Average Error: 0.1 → 0.1
Time: 21.5s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}} \cdot \sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}} \cdot \sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)
double f(double a, double b) {
        double r786157 = b;
        double r786158 = atan2(r786157, r786157);
        double r786159 = sqrt(r786158);
        double r786160 = a;
        double r786161 = r786157 - r786160;
        double r786162 = pow(r786159, r786161);
        double r786163 = sin(r786162);
        return r786163;
}
↓
double f(double a, double b) {
        double r786164 = b;
        double r786165 = atan2(r786164, r786164);
        double r786166 = sqrt(r786165);
        double r786167 = sqrt(r786166);
        double r786168 = r786167 * r786167;
        double r786169 = a;
        double r786170 = r786164 - r786169;
        double r786171 = pow(r786168, r786170);
        double r786172 = sin(r786171);
        return r786172;
}

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

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019143 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))