Average Error: 0.1 → 0.1
Time: 3.4s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\log \left(e^{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)\right)}^{\left(b - a\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left(\log \left(e^{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)\right)}^{\left(b - a\right)}\right)
double f(double a, double b) {
        double r19223 = b;
        double r19224 = atan2(r19223, r19223);
        double r19225 = sqrt(r19224);
        double r19226 = a;
        double r19227 = r19223 - r19226;
        double r19228 = pow(r19225, r19227);
        double r19229 = sin(r19228);
        return r19229;
}
↓
double f(double a, double b) {
        double r19230 = b;
        double r19231 = atan2(r19230, r19230);
        double r19232 = sqrt(r19231);
        double r19233 = exp(r19232);
        double r19234 = log(r19233);
        double r19235 = a;
        double r19236 = r19230 - r19235;
        double r19237 = pow(r19234, r19236);
        double r19238 = sin(r19237);
        return r19238;
}

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-log-exp0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020060 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))