Average Error: 0.0 → 0.0
Time: 7.6s
Precision: binary64
Cost: 960
\[\frac{x - y}{2 - \left(x + y\right)} \]
↓
\[\begin{array}{l} t_0 := 2 - \left(x + y\right)\\ \frac{x}{t_0} - \frac{y}{t_0} \end{array} \]
(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))
↓
(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 2.0 (+ x y)))) (- (/ x t_0) (/ y t_0))))
double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}
↓
double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	return (x / t_0) - (y / t_0);
}

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
    real(8) :: t_0
    t_0 = 2.0d0 - (x + y)
    code = (x / t_0) - (y / t_0)
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) {
	double t_0 = 2.0 - (x + y);
	return (x / t_0) - (y / t_0);
}

def code(x, y):
	return (x - y) / (2.0 - (x + y))
↓
def code(x, y):
	t_0 = 2.0 - (x + y)
	return (x / t_0) - (y / t_0)

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end
↓
function code(x, y)
	t_0 = Float64(2.0 - Float64(x + y))
	return Float64(Float64(x / t_0) - Float64(y / t_0))
end

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end
↓
function tmp = code(x, y)
	t_0 = 2.0 - (x + y);
	tmp = (x / t_0) - (y / t_0);
end

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := Block[{t$95$0 = N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]}, N[(N[(x / t$95$0), $MachinePrecision] - N[(y / t$95$0), $MachinePrecision]), $MachinePrecision]]

\frac{x - y}{2 - \left(x + y\right)}
↓
\begin{array}{l}
t_0 := 2 - \left(x + y\right)\\
\frac{x}{t_0} - \frac{y}{t_0}
\end{array}

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. Applied egg-rr0.0

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

  4. Final simplification0.0

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

Alternatives

Alternative 1
Error18.0
Cost976
\[\begin{array}{l} t_0 := 1 + \frac{x \cdot -2}{y}\\ \mathbf{if}\;y \leq -1.0814402661084875 \cdot 10^{+116}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.310103937282823 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 5.839597040537266 \cdot 10^{+66}:\\ \;\;\;\;\frac{-y}{2 - y}\\ \mathbf{elif}\;y \leq 1.0445455747685532 \cdot 10^{+113}:\\ \;\;\;\;-1 - -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 2
Error26.2
Cost848
\[\begin{array}{l} \mathbf{if}\;y \leq -1.0814402661084875 \cdot 10^{+116}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -9.197178315403776 \cdot 10^{-183}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 5.995276557546396 \cdot 10^{-263}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 28.915651415127492:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{2}{y}\\ \end{array} \]
Alternative 3
Error17.5
Cost648
\[\begin{array}{l} \mathbf{if}\;y \leq -1.0814402661084875 \cdot 10^{+116}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.310103937282823 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{2 - y}\\ \end{array} \]
Alternative 4
Error24.0
Cost592
\[\begin{array}{l} \mathbf{if}\;x \leq -2.258594947245552 \cdot 10^{+20}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 3.4227717972263933 \cdot 10^{-305}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.1436441326877896 \cdot 10^{-262}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 1.9823435904249616 \cdot 10^{+26}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
Alternative 5
Error26.3
Cost592
\[\begin{array}{l} \mathbf{if}\;y \leq -1.0814402661084875 \cdot 10^{+116}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -9.197178315403776 \cdot 10^{-183}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 5.995276557546396 \cdot 10^{-263}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 28.915651415127492:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 6
Error17.6
Cost584
\[\begin{array}{l} \mathbf{if}\;y \leq -1.0814402661084875 \cdot 10^{+116}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 28.915651415127492:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{2}{y}\\ \end{array} \]
Alternative 7
Error0.0
Cost576
\[\frac{x - y}{\left(2 - x\right) - y} \]
Alternative 8
Error25.1
Cost328
\[\begin{array}{l} \mathbf{if}\;y \leq -1.0814402661084875 \cdot 10^{+116}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 28.915651415127492:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 9
Error39.4
Cost64
\[-1 \]

Error

Reproduce

herbie shell --seed 2022291 
(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))))