Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Average Error: 0.0 → 0.0

Time: 8.6s

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	9.1
Cost	976

\[\begin{array}{l} t_0 := 1 - \frac{1 - x}{y}\\ t_1 := \frac{x}{y - -1}\\ \mathbf{if}\;y \leq -1700:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.75 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-79}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 460000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	9.2
Cost	912

\[\begin{array}{l} t_0 := 1 - \left(-\frac{x}{y}\right)\\ t_1 := \frac{x}{y - -1}\\ \mathbf{if}\;y \leq -72000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.75 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-82}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 390000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	16.8
Cost	848

\[\begin{array}{l} t_0 := \frac{x}{y - -1}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+17}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-103}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-82}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 720000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Error	16.6
Cost	848

\[\begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{+18}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-103}:\\ \;\;\;\;\frac{x}{y - -1}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-82}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - -1}\\ \end{array} \]

Alternative 5
Error	17.4
Cost	592

\[\begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-82}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 195000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Error	17.1
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 195000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Error	39.7
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023075 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))