Average Error: 0.1 → 0.1
Time: 30.2s
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 r20205 = b;
        double r20206 = atan2(r20205, r20205);
        double r20207 = sqrt(r20206);
        double r20208 = a;
        double r20209 = r20205 - r20208;
        double r20210 = pow(r20207, r20209);
        double r20211 = sin(r20210);
        return r20211;
}
↓
double f(double a, double b) {
        double r20212 = b;
        double r20213 = atan2(r20212, r20212);
        double r20214 = sqrt(r20213);
        double r20215 = a;
        double r20216 = r20212 - r20215;
        double r20217 = pow(r20214, r20216);
        double r20218 = sin(r20217);
        double r20219 = sqrt(r20218);
        double r20220 = r20219 * r20219;
        return r20220;
}

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 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))