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

Average Error: 0.2 → 0.3

Time: 4.5s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

(FPCore (x y) :precision binary64 (* (* 3.0 y) (+ x -0.13793103448275862)))

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 + -0.13793103448275862);
}

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 + (-0.13793103448275862d0))
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 + -0.13793103448275862);
}

Python

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

↓

def code(x, y):
	return (3.0 * y) * (x + -0.13793103448275862)

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 * y) * Float64(x + -0.13793103448275862))
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 + -0.13793103448275862);
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 * y), $MachinePrecision] * N[(x + -0.13793103448275862), $MachinePrecision]), $MachinePrecision]

Target

Original	0.2
Target	0.2
Herbie	0.3

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

Derivation

1. Initial program 0.2

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

2. Simplified 0.3

   \[\leadsto \color{blue}{\left(x + -0.13793103448275862\right) \cdot \left(3 \cdot y\right)} \]
   Proof
   (*.f64 (+.f64 x -4/29) (*.f64 3 y)): 0 points increase in error, 0 points decrease in error
   (*.f64 (+.f64 x (Rewrite<= metadata-eval (neg.f64 4/29))) (*.f64 3 y)): 0 points increase in error, 0 points decrease in error
   (*.f64 (+.f64 x (neg.f64 (Rewrite<= metadata-eval (/.f64 16 116)))) (*.f64 3 y)): 4 points increase in error, 0 points decrease in error
   (*.f64 (Rewrite<= sub-neg_binary64 (-.f64 x (/.f64 16 116))) (*.f64 3 y)): 0 points increase in error, 4 points decrease in error
   (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (-.f64 x (/.f64 16 116)) 3) y)): 0 points increase in error, 0 points decrease in error

3. Final simplification 0.3

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

Alternatives

Alternative 1
Error	1.7
Cost	585

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

Alternative 2
Error	1.7
Cost	584

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

Alternative 3
Error	1.7
Cost	584

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

Alternative 4
Error	0.3
Cost	448

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

Alternative 5
Error	27.4
Cost	192

\[y \cdot -0.41379310344827586 \]

Reproduce

herbie shell --seed 2022343 
(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))