Average Error: 0.1 → 0.1
Time: 21.8s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\frac{b - a}{2}}{2}\right)} \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\frac{b - a}{2}}{2}\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\frac{b - a}{2}}{2}\right)} \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\frac{b - a}{2}}{2}\right)}\right)
double f(double a, double b) {
        double r2741055 = b;
        double r2741056 = atan2(r2741055, r2741055);
        double r2741057 = sqrt(r2741056);
        double r2741058 = a;
        double r2741059 = r2741055 - r2741058;
        double r2741060 = pow(r2741057, r2741059);
        double r2741061 = sin(r2741060);
        return r2741061;
}
↓
double f(double a, double b) {
        double r2741062 = b;
        double r2741063 = atan2(r2741062, r2741062);
        double r2741064 = a;
        double r2741065 = r2741062 - r2741064;
        double r2741066 = 2.0;
        double r2741067 = r2741065 / r2741066;
        double r2741068 = r2741067 / r2741066;
        double r2741069 = pow(r2741063, r2741068);
        double r2741070 = r2741069 * r2741069;
        double r2741071 = sin(r2741070);
        return r2741071;
}

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 sqrt-pow20.1

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

  5. Applied sqr-pow0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))