Average Error: 15.2 → 0.8
Time: 1.5s
Precision: binary64
\[\frac{x - y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -6.80562597648927385 \cdot 10^{120} \lor \neg \left(y \le 2.73343986558032774 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{1}{x \cdot 2} \cdot \left(\frac{x}{y} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x - y}{x \cdot 2}}{y}\\ \end{array}\]
\frac{x - y}{\left(x \cdot 2\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -6.80562597648927385 \cdot 10^{120} \lor \neg \left(y \le 2.73343986558032774 \cdot 10^{-12}\right):\\
\;\;\;\;\frac{1}{x \cdot 2} \cdot \left(\frac{x}{y} + -1\right)\\

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

\end{array}
double code(double x, double y) {
	return (((double) (x - y)) / ((double) (((double) (x * 2.0)) * y)));
}
↓
double code(double x, double y) {
	double VAR;
	if (((y <= -6.805625976489274e+120) || !(y <= 2.7334398655803277e-12))) {
		VAR = ((double) ((1.0 / ((double) (x * 2.0))) * ((double) ((x / y) + -1.0))));
	} else {
		VAR = ((((double) (x - y)) / ((double) (x * 2.0))) / 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

Original15.2
Target0.0
Herbie0.8
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -6.80562597648927385e120 or 2.73343986558032774e-12 < y

    1. Initial program 17.7

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

    3. Applied *-un-lft-identity17.7

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

    4. Applied times-frac0.1

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

    5. Simplified0.1

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

    if -6.80562597648927385e120 < y < 2.73343986558032774e-12

    1. Initial program 13.4

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

    3. Applied associate-/r*1.2

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -6.80562597648927385 \cdot 10^{120} \lor \neg \left(y \le 2.73343986558032774 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{1}{x \cdot 2} \cdot \left(\frac{x}{y} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x - y}{x \cdot 2}}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020182 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, B"
  :precision binary64

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

  (/ (- x y) (* (* x 2.0) y)))