Data.Colour.CIE:cieLAB from colour-2.3.3, A

Average Error: 0.2 → 0.2

Time: 12.1s

Precision: binary64

Cost: 576

Math

\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]

↓

\[3 \cdot \left(y \cdot x\right) + -0.41379310344827586 \cdot y \]

FPCore

(FPCore (x y) :precision binary64 (* (* (- x (/ 16.0 116.0)) 3.0) y))

↓

(FPCore (x y)
 :precision binary64
 (+ (* 3.0 (* y x)) (* -0.41379310344827586 y)))

C

double code(double x, double y) {
	return ((x - (16.0 / 116.0)) * 3.0) * y;
}

↓

double code(double x, double y) {
	return (3.0 * (y * x)) + (-0.41379310344827586 * y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x - (16.0d0 / 116.0d0)) * 3.0d0) * y
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (3.0d0 * (y * x)) + ((-0.41379310344827586d0) * y)
end function

Java

public static double code(double x, double y) {
	return ((x - (16.0 / 116.0)) * 3.0) * y;
}

↓

public static double code(double x, double y) {
	return (3.0 * (y * x)) + (-0.41379310344827586 * y);
}

Python

def code(x, y):
	return ((x - (16.0 / 116.0)) * 3.0) * y

↓

def code(x, y):
	return (3.0 * (y * x)) + (-0.41379310344827586 * y)

Julia

function code(x, y)
	return Float64(Float64(Float64(x - Float64(16.0 / 116.0)) * 3.0) * y)
end

↓

function code(x, y)
	return Float64(Float64(3.0 * Float64(y * x)) + Float64(-0.41379310344827586 * y))
end

MATLAB

function tmp = code(x, y)
	tmp = ((x - (16.0 / 116.0)) * 3.0) * y;
end

↓

function tmp = code(x, y)
	tmp = (3.0 * (y * x)) + (-0.41379310344827586 * y);
end

Wolfram

code[x_, y_] := N[(N[(N[(x - N[(16.0 / 116.0), $MachinePrecision]), $MachinePrecision] * 3.0), $MachinePrecision] * y), $MachinePrecision]

↓

code[x_, y_] := N[(N[(3.0 * N[(y * x), $MachinePrecision]), $MachinePrecision] + N[(-0.41379310344827586 * y), $MachinePrecision]), $MachinePrecision]

Target

Original	0.2
Target	0.2
Herbie	0.2

\[y \cdot \left(x \cdot 3 - 0.41379310344827586\right) \]

Derivation

1. Initial program 0.2

   \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]

2. Simplified 0.2

   \[\leadsto \color{blue}{\left(\left(x - 0.13793103448275862\right) \cdot 3\right) \cdot y} \]
   Proof

   [Start] 0.2	\[ \left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
   metadata-eval [=>] 0.2	\[ \left(\left(x - \color{blue}{0.13793103448275862}\right) \cdot 3\right) \cdot y \]

3. Taylor expanded in x around 0 0.2

   \[\leadsto \color{blue}{3 \cdot \left(y \cdot x\right) + -0.41379310344827586 \cdot y} \]

4. Final simplification 0.2

   \[\leadsto 3 \cdot \left(y \cdot x\right) + -0.41379310344827586 \cdot y \]

Alternatives

Alternative 1
Error	1.6
Cost	584

\[\begin{array}{l} t_0 := 3 \cdot \left(y \cdot x\right)\\ \mathbf{if}\;x \leq -0.14:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.135:\\ \;\;\;\;-0.41379310344827586 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	1.6
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -0.14:\\ \;\;\;\;x \cdot \left(3 \cdot y\right)\\ \mathbf{elif}\;x \leq 0.135:\\ \;\;\;\;-0.41379310344827586 \cdot y\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 3
Error	1.6
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -0.14:\\ \;\;\;\;x \cdot \left(3 \cdot y\right)\\ \mathbf{elif}\;x \leq 0.135:\\ \;\;\;\;-0.41379310344827586 \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 3\right) \cdot y\\ \end{array} \]

Alternative 4
Error	0.3
Cost	448

\[3 \cdot \left(y \cdot \left(x - 0.13793103448275862\right)\right) \]

Alternative 5
Error	0.2
Cost	448

\[\left(\left(x - 0.13793103448275862\right) \cdot 3\right) \cdot y \]

Alternative 6
Error	0.2
Cost	448

\[\left(3 \cdot x - 0.41379310344827586\right) \cdot y \]

Alternative 7
Error	26.7
Cost	192

\[-0.41379310344827586 \cdot y \]

Reproduce

herbie shell --seed 2023074 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3.0) 0.41379310344827586))

  (* (* (- x (/ 16.0 116.0)) 3.0) y))