Average Error: 0.0 → 0.0
Time: 3.1s
Precision: binary64
Cost: 704
\[\frac{x - y}{x + y} \]
↓
\[\frac{x}{x + y} - \frac{y}{x + y} \]
(FPCore (x y) :precision binary64 (/ (- x y) (+ x y)))
↓
(FPCore (x y) :precision binary64 (- (/ x (+ x y)) (/ y (+ x y))))
double code(double x, double y) {
	return (x - y) / (x + y);
}
↓
double code(double x, double y) {
	return (x / (x + y)) - (y / (x + y));
}

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (x + y)
end function
↓
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x / (x + y)) - (y / (x + y))
end function

public static double code(double x, double y) {
	return (x - y) / (x + y);
}
↓
public static double code(double x, double y) {
	return (x / (x + y)) - (y / (x + y));
}

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

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

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

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\frac{x - y}{x + y}
↓
\frac{x}{x + y} - \frac{y}{x + y}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\frac{x}{x + y} - \frac{y}{x + y} \]

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{x + y} \]

  2. Applied egg-rr0.0

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

  3. Final simplification0.0

    \[\leadsto \frac{x}{x + y} - \frac{y}{x + y} \]

Alternatives

Alternative 1
Error17.9
Cost976
\[\begin{array}{l} t_0 := 2 \cdot \frac{x}{y} + -1\\ \mathbf{if}\;y \leq -2.222519678424655 \cdot 10^{-14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.5829606774030727 \cdot 10^{-247}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.437860450261574 \cdot 10^{-218}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.078748506667967 \cdot 10^{+37}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 2
Error17.5
Cost976
\[\begin{array}{l} t_0 := 2 \cdot \frac{x}{y} + -1\\ t_1 := 1 + -2 \cdot \frac{y}{x}\\ \mathbf{if}\;y \leq -2.222519678424655 \cdot 10^{-14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.5829606774030727 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.437860450261574 \cdot 10^{-218}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.078748506667967 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 3
Error18.2
Cost592
\[\begin{array}{l} \mathbf{if}\;y \leq -2.222519678424655 \cdot 10^{-14}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.5829606774030727 \cdot 10^{-247}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.437860450261574 \cdot 10^{-218}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 6.078748506667967 \cdot 10^{+37}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
Alternative 4
Error0.0
Cost448
\[\frac{x - y}{x + y} \]
Alternative 5
Error32.2
Cost64
\[-1 \]

Error

Reproduce

herbie shell --seed 2022217 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

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

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