Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Average Error: 0.03% → 0.03%

Time: 4.1s

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 0.03

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

2. Final simplification 0.03

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

Alternatives

Alternative 1
Error	13.63%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+16} \lor \neg \left(y \leq 8000\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y + 1}\\ \end{array} \]

Alternative 2
Error	13.55%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+16}:\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{elif}\;y \leq 2000:\\ \;\;\;\;x \cdot \frac{1}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x + -1}{y}\\ \end{array} \]

Alternative 3
Error	25.19%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -11.5 \lor \neg \left(x \leq 4.35 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + 1}\\ \end{array} \]

Alternative 4
Error	13.84%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{+19} \lor \neg \left(y \leq 11200\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \]

Alternative 5
Error	25.91%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+88}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 26000000000000:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Error	26.26%
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.46:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Error	61.33%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023121 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))