Average Error: 0.0 → 0.0
Time: 2.7s
Precision: binary64
Cost: 448
\[\frac{x - y}{x + y} \]
↓
\[\frac{x - y}{x + y} \]
(FPCore (x y) :precision binary64 (/ (- x y) (+ x y)))
↓
(FPCore (x y) :precision binary64 (/ (- x y) (+ x y)))
double code(double x, double y) {
	return (x - y) / (x + y);
}
↓
double code(double x, double y) {
	return (x - 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 - 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 - y) / (x + y);
}

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

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

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

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

\frac{x - y}{x + y}
↓
\frac{x - 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. Final simplification0.0

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

Alternatives

Alternative 1
Error17.9
Cost976
\[\begin{array}{l} t_0 := 1 + -2 \cdot \frac{y}{x}\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{-14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-127}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+49}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 2
Error16.6
Cost976
\[\begin{array}{l} t_0 := 1 + -2 \cdot \frac{y}{x}\\ t_1 := 2 \cdot \frac{x}{y} + -1\\ \mathbf{if}\;x \leq -6 \cdot 10^{-13}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-12}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 3
Error18.2
Cost592
\[\begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-12}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-127}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-13}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+39}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 4
Error32.5
Cost64
\[-1 \]

Error

Reproduce

herbie shell --seed 2022338 
(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)))