Average Error: 14.8 → 0.3
Time: 3.0s
Precision: binary64
\[\frac{x + y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.2137323963604039 \cdot 10^{-17} \lor \neg \left(x \le 2.7674407540267516 \cdot 10^{-85}\right):\\ \;\;\;\;\frac{1}{y \cdot \frac{x}{\frac{x + y}{2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot 2} \cdot \frac{x + y}{y}\\ \end{array}\]
\frac{x + y}{\left(x \cdot 2\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.2137323963604039 \cdot 10^{-17} \lor \neg \left(x \le 2.7674407540267516 \cdot 10^{-85}\right):\\
\;\;\;\;\frac{1}{y \cdot \frac{x}{\frac{x + y}{2}}}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{x \cdot 2} \cdot \frac{x + y}{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 (((x <= -1.213732396360404e-17) || !(x <= 2.7674407540267516e-85))) {
		VAR = ((double) (1.0 / ((double) (y * ((double) (x / ((double) (((double) (x + y)) / 2.0))))))));
	} else {
		VAR = ((double) (((double) (1.0 / ((double) (x * 2.0)))) * ((double) (((double) (x + y)) / 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

Original14.8
Target0.0
Herbie0.3
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.2137323963604039e-17 or 2.7674407540267516e-85 < x

    1. Initial program 12.8

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

    3. Applied clear-num12.6

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

    4. Simplified0.4

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

    if -1.2137323963604039e-17 < x < 2.7674407540267516e-85

    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

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.2137323963604039 \cdot 10^{-17} \lor \neg \left(x \le 2.7674407540267516 \cdot 10^{-85}\right):\\ \;\;\;\;\frac{1}{y \cdot \frac{x}{\frac{x + y}{2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot 2} \cdot \frac{x + y}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020179 
(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)))