Data.Colour.SRGB:transferFunction from colour-2.3.3

Average Error: 0.0 → 0.0

Time: 4.1s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Simplified 0.0

   \[\leadsto \color{blue}{y + \left(x \cdot y - x\right)} \]
   Proof

   [Start] 0.0	\[ \left(x + 1\right) \cdot y - x \]
   rational_best_oopsla_all_46_json_45_simplify-74 [=>] 0.0	\[ \color{blue}{y \cdot \left(x + 1\right)} - x \]
   rational_best_oopsla_all_46_json_45_simplify-37 [=>] 0.0	\[ \color{blue}{\left(x \cdot y + y \cdot 1\right)} - x \]
   rational_best_oopsla_all_46_json_45_simplify-52 [=>] 0.0	\[ \left(x \cdot y + \color{blue}{y}\right) - x \]
   rational_best_oopsla_all_46_json_45_simplify-107 [=>] 0.0	\[ \color{blue}{y + \left(x \cdot y - x\right)} \]

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	0.9
Cost	584

\[\begin{array}{l} t_0 := \left(1 + x\right) \cdot y\\ \mathbf{if}\;y \leq -360000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	0.9
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -360000000000:\\ \;\;\;\;\left(1 + x\right) \cdot y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y + y \cdot x\\ \end{array} \]

Alternative 3
Error	19.0
Cost	392

\[\begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-20}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-68}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 4
Error	9.8
Cost	192

\[y - x \]

Alternative 5
Error	36.0
Cost	64

\[y \]

Reproduce

herbie shell --seed 2023090 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))