Average Error: 15.5 → 0.3
Time: 1.4s
Precision: binary64
\[\frac{x - y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -2.85153879778384713 \cdot 10^{-58} \lor \neg \left(y \le 3.39728574246810265 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{\frac{x}{y} - 1}{x \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x - y}{x \cdot 2}}{y}\\ \end{array}\]
\frac{x - y}{\left(x \cdot 2\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -2.85153879778384713 \cdot 10^{-58} \lor \neg \left(y \le 3.39728574246810265 \cdot 10^{-67}\right):\\
\;\;\;\;\frac{\frac{x}{y} - 1}{x \cdot 2}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{x - y}{x \cdot 2}}{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 <= -2.851538797783847e-58) || !(y <= 3.3972857424681027e-67))) {
		VAR = ((double) (((double) (((double) (x / y)) - 1.0)) / ((double) (x * 2.0))));
	} else {
		VAR = ((double) (((double) (((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

Original15.5
Target0.0
Herbie0.3
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -2.85153879778384713e-58 or 3.39728574246810265e-67 < y

    1. Initial program 13.5

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

    3. Applied *-un-lft-identity13.5

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

    4. Applied times-frac0.6

      \[\leadsto \color{blue}{\frac{1}{x \cdot 2} \cdot \frac{x - y}{y}}\]
    5. Using strategy rm

    6. Applied associate-*l/0.5

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

    7. Simplified0.5

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

    9. Applied div-sub0.5

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

    10. Simplified0.5

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

    if -2.85153879778384713e-58 < y < 3.39728574246810265e-67

    1. Initial program 18.6

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

    3. Applied associate-/r*0.1

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.85153879778384713 \cdot 10^{-58} \lor \neg \left(y \le 3.39728574246810265 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{\frac{x}{y} - 1}{x \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x - y}{x \cdot 2}}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020153 
(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)))