Average Error: 0.2 → 0.2
Time: 3.7s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(2 \cdot \left(b - a\right)\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(2 \cdot \left(b - a\right)\right)}\right)
double f(double a, double b) {
        double r10301 = b;
        double r10302 = atan2(r10301, r10301);
        double r10303 = sqrt(r10302);
        double r10304 = a;
        double r10305 = r10301 - r10304;
        double r10306 = pow(r10303, r10305);
        double r10307 = sin(r10306);
        return r10307;
}
↓
double f(double a, double b) {
        double r10308 = b;
        double r10309 = atan2(r10308, r10308);
        double r10310 = sqrt(r10309);
        double r10311 = sqrt(r10310);
        double r10312 = 2.0;
        double r10313 = a;
        double r10314 = r10308 - r10313;
        double r10315 = r10312 * r10314;
        double r10316 = pow(r10311, r10315);
        double r10317 = sin(r10316);
        return r10317;
}

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 0.2

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

  3. Applied add-sqr-sqrt0.2

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

  4. Applied sqrt-prod0.2

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

  5. Applied unpow-prod-down0.2

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

  7. Applied pow-prod-up0.2

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

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020002 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))