Average Error: 0.1 → 0.1
Time: 25.9s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\frac{b - a}{2}}{2}\right)} \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\frac{b - a}{2}}{2}\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\frac{b - a}{2}}{2}\right)} \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\frac{b - a}{2}}{2}\right)}\right)
double f(double a, double b) {
        double r1328478 = b;
        double r1328479 = atan2(r1328478, r1328478);
        double r1328480 = sqrt(r1328479);
        double r1328481 = a;
        double r1328482 = r1328478 - r1328481;
        double r1328483 = pow(r1328480, r1328482);
        double r1328484 = sin(r1328483);
        return r1328484;
}
↓
double f(double a, double b) {
        double r1328485 = b;
        double r1328486 = atan2(r1328485, r1328485);
        double r1328487 = a;
        double r1328488 = r1328485 - r1328487;
        double r1328489 = 2.0;
        double r1328490 = r1328488 / r1328489;
        double r1328491 = r1328490 / r1328489;
        double r1328492 = pow(r1328486, r1328491);
        double r1328493 = r1328492 * r1328492;
        double r1328494 = sin(r1328493);
        return r1328494;
}

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 sqrt-pow20.1

    \[\leadsto \sin \color{blue}{\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{b - a}{2}\right)}\right)}\]
  4. Using strategy rm

  5. Applied sqr-pow0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  (sin (pow (sqrt (atan2 b b)) (- b a))))