Average Error: 0.0 → 0.0
Time: 4.7s
Precision: binary64
\[\frac{x + y}{y + 1} \]
↓
\[\frac{y}{y + 1} + \frac{x}{y + 1} \]
(FPCore (x y) :precision binary64 (/ (+ x y) (+ y 1.0)))
↓
(FPCore (x y) :precision binary64 (+ (/ y (+ y 1.0)) (/ x (+ y 1.0))))
double code(double x, double y) {
	return (x + y) / (y + 1.0);
}
↓
double code(double x, double y) {
	return (y / (y + 1.0)) + (x / (y + 1.0));
}

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x + y) / (y + 1.0d0)
end function
↓
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y / (y + 1.0d0)) + (x / (y + 1.0d0))
end function

public static double code(double x, double y) {
	return (x + y) / (y + 1.0);
}
↓
public static double code(double x, double y) {
	return (y / (y + 1.0)) + (x / (y + 1.0));
}

def code(x, y):
	return (x + y) / (y + 1.0)
↓
def code(x, y):
	return (y / (y + 1.0)) + (x / (y + 1.0))

function code(x, y)
	return Float64(Float64(x + y) / Float64(y + 1.0))
end
↓
function code(x, y)
	return Float64(Float64(y / Float64(y + 1.0)) + Float64(x / Float64(y + 1.0)))
end

function tmp = code(x, y)
	tmp = (x + y) / (y + 1.0);
end
↓
function tmp = code(x, y)
	tmp = (y / (y + 1.0)) + (x / (y + 1.0));
end

code[x_, y_] := N[(N[(x + y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] + N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\frac{x + y}{y + 1}
↓
\frac{y}{y + 1} + \frac{x}{y + 1}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{x + y}{y + 1} \]

  2. Taylor expanded in x around 0 0.0

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

  3. Final simplification0.0

    \[\leadsto \frac{y}{y + 1} + \frac{x}{y + 1} \]

Reproduce

herbie shell --seed 2022210 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))