = b;
        double r7355 = atan2(r7354, r7354);
        double r7356 = sqrt(r7355);
        double r7357 = a;
        double r7358 = r7354 - r7357;
        double r7359 = pow(r7356, r7358);
        double r7360 = sin(r7359);
        return r7360;
}
↓
double f(double a, double b) {
        double r7361 = b;
        double r7362 = atan2(r7361, r7361);
        double r7363 = sqrt(r7362);
        double r7364 = sqrt(r7363);
        double r7365 = 2.0;
        double r7366 = a;
        double r7367 = r7361 - r7366;
        double r7368 = r7365 * r7367;
        double r7369 = pow(r7364, r7368);
        double r7370 = sin(r7369);
        double r7371 = log(r7370);
        double r7372 = exp(r7371);
        return r7372;
}

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-exp-log0.1

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

  5. Applied add-sqr-sqrt0.1

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

  6. Applied sqrt-prod0.1

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

  7. Applied unpow-prod-down0.1

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

  9. Applied pow-prod-up0.1

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2020033 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))