Average Error: 0.1 → 0.1
Time: 3.4s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left(\mathsf{expm1}\left(\mathsf{log1p}\left({\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\frac{1}{2}} \cdot {\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\frac{1}{2}}\right)}^{\left(b - a\right)}\right)\right)\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left(\mathsf{expm1}\left(\mathsf{log1p}\left({\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\frac{1}{2}} \cdot {\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\frac{1}{2}}\right)}^{\left(b - a\right)}\right)\right)\right)
double f(double a, double b) {
        double r4268 = b;
        double r4269 = atan2(r4268, r4268);
        double r4270 = sqrt(r4269);
        double r4271 = a;
        double r4272 = r4268 - r4271;
        double r4273 = pow(r4270, r4272);
        double r4274 = sin(r4273);
        return r4274;
}
↓
double f(double a, double b) {
        double r4275 = b;
        double r4276 = atan2(r4275, r4275);
        double r4277 = sqrt(r4276);
        double r4278 = 0.5;
        double r4279 = pow(r4277, r4278);
        double r4280 = r4279 * r4279;
        double r4281 = a;
        double r4282 = r4275 - r4281;
        double r4283 = pow(r4280, r4282);
        double r4284 = log1p(r4283);
        double r4285 = expm1(r4284);
        double r4286 = sin(r4285);
        return r4286;
}

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 expm1-log1p-u0.1

    \[\leadsto \sin \color{blue}{\left(\mathsf{expm1}\left(\mathsf{log1p}\left({\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\frac{1}{2}} \cdot {\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\frac{1}{2}}\right)}^{\left(b - a\right)}\right)\right)\right)}\]

  9. Final simplification0.1

    \[\leadsto \sin \left(\mathsf{expm1}\left(\mathsf{log1p}\left({\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\frac{1}{2}} \cdot {\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\frac{1}{2}}\right)}^{\left(b - a\right)}\right)\right)\right)\]

Reproduce

herbie shell --seed 2020024 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))