Average Error: 0.1 → 0.1
Time: 16.9s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}} \cdot \sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left(\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}} \cdot \sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)
double f(double a, double b) {
        double r19218 = b;
        double r19219 = atan2(r19218, r19218);
        double r19220 = sqrt(r19219);
        double r19221 = a;
        double r19222 = r19218 - r19221;
        double r19223 = pow(r19220, r19222);
        double r19224 = sin(r19223);
        return r19224;
}
↓
double f(double a, double b) {
        double r19225 = b;
        double r19226 = atan2(r19225, r19225);
        double r19227 = sqrt(r19226);
        double r19228 = cbrt(r19227);
        double r19229 = r19228 * r19228;
        double r19230 = a;
        double r19231 = r19225 - r19230;
        double r19232 = pow(r19229, r19231);
        double r19233 = pow(r19228, r19231);
        double r19234 = r19232 * r19233;
        double r19235 = sin(r19234);
        return r19235;
}

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-cube-cbrt0.1

    \[\leadsto \sin \left({\color{blue}{\left(\left(\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}} \cdot \sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right) \cdot \sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}}^{\left(b - a\right)}\right)\]

  4. Applied unpow-prod-down0.1

    \[\leadsto \sin \color{blue}{\left({\left(\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}} \cdot \sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)}\]

  5. Final simplification0.1

    \[\leadsto \sin \left({\left(\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}} \cdot \sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]

Reproduce

herbie shell --seed 2019179 
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  (sin (pow (sqrt (atan2 b b)) (- b a))))