Average Error: 0.1 → 0.1
Time: 2.8s
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 r16999 = b;
        double r17000 = atan2(r16999, r16999);
        double r17001 = sqrt(r17000);
        double r17002 = a;
        double r17003 = r16999 - r17002;
        double r17004 = pow(r17001, r17003);
        double r17005 = sin(r17004);
        return r17005;
}
↓
double f(double a, double b) {
        double r17006 = b;
        double r17007 = atan2(r17006, r17006);
        double r17008 = sqrt(r17007);
        double r17009 = exp(r17008);
        double r17010 = log(r17009);
        double r17011 = a;
        double r17012 = r17006 - r17011;
        double r17013 = pow(r17010, r17012);
        double r17014 = sin(r17013);
        return r17014;
}

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 2020024 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))