Data.Colour.SRGB:transferFunction from colour-2.3.3

Average Error: 0.0 → 0.0

Time: 7.5s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Simplified 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, y\right) - x} \]
   Proof

3. Applied egg-rr 0.0

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

Alternatives

Alternative 1
Error	20.3
Cost	984

\[\begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+107}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{+22}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-47}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-21}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+34}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+116}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 2
Error	11.0
Cost	720

\[\begin{array}{l} \mathbf{if}\;x \leq -9.4 \cdot 10^{+108}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{+22}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+31}:\\ \;\;\;\;y - x\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+117}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 3
Error	1.3
Cost	584

\[\begin{array}{l} t_0 := \left(1 + x\right) \cdot y\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-21}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	1.2
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot x + y\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-21}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;\left(1 + x\right) \cdot y\\ \end{array} \]

Alternative 5
Error	18.9
Cost	392

\[\begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{-47}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-18}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 6
Error	36.6
Cost	64

\[y \]

Reproduce

herbie shell --seed 2023010 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))