Average Error: 35.1 → 28.0
Time: 18.5s
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 r31393554 = x;
        double r31393555 = y;
        double r31393556 = 2.0;
        double r31393557 = r31393555 * r31393556;
        double r31393558 = r31393554 / r31393557;
        double r31393559 = tan(r31393558);
        double r31393560 = sin(r31393558);
        double r31393561 = r31393559 / r31393560;
        return r31393561;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y) {
        double r31393562 = 1.0;
        return r31393562;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original35.1
Target28.4
Herbie28.0
\[\begin{array}{l} \mathbf{if}\;y \lt -1.2303690911306994 \cdot 10^{+114}:\\ \;\;\;\;1.0\\ \mathbf{elif}\;y \lt -9.102852406811914 \cdot 10^{-222}:\\ \;\;\;\;\frac{\sin \left(\frac{x}{y \cdot 2.0}\right)}{\sin \left(\frac{x}{y \cdot 2.0}\right) \cdot \log \left(e^{\cos \left(\frac{x}{y \cdot 2.0}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1.0\\ \end{array}\]

Derivation

  1. Initial program 35.1

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

  2. Taylor expanded around 0 28.0

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

  3. Final simplification28.0

    \[\leadsto 1.0\]

Reproduce

herbie shell --seed 2019163 +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)))))