Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Average Error: 0.0 → 0.0

Time: 2.8s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

(FPCore (x y) :precision binary64 (/ (+ x y) (+ y 1.0)))

↓

(FPCore (x y) :precision binary64 (/ (+ x y) (+ y 1.0)))

C

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

↓

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

Fortran

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 = (x + y) / (y + 1.0d0)
end function

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	17.6
Cost	724

\[\begin{array}{l} \mathbf{if}\;y \leq -3.32799837217863 \cdot 10^{+126}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.513010796666266 \cdot 10^{+76}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -8.798686154677553 \cdot 10^{+34}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -810.3510330675228:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 14832952.711691001:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Error	9.0
Cost	584

\[\begin{array}{l} t_0 := 1 + \frac{x}{y}\\ \mathbf{if}\;y \leq -810.3510330675228:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.0077277807487019495:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	8.5
Cost	584

\[\begin{array}{l} t_0 := 1 + \frac{x}{y}\\ \mathbf{if}\;y \leq -4014.683235362648:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 14832952.711691001:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	35.1
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -6.58842370938457 \cdot 10^{-171}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.402186899483856 \cdot 10^{-216}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Error	16.9
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -810.3510330675228:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 14832952.711691001:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Error	54.8
Cost	64

\[y \]

Reproduce

herbie shell --seed 2022325 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))