Average Error: 0.1 → 0.1
Time: 4.9s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left(e^{\log \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left(e^{\log \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)}\right)
double f(double a, double b) {
        double r8214 = b;
        double r8215 = atan2(r8214, r8214);
        double r8216 = sqrt(r8215);
        double r8217 = a;
        double r8218 = r8214 - r8217;
        double r8219 = pow(r8216, r8218);
        double r8220 = sin(r8219);
        return r8220;
}
↓
double f(double a, double b) {
        double r8221 = b;
        double r8222 = atan2(r8221, r8221);
        double r8223 = sqrt(r8222);
        double r8224 = a;
        double r8225 = r8221 - r8224;
        double r8226 = pow(r8223, r8225);
        double r8227 = log(r8226);
        double r8228 = exp(r8227);
        double r8229 = sin(r8228);
        return r8229;
}

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-exp-log0.1

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

  4. Applied pow-exp0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020039 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))