Average Error: 0.1 → 0.1
Time: 16.6s
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 r1534254 = b;
        double r1534255 = atan2(r1534254, r1534254);
        double r1534256 = sqrt(r1534255);
        double r1534257 = a;
        double r1534258 = r1534254 - r1534257;
        double r1534259 = pow(r1534256, r1534258);
        double r1534260 = sin(r1534259);
        return r1534260;
}
↓
double f(double a, double b) {
        double r1534261 = b;
        double r1534262 = atan2(r1534261, r1534261);
        double r1534263 = a;
        double r1534264 = r1534261 - r1534263;
        double r1534265 = 0.5;
        double r1534266 = r1534264 * r1534265;
        double r1534267 = pow(r1534262, r1534266);
        double r1534268 = sin(r1534267);
        return r1534268;
}

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