Average Error: 35.9 → 28.6
Time: 25.7s
Precision: 64
\[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\]
↓
\[1\]
\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}
↓
1
double f(double x, double y) {
        double r451215 = x;
        double r451216 = y;
        double r451217 = 2.0;
        double r451218 = r451216 * r451217;
        double r451219 = r451215 / r451218;
        double r451220 = tan(r451219);
        double r451221 = sin(r451219);
        double r451222 = r451220 / r451221;
        return r451222;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y) {
        double r451223 = 1.0;
        return r451223;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original35.9
Target29.1
Herbie28.6
\[\begin{array}{l} \mathbf{if}\;y \lt -1.230369091130699363447511617672816900781 \cdot 10^{114}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \lt -9.102852406811913849731222630299032206502 \cdot 10^{-222}:\\ \;\;\;\;\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right) \cdot \log \left(e^{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]

Derivation

  1. Initial program 35.9

    \[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\]

  2. Taylor expanded around 0 28.6

    \[\leadsto \color{blue}{1}\]

  3. Final simplification28.6

    \[\leadsto 1\]

Reproduce

herbie shell --seed 2019304 
(FPCore (x y)
  :name "Diagrams.TwoD.Layout.CirclePacking:approxRadius from diagrams-contrib-1.3.0.5"
  :precision binary64

  :herbie-target
  (if (< y -1.23036909113069936e114) 1 (if (< y -9.1028524068119138e-222) (/ (sin (/ x (* y 2))) (* (sin (/ x (* y 2))) (log (exp (cos (/ x (* y 2))))))) 1))

  (/ (tan (/ x (* y 2))) (sin (/ x (* y 2)))))