Data.Colour.SRGB:transferFunction from colour-2.3.3

Average Accuracy: 87.2% → 87.2%

Time: 2.7s

Precision: binary64

Cost: 448

Math

\[\left(x + 1\right) \cdot y - x \]

↓

\[\left(x + 1\right) \cdot y - x \]

FPCore

(FPCore (x y) :precision binary64 (- (* (+ x 1.0) y) x))

↓

(FPCore (x y) :precision binary64 (- (* (+ x 1.0) y) x))

C

double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

↓

double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x + 1.0d0) * y) - x
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x + 1.0d0) * y) - x
end function

Java

public static double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

↓

public static double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

Python

def code(x, y):
	return ((x + 1.0) * y) - x

↓

def code(x, y):
	return ((x + 1.0) * y) - x

Julia

function code(x, y)
	return Float64(Float64(Float64(x + 1.0) * y) - x)
end

↓

function code(x, y)
	return Float64(Float64(Float64(x + 1.0) * y) - x)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x + 1.0) * y) - x;
end

↓

function tmp = code(x, y)
	tmp = ((x + 1.0) * y) - x;
end

Wolfram

code[x_, y_] := N[(N[(N[(x + 1.0), $MachinePrecision] * y), $MachinePrecision] - x), $MachinePrecision]

↓

code[x_, y_] := N[(N[(N[(x + 1.0), $MachinePrecision] * y), $MachinePrecision] - x), $MachinePrecision]

Derivation

1. Initial program 84.8%

   \[\left(x + 1\right) \cdot y - x \]

2. Final simplification 84.8%

   \[\leadsto \left(x + 1\right) \cdot y - x \]

Alternatives

Alternative 1
Accuracy	60.6%
Cost	656

\[\begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-101}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-89}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-42}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-17}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 2
Accuracy	86.0%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -95000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;\left(x + 1\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]

Alternative 3
Accuracy	85.9%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 4.8 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot y - x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]

Alternative 4
Accuracy	75.4%
Cost	192

\[y - x \]

Alternative 5
Accuracy	38.9%
Cost	64

\[y \]

Reproduce

herbie shell --seed 2023153 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))