Data.Colour.SRGB:transferFunction from colour-2.3.3

Average Error: 0.0 → 0.0

Time: 1.4s

Precision: binary64

Cost: 448

Math

\[\left(x + 1\right) \cdot y - x \]

↓

\[\left(y + y \cdot x\right) - x \]

FPCore

(FPCore (x y) :precision binary64 (- (* (+ x 1.0) y) x))

↓

(FPCore (x y) :precision binary64 (- (+ y (* y x)) x))

C

double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

↓

double code(double x, double y) {
	return (y + (y * x)) - x;
}

Fortran

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

↓

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

Java

public static double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

↓

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

Python

def code(x, y):
	return ((x + 1.0) * y) - x

↓

def code(x, y):
	return (y + (y * x)) - x

Julia

function code(x, y)
	return Float64(Float64(Float64(x + 1.0) * y) - x)
end

↓

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

MATLAB

function tmp = code(x, y)
	tmp = ((x + 1.0) * y) - x;
end

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

   \[\left(x + 1\right) \cdot y - x \]

2. Taylor expanded in x around 0 0.0

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

3. Final simplification 0.0

   \[\leadsto \left(y + y \cdot x\right) - x \]

Alternatives

Alternative 1
Error	0.8
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -1850000 \lor \neg \left(x \leq 0.0009\right):\\ \;\;\;\;y \cdot x - x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]

Alternative 2
Error	0.0
Cost	448

\[y \cdot \left(x + 1\right) - x \]

Alternative 3
Error	9.5
Cost	192

\[y - x \]

Reproduce

herbie shell --seed 2023018 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))