Average Error: 15.7 → 0.3
Time: 18.4s
Precision: binary64
\[\frac{x - y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.3704740820341672 \cdot 10^{65} \lor \neg \left(y \le 4.60493409797871949 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{\frac{1}{x}}{\frac{y}{\frac{x - y}{2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x - y}{x \cdot 2}}{y}\\ \end{array}\]
\frac{x - y}{\left(x \cdot 2\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.3704740820341672 \cdot 10^{65} \lor \neg \left(y \le 4.60493409797871949 \cdot 10^{-45}\right):\\
\;\;\;\;\frac{\frac{1}{x}}{\frac{y}{\frac{x - y}{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 <= -1.3704740820341672e+65) || !(y <= 4.6049340979787195e-45))) {
		VAR = ((double) (((double) (1.0 / x)) / ((double) (y / ((double) (((double) (x - y)) / 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

Original15.7
Target0.0
Herbie0.3
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.3704740820341672e65 or 4.60493409797871949e-45 < y

    1. Initial program 16.3

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

    3. Applied associate-/r*15.9

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

    5. Applied *-un-lft-identity15.9

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

    6. Applied times-frac15.9

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

    7. Applied associate-/l*0.2

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

    if -1.3704740820341672e65 < y < 4.60493409797871949e-45

    1. Initial program 15.2

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

    3. Applied associate-/r*0.4

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.3704740820341672 \cdot 10^{65} \lor \neg \left(y \le 4.60493409797871949 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{\frac{1}{x}}{\frac{y}{\frac{x - y}{2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x - y}{x \cdot 2}}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020147 
(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)))