Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Average Error: 0.02% → 0.02%

Time: 4.0s

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 0.02

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

2. Final simplification 0.02

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

Alternatives

Alternative 1
Error	14%
Cost	848

\[\begin{array}{l} t_0 := 1 + \frac{x}{y}\\ t_1 := \frac{x}{y + 1}\\ \mathbf{if}\;y \leq -20000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-56}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3500000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	13.98%
Cost	848

\[\begin{array}{l} t_0 := 1 + \frac{x}{y}\\ \mathbf{if}\;y \leq -6700000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \frac{1}{y + 1}\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-57}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3500000000000:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	1.86%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.84\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 4
Error	1.55%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;1 - \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 5
Error	14.22%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 4.7 \cdot 10^{-10}\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	14.04%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 4.7 \cdot 10^{-10}\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot y\\ \end{array} \]

Alternative 7
Error	25.91%
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8
Error	60.43%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023088 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))