Average Error: 0.1 → 0.1
Time: 23.6s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\left(b - a\right) \cdot \frac{1}{2}}{2}\right)} \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\left(b - a\right) \cdot \frac{1}{2}}{2}\right)}\right)\]
\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{\left(b - a\right) \cdot \frac{1}{2}}{2}\right)} \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\left(b - a\right) \cdot \frac{1}{2}}{2}\right)}\right)
double f(double a, double b) {
        double r2579600 = b;
        double r2579601 = atan2(r2579600, r2579600);
        double r2579602 = sqrt(r2579601);
        double r2579603 = a;
        double r2579604 = r2579600 - r2579603;
        double r2579605 = pow(r2579602, r2579604);
        double r2579606 = sin(r2579605);
        return r2579606;
}
↓
double f(double a, double b) {
        double r2579607 = b;
        double r2579608 = atan2(r2579607, r2579607);
        double r2579609 = a;
        double r2579610 = r2579607 - r2579609;
        double r2579611 = 0.5;
        double r2579612 = r2579610 * r2579611;
        double r2579613 = 2.0;
        double r2579614 = r2579612 / r2579613;
        double r2579615 = pow(r2579608, r2579614);
        double r2579616 = r2579615 * r2579615;
        double r2579617 = sin(r2579616);
        return r2579617;
}

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. Using strategy rm

  6. Applied sqr-pow0.1

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

  7. Final simplification0.1

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

Reproduce

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