Average Error: 0.1 → 0.1
Time: 27.8s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sqrt{\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)} \cdot \sqrt{\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)}\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sqrt{\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)} \cdot \sqrt{\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)}
double f(double a, double b) {
        double r22155 = b;
        double r22156 = atan2(r22155, r22155);
        double r22157 = sqrt(r22156);
        double r22158 = a;
        double r22159 = r22155 - r22158;
        double r22160 = pow(r22157, r22159);
        double r22161 = sin(r22160);
        return r22161;
}
↓
double f(double a, double b) {
        double r22162 = b;
        double r22163 = atan2(r22162, r22162);
        double r22164 = sqrt(r22163);
        double r22165 = a;
        double r22166 = r22162 - r22165;
        double r22167 = pow(r22164, r22166);
        double r22168 = sin(r22167);
        double r22169 = sqrt(r22168);
        double r22170 = r22169 * r22169;
        return r22170;
}

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 add-sqr-sqrt0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019306 
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))