Average Error: 35.0 → 28.5
Time: 14.4s
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 r597466 = x;
        double r597467 = y;
        double r597468 = 2.0;
        double r597469 = r597467 * r597468;
        double r597470 = r597466 / r597469;
        double r597471 = tan(r597470);
        double r597472 = sin(r597470);
        double r597473 = r597471 / r597472;
        return r597473;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y) {
        double r597474 = 1.0;
        return r597474;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original35.0
Target29.0
Herbie28.5
\[\begin{array}{l} \mathbf{if}\;y \lt -1.230369091130699363447511617672816900781 \cdot 10^{114}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \lt -9.102852406811913849731222630299032206502 \cdot 10^{-222}:\\ \;\;\;\;\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right) \cdot \log \left(e^{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]

Derivation

  1. Initial program 35.0

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

  2. Simplified35.0

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

  3. Taylor expanded around 0 28.5

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

  4. Final simplification28.5

    \[\leadsto 1\]

Reproduce

herbie shell --seed 2019194 +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)))))