Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Average Accuracy: 100.0% → 100.0%

Time: 4.2s

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 100.0%

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

2. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	71.7%
Cost	980

\[\begin{array}{l} t_0 := \frac{x}{y + 1}\\ \mathbf{if}\;y \leq -2 \cdot 10^{+78}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{+51}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-115}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+17}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Accuracy	73.3%
Cost	850

\[\begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+29} \lor \neg \left(x \leq -9.4 \cdot 10^{-79} \lor \neg \left(x \leq -2.5 \cdot 10^{-97}\right) \land x \leq 2.05 \cdot 10^{+73}\right):\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + 1}\\ \end{array} \]

Alternative 3
Accuracy	84.7%
Cost	844

\[\begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+18}:\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-115}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 16500000:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{1 - x}{y}\\ \end{array} \]

Alternative 4
Accuracy	84.5%
Cost	716

\[\begin{array}{l} t_0 := 1 + \frac{x}{y}\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{+18}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-117}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 13000000:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Accuracy	71.5%
Cost	460

\[\begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-115}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 0.22:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Accuracy	73.4%
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.65:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Accuracy	38.1%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023143 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))