Average Error: 0.1 → 0.1
Time: 22.7s
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 r1414710 = b;
        double r1414711 = atan2(r1414710, r1414710);
        double r1414712 = sqrt(r1414711);
        double r1414713 = a;
        double r1414714 = r1414710 - r1414713;
        double r1414715 = pow(r1414712, r1414714);
        double r1414716 = sin(r1414715);
        return r1414716;
}
↓
double f(double a, double b) {
        double r1414717 = b;
        double r1414718 = atan2(r1414717, r1414717);
        double r1414719 = a;
        double r1414720 = r1414717 - r1414719;
        double r1414721 = 2.0;
        double r1414722 = r1414720 / r1414721;
        double r1414723 = r1414722 / r1414721;
        double r1414724 = pow(r1414718, r1414723);
        double r1414725 = r1414724 * r1414724;
        double r1414726 = sin(r1414725);
        return r1414726;
}

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