Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Average Error: 0.0 → 0.0

Time: 3.3s

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	8.9
Cost	712

\[\begin{array}{l} t_0 := \frac{y}{y + 1}\\ \mathbf{if}\;y \leq -9305.724490068953:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 5.901783054998034 \cdot 10^{-11}:\\ \;\;\;\;x + y \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	9.0
Cost	584

\[\begin{array}{l} t_0 := \frac{y}{y + 1}\\ \mathbf{if}\;y \leq -9305.724490068953:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 5.901783054998034 \cdot 10^{-11}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	9.3
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -9305.724490068953:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.007527920610455143:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Error	16.4
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -9305.724490068953:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.007527920610455143:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Error	38.6
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022300 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))