Average Error: 0.1 → 0.1
Time: 5.3s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{2} \cdot \left(b - a\right)\right)}\right)\]
\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{1}{2} \cdot \left(b - a\right)\right)}\right)
double f(double a, double b) {
        double r9809 = b;
        double r9810 = atan2(r9809, r9809);
        double r9811 = sqrt(r9810);
        double r9812 = a;
        double r9813 = r9809 - r9812;
        double r9814 = pow(r9811, r9813);
        double r9815 = sin(r9814);
        return r9815;
}
↓
double f(double a, double b) {
        double r9816 = b;
        double r9817 = atan2(r9816, r9816);
        double r9818 = 0.5;
        double r9819 = a;
        double r9820 = r9816 - r9819;
        double r9821 = r9818 * r9820;
        double r9822 = pow(r9817, r9821);
        double r9823 = sin(r9822);
        return r9823;
}

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

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

Reproduce

herbie shell --seed 2019352 
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))