Average Error: 15.0 → 0.3
Time: 1.3s
Precision: binary64
\[\frac{x + y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -6.70165043892356 \cdot 10^{62} \lor \neg \left(y \le 8348804843464008\right):\\ \;\;\;\;\frac{1}{x \cdot 2} \cdot \frac{x + y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x + y}{x \cdot 2}}{y}\\ \end{array}\]
\frac{x + y}{\left(x \cdot 2\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -6.70165043892356 \cdot 10^{62} \lor \neg \left(y \le 8348804843464008\right):\\
\;\;\;\;\frac{1}{x \cdot 2} \cdot \frac{x + y}{y}\\

\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 <= -6.70165043892356e+62) || !(y <= 8348804843464008.0))) {
		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)))) / 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

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

Derivation

  1. Split input into 2 regimes

  2. if y < -6.70165043892356e62 or 8348804843464008 < y

    1. Initial program 16.6

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

    3. Applied *-un-lft-identity16.6

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

    4. Applied times-frac0.1

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

    if -6.70165043892356e62 < y < 8348804843464008

    1. Initial program 13.8

      \[\frac{x + y}{\left(x \cdot 2\right) \cdot y}\]
    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

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -6.70165043892356 \cdot 10^{62} \lor \neg \left(y \le 8348804843464008\right):\\ \;\;\;\;\frac{1}{x \cdot 2} \cdot \frac{x + y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x + y}{x \cdot 2}}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020175 
(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)))