Average Error: 0.1 → 0.1
Time: 23.4s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{b - a}{2}\right)} \cdot {\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{b - a}{2}\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{b - a}{2}\right)} \cdot {\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{b - a}{2}\right)}\right)
double f(double a, double b) {
        double r17263 = b;
        double r17264 = atan2(r17263, r17263);
        double r17265 = sqrt(r17264);
        double r17266 = a;
        double r17267 = r17263 - r17266;
        double r17268 = pow(r17265, r17267);
        double r17269 = sin(r17268);
        return r17269;
}
↓
double f(double a, double b) {
        double r17270 = b;
        double r17271 = atan2(r17270, r17270);
        double r17272 = sqrt(r17271);
        double r17273 = a;
        double r17274 = r17270 - r17273;
        double r17275 = 2.0;
        double r17276 = r17274 / r17275;
        double r17277 = pow(r17272, r17276);
        double r17278 = r17277 * r17277;
        double r17279 = sin(r17278);
        return r17279;
}

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 sqr-pow0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  (sin (pow (sqrt (atan2 b b)) (- b a))))