Average Error: 0.1 → 0.1
Time: 20.8s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)}\right)\]
\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(\left(b - a\right) \cdot \frac{1}{2}\right)}\right)
double f(double a, double b) {
        double r1254880 = b;
        double r1254881 = atan2(r1254880, r1254880);
        double r1254882 = sqrt(r1254881);
        double r1254883 = a;
        double r1254884 = r1254880 - r1254883;
        double r1254885 = pow(r1254882, r1254884);
        double r1254886 = sin(r1254885);
        return r1254886;
}
↓
double f(double a, double b) {
        double r1254887 = b;
        double r1254888 = atan2(r1254887, r1254887);
        double r1254889 = a;
        double r1254890 = r1254887 - r1254889;
        double r1254891 = 0.5;
        double r1254892 = r1254890 * r1254891;
        double r1254893 = pow(r1254888, r1254892);
        double r1254894 = sin(r1254893);
        return r1254894;
}

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 pow1/20.1

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

  4. Applied pow-pow0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  (sin (pow (sqrt (atan2 b b)) (- b a))))