Average Error: 35.5 → 28.7
Time: 19.1s
Precision: 64
\[\frac{\tan \left(\frac{x}{y \cdot 2.0}\right)}{\sin \left(\frac{x}{y \cdot 2.0}\right)}\]
↓
\[1.0\]
\frac{\tan \left(\frac{x}{y \cdot 2.0}\right)}{\sin \left(\frac{x}{y \cdot 2.0}\right)}
↓
1.0
double f(double x, double y) {
        double r31976749 = x;
        double r31976750 = y;
        double r31976751 = 2.0;
        double r31976752 = r31976750 * r31976751;
        double r31976753 = r31976749 / r31976752;
        double r31976754 = tan(r31976753);
        double r31976755 = sin(r31976753);
        double r31976756 = r31976754 / r31976755;
        return r31976756;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y) {
        double r31976757 = 1.0;
        return r31976757;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original35.5
Target29.2
Herbie28.7
\[\begin{array}{l} \mathbf{if}\;y \lt -1.2303690911306994 \cdot 10^{+114}:\\ \;\;\;\;1.0\\ \mathbf{elif}\;y \lt -9.102852406811914 \cdot 10^{-222}:\\ \;\;\;\;\frac{\sin \left(\frac{x}{y \cdot 2.0}\right)}{\sin \left(\frac{x}{y \cdot 2.0}\right) \cdot \log \left(e^{\cos \left(\frac{x}{y \cdot 2.0}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1.0\\ \end{array}\]

Derivation

  1. Initial program 35.5

    \[\frac{\tan \left(\frac{x}{y \cdot 2.0}\right)}{\sin \left(\frac{x}{y \cdot 2.0}\right)}\]

  2. Taylor expanded around 0 28.7

    \[\leadsto \color{blue}{1.0}\]

  3. Final simplification28.7

    \[\leadsto 1.0\]

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.TwoD.Layout.CirclePacking:approxRadius from diagrams-contrib-1.3.0.5"

  :herbie-target
  (if (< y -1.2303690911306994e+114) 1.0 (if (< y -9.102852406811914e-222) (/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (log (exp (cos (/ x (* y 2.0))))))) 1.0))

  (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))