Average Error: 0.1 → 0.1
Time: 4.6s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\frac{1}{2}}\right)}^{\left(2 \cdot \left(b - a\right)\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\frac{1}{2}}\right)}^{\left(2 \cdot \left(b - a\right)\right)}\right)
double f(double a, double b) {
        double r17487 = b;
        double r17488 = atan2(r17487, r17487);
        double r17489 = sqrt(r17488);
        double r17490 = a;
        double r17491 = r17487 - r17490;
        double r17492 = pow(r17489, r17491);
        double r17493 = sin(r17492);
        return r17493;
}
↓
double f(double a, double b) {
        double r17494 = b;
        double r17495 = atan2(r17494, r17494);
        double r17496 = sqrt(r17495);
        double r17497 = 0.5;
        double r17498 = pow(r17496, r17497);
        double r17499 = 2.0;
        double r17500 = a;
        double r17501 = r17494 - r17500;
        double r17502 = r17499 * r17501;
        double r17503 = pow(r17498, r17502);
        double r17504 = sin(r17503);
        return r17504;
}

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. Simplified0.1

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

  6. Simplified0.1

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

  8. Applied pow20.1

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

  9. Applied pow-pow0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019352 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))