Average Error: 0.0 → 0.0
Time: 4.4s
Precision: binary64
Cost: 576
\[\frac{x - y}{2 - \left(x + y\right)} \]
\[\frac{x - y}{\left(2 - x\right) - y} \]
(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))
(FPCore (x y) :precision binary64 (/ (- x y) (- (- 2.0 x) y)))
double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}
double code(double x, double y) {
	return (x - y) / ((2.0 - x) - y);
}
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / ((2.0d0 - x) - y)
end function
public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}
public static double code(double x, double y) {
	return (x - y) / ((2.0 - x) - y);
}
def code(x, y):
	return (x - y) / (2.0 - (x + y))
def code(x, y):
	return (x - y) / ((2.0 - x) - y)
function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end
function code(x, y)
	return Float64(Float64(x - y) / Float64(Float64(2.0 - x) - y))
end
function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end
function tmp = code(x, y)
	tmp = (x - y) / ((2.0 - x) - y);
end
code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(N[(2.0 - x), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]
\frac{x - y}{2 - \left(x + y\right)}
\frac{x - y}{\left(2 - x\right) - y}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)} \]

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{2 - \left(x + y\right)} \]
  2. Simplified0.0

    \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]
    Proof
    (/.f64 (-.f64 x y) (-.f64 (-.f64 2 x) y)): 0 points increase in error, 0 points decrease in error
    (/.f64 (-.f64 x y) (Rewrite<= associate--r+_binary64 (-.f64 2 (+.f64 x y)))): 0 points increase in error, 0 points decrease in error
  3. Final simplification0.0

    \[\leadsto \frac{x - y}{\left(2 - x\right) - y} \]

Alternatives

Alternative 1
Error16.5
Cost1112
\[\begin{array}{l} t_0 := \frac{y}{y + -2}\\ t_1 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -1.5828282294461644 \cdot 10^{+51}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -530072407084116.56:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.338008206742224 \cdot 10^{-61}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.447487254923756 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1966594.4482695544:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.4004448633078727 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 2
Error16.7
Cost1112
\[\begin{array}{l} t_0 := \frac{y}{y + -2}\\ t_1 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -2.790628277974997 \cdot 10^{+57}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -530072407084116.56:\\ \;\;\;\;2 \cdot \frac{y}{x} + -1\\ \mathbf{elif}\;y \leq -5.338008206742224 \cdot 10^{-61}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.447487254923756 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1966594.4482695544:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.4004448633078727 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 3
Error16.9
Cost584
\[\begin{array}{l} \mathbf{if}\;x \leq -561953328597.0264:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.4919194996068743 \cdot 10^{+78}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
Alternative 4
Error24.4
Cost328
\[\begin{array}{l} \mathbf{if}\;y \leq -1.5828282294461644 \cdot 10^{+51}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.4004448633078727 \cdot 10^{+41}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 5
Error39.4
Cost64
\[-1 \]

Error

Reproduce

herbie shell --seed 2022300 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :herbie-target
  (- (/ x (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))

  (/ (- x y) (- 2.0 (+ x y))))