Average Error: 35.3 → 28.4
Time: 22.6s
Precision: 64
\[\frac{\tan \left(\frac{x}{y \cdot 2.0}\right)}{\sin \left(\frac{x}{y \cdot 2.0}\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x}{2.0 \cdot y} \le 4.3945246018946 \cdot 10^{-310}:\\ \;\;\;\;1.0\\ \mathbf{elif}\;\frac{x}{2.0 \cdot y} \le 5.725300019950944 \cdot 10^{+237}:\\ \;\;\;\;\frac{\sin \left(\frac{x}{2.0 \cdot y}\right)}{\sin \left(\frac{x}{2.0 \cdot y}\right) \cdot \cos \left(\frac{x}{2.0 \cdot y}\right)}\\ \mathbf{else}:\\ \;\;\;\;1.0\\ \end{array}\]
\frac{\tan \left(\frac{x}{y \cdot 2.0}\right)}{\sin \left(\frac{x}{y \cdot 2.0}\right)}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x}{2.0 \cdot y} \le 4.3945246018946 \cdot 10^{-310}:\\
\;\;\;\;1.0\\

\mathbf{elif}\;\frac{x}{2.0 \cdot y} \le 5.725300019950944 \cdot 10^{+237}:\\
\;\;\;\;\frac{\sin \left(\frac{x}{2.0 \cdot y}\right)}{\sin \left(\frac{x}{2.0 \cdot y}\right) \cdot \cos \left(\frac{x}{2.0 \cdot y}\right)}\\

\mathbf{else}:\\
\;\;\;\;1.0\\

\end{array}
double f(double x, double y) {
        double r31707117 = x;
        double r31707118 = y;
        double r31707119 = 2.0;
        double r31707120 = r31707118 * r31707119;
        double r31707121 = r31707117 / r31707120;
        double r31707122 = tan(r31707121);
        double r31707123 = sin(r31707121);
        double r31707124 = r31707122 / r31707123;
        return r31707124;
}
↓
double f(double x, double y) {
        double r31707125 = x;
        double r31707126 = 2.0;
        double r31707127 = y;
        double r31707128 = r31707126 * r31707127;
        double r31707129 = r31707125 / r31707128;
        double r31707130 = 4.3945246018946e-310;
        bool r31707131 = r31707129 <= r31707130;
        double r31707132 = 1.0;
        double r31707133 = 5.725300019950944e+237;
        bool r31707134 = r31707129 <= r31707133;
        double r31707135 = sin(r31707129);
        double r31707136 = cos(r31707129);
        double r31707137 = r31707135 * r31707136;
        double r31707138 = r31707135 / r31707137;
        double r31707139 = r31707134 ? r31707138 : r31707132;
        double r31707140 = r31707131 ? r31707132 : r31707139;
        return r31707140;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original35.3
Target29.4
Herbie28.4
\[\begin{array}{l} \mathbf{if}\;y \lt -1.2303690911306994 \cdot 10^{+114}:\\ \;\;\;\;1.0\\ \mathbf{elif}\;y \lt -9.102852406811914 \cdot 10^{-222}:\\ \;\;\;\;\frac{\sin \left(\frac{x}{y \cdot 2.0}\right)}{\sin \left(\frac{x}{y \cdot 2.0}\right) \cdot \log \left(e^{\cos \left(\frac{x}{y \cdot 2.0}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1.0\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ x (* y 2.0)) < 4.3945246018946e-310 or 5.725300019950944e+237 < (/ x (* y 2.0))

    1. Initial program 41.0

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

    2. Taylor expanded around 0 30.5

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

    if 4.3945246018946e-310 < (/ x (* y 2.0)) < 5.725300019950944e+237

    1. Initial program 24.5

      \[\frac{\tan \left(\frac{x}{y \cdot 2.0}\right)}{\sin \left(\frac{x}{y \cdot 2.0}\right)}\]
    2. Using strategy rm

    3. Applied tan-quot24.5

      \[\leadsto \frac{\color{blue}{\frac{\sin \left(\frac{x}{y \cdot 2.0}\right)}{\cos \left(\frac{x}{y \cdot 2.0}\right)}}}{\sin \left(\frac{x}{y \cdot 2.0}\right)}\]
    4. Using strategy rm

    5. Applied associate-/l/24.5

      \[\leadsto \color{blue}{\frac{\sin \left(\frac{x}{y \cdot 2.0}\right)}{\sin \left(\frac{x}{y \cdot 2.0}\right) \cdot \cos \left(\frac{x}{y \cdot 2.0}\right)}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification28.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{2.0 \cdot y} \le 4.3945246018946 \cdot 10^{-310}:\\ \;\;\;\;1.0\\ \mathbf{elif}\;\frac{x}{2.0 \cdot y} \le 5.725300019950944 \cdot 10^{+237}:\\ \;\;\;\;\frac{\sin \left(\frac{x}{2.0 \cdot y}\right)}{\sin \left(\frac{x}{2.0 \cdot y}\right) \cdot \cos \left(\frac{x}{2.0 \cdot y}\right)}\\ \mathbf{else}:\\ \;\;\;\;1.0\\ \end{array}\]

Reproduce

herbie shell --seed 2019162 
(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)))))