Average Error: 15.1 → 0.2
Time: 1.5s
Precision: binary64
\[\frac{x + y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -8.0294973500091967 \cdot 10^{55} \lor \neg \left(y \le 1.6150102836158609 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{1}{x \cdot 2} \cdot \frac{x + y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{x \cdot 2} \cdot \frac{1}{y}\\ \end{array}\]
\frac{x + y}{\left(x \cdot 2\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -8.0294973500091967 \cdot 10^{55} \lor \neg \left(y \le 1.6150102836158609 \cdot 10^{-28}\right):\\
\;\;\;\;\frac{1}{x \cdot 2} \cdot \frac{x + y}{y}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + y}{x \cdot 2} \cdot \frac{1}{y}\\

\end{array}
double code(double x, double y) {
	return ((double) (((double) (x + y)) / ((double) (((double) (x * 2.0)) * y))));
}
↓
double code(double x, double y) {
	double VAR;
	if (((y <= -8.029497350009197e+55) || !(y <= 1.615010283615861e-28))) {
		VAR = ((double) (((double) (1.0 / ((double) (x * 2.0)))) * ((double) (((double) (x + y)) / y))));
	} else {
		VAR = ((double) (((double) (((double) (x + y)) / ((double) (x * 2.0)))) * ((double) (1.0 / y))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.1
Target0.0
Herbie0.2
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -8.0294973500091967e55 or 1.6150102836158609e-28 < y

    1. Initial program 15.7

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

    3. Applied *-un-lft-identity15.7

      \[\leadsto \frac{\color{blue}{1 \cdot \left(x + y\right)}}{\left(x \cdot 2\right) \cdot y}\]

    4. Applied times-frac0.1

      \[\leadsto \color{blue}{\frac{1}{x \cdot 2} \cdot \frac{x + y}{y}}\]

    if -8.0294973500091967e55 < y < 1.6150102836158609e-28

    1. Initial program 14.5

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

    3. Applied associate-/r*0.3

      \[\leadsto \color{blue}{\frac{\frac{x + y}{x \cdot 2}}{y}}\]
    4. Using strategy rm

    5. Applied div-inv0.3

      \[\leadsto \color{blue}{\frac{x + y}{x \cdot 2} \cdot \frac{1}{y}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -8.0294973500091967 \cdot 10^{55} \lor \neg \left(y \le 1.6150102836158609 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{1}{x \cdot 2} \cdot \frac{x + y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{x \cdot 2} \cdot \frac{1}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020155 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, C"
  :precision binary64

  :herbie-target
  (+ (/ 0.5 x) (/ 0.5 y))

  (/ (+ x y) (* (* x 2.0) y)))