Average Error: 0.1 → 0.1
Time: 3.9s
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 r17590 = b;
        double r17591 = atan2(r17590, r17590);
        double r17592 = sqrt(r17591);
        double r17593 = a;
        double r17594 = r17590 - r17593;
        double r17595 = pow(r17592, r17594);
        double r17596 = sin(r17595);
        return r17596;
}
↓
double f(double a, double b) {
        double r17597 = b;
        double r17598 = atan2(r17597, r17597);
        double r17599 = sqrt(r17598);
        double r17600 = 0.5;
        double r17601 = pow(r17599, r17600);
        double r17602 = 2.0;
        double r17603 = a;
        double r17604 = r17597 - r17603;
        double r17605 = r17602 * r17604;
        double r17606 = pow(r17601, r17605);
        double r17607 = sin(r17606);
        return r17607;
}

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 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))