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

Percentage Accurate: 99.7% → 99.7%

Time: 6.6s

Alternatives: 6

Speedup: 1.3×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 3 + -0.41379310344827586\right) \cdot y \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
2. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\left(x - \frac{16}{116}\right) \cdot 3\right), \color{blue}{y}\right) \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x - \frac{16}{116}\right), 3\right), y\right) \]

   3. sub-neg N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{16}{116}\right)\right)\right), 3\right), y\right) \]

   4. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\frac{16}{116}\right)\right)\right), 3\right), y\right) \]

   5. metadata-eval N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\frac{4}{29}\right)\right)\right), 3\right), y\right) \]

   6. metadata-eval 99.8%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{-4}{29}\right), 3\right), y\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\left(\left(x + -0.13793103448275862\right) \cdot 3\right) \cdot y} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(\left(3 \cdot \left(x + \frac{-4}{29}\right)\right), y\right) \]

   2. distribute-lft-in N/A

      \[\leadsto \mathsf{*.f64}\left(\left(3 \cdot x + 3 \cdot \frac{-4}{29}\right), y\right) \]

   3. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(\left(x \cdot 3 + 3 \cdot \frac{-4}{29}\right), y\right) \]

   4. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(x \cdot 3\right), \left(3 \cdot \frac{-4}{29}\right)\right), y\right) \]

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 3\right), \left(3 \cdot \frac{-4}{29}\right)\right), y\right) \]

   6. metadata-eval 99.8%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 3\right), \frac{-12}{29}\right), y\right) \]

6. Applied egg-rr 99.8%

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

Alternative 2: 97.5% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.14)
   (* (* x 3.0) y)
   (if (<= x 0.14) (* -0.41379310344827586 y) (* 3.0 (* x y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.14) {
		tmp = (x * 3.0) * y;
	} else if (x <= 0.14) {
		tmp = -0.41379310344827586 * y;
	} else {
		tmp = 3.0 * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.14d0)) then
        tmp = (x * 3.0d0) * y
    else if (x <= 0.14d0) then
        tmp = (-0.41379310344827586d0) * y
    else
        tmp = 3.0d0 * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.14) {
		tmp = (x * 3.0) * y;
	} else if (x <= 0.14) {
		tmp = -0.41379310344827586 * y;
	} else {
		tmp = 3.0 * (x * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.14:
		tmp = (x * 3.0) * y
	elif x <= 0.14:
		tmp = -0.41379310344827586 * y
	else:
		tmp = 3.0 * (x * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.14)
		tmp = Float64(Float64(x * 3.0) * y);
	elseif (x <= 0.14)
		tmp = Float64(-0.41379310344827586 * y);
	else
		tmp = Float64(3.0 * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.14)
		tmp = (x * 3.0) * y;
	elseif (x <= 0.14)
		tmp = -0.41379310344827586 * y;
	else
		tmp = 3.0 * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.14], N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[x, 0.14], N[(-0.41379310344827586 * y), $MachinePrecision], N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.14000000000000001

   1. Initial program 99.8%

      \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
   2. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(x - \frac{16}{116}\right) \cdot 3\right), \color{blue}{y}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x - \frac{16}{116}\right), 3\right), y\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{16}{116}\right)\right)\right), 3\right), y\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\frac{16}{116}\right)\right)\right), 3\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\frac{4}{29}\right)\right)\right), 3\right), y\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{-4}{29}\right), 3\right), y\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(\left(x + -0.13793103448275862\right) \cdot 3\right) \cdot y} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{x}, 3\right), y\right) \]
   6. Step-by-step derivation

   7. Simplified 97.9%

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

   if -0.14000000000000001 < x < 0.14000000000000001

   1. Initial program 99.9%

      \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
   2. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(x - \frac{16}{116}\right) \cdot 3\right), \color{blue}{y}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x - \frac{16}{116}\right), 3\right), y\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{16}{116}\right)\right)\right), 3\right), y\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\frac{16}{116}\right)\right)\right), 3\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\frac{4}{29}\right)\right)\right), 3\right), y\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{-4}{29}\right), 3\right), y\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(\left(x + -0.13793103448275862\right) \cdot 3\right) \cdot y} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-12}{29} \cdot y} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 97.5%

         \[\leadsto \mathsf{*.f64}\left(\frac{-12}{29}, \color{blue}{y}\right) \]

   7. Simplified 97.5%

      \[\leadsto \color{blue}{-0.41379310344827586 \cdot y} \]

   if 0.14000000000000001 < x

   1. Initial program 99.7%

      \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
   2. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(x - \frac{16}{116}\right) \cdot 3\right), \color{blue}{y}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x - \frac{16}{116}\right), 3\right), y\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{16}{116}\right)\right)\right), 3\right), y\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\frac{16}{116}\right)\right)\right), 3\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\frac{4}{29}\right)\right)\right), 3\right), y\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{-4}{29}\right), 3\right), y\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(\left(x + -0.13793103448275862\right) \cdot 3\right) \cdot y} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{\left(\left(x + \frac{-4}{29}\right) \cdot 3\right)} \]

      2. associate-*r* N/A

         \[\leadsto \left(y \cdot \left(x + \frac{-4}{29}\right)\right) \cdot \color{blue}{3} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y \cdot \left(x + \frac{-4}{29}\right)\right), \color{blue}{3}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(x + \frac{-4}{29}\right) \cdot y\right), 3\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x + \frac{-4}{29}\right), y\right), 3\right) \]

      6. +-lowering-+.f64 99.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{-4}{29}\right), y\right), 3\right) \]

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(x \cdot y\right)}, 3\right) \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y \cdot x\right), 3\right) \]

      2. *-lowering-*.f64 97.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, x\right), 3\right) \]

   9. Simplified 97.4%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot 3 \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.6%

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

Alternative 3: 97.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x \cdot 3\right) \cdot y\\ \mathbf{if}\;x \leq -0.14:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.14:\\ \;\;\;\;-0.41379310344827586 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (* x 3.0) y)))
   (if (<= x -0.14) t_0 (if (<= x 0.14) (* -0.41379310344827586 y) t_0))))

C

double code(double x, double y) {
	double t_0 = (x * 3.0) * y;
	double tmp;
	if (x <= -0.14) {
		tmp = t_0;
	} else if (x <= 0.14) {
		tmp = -0.41379310344827586 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * 3.0d0) * y
    if (x <= (-0.14d0)) then
        tmp = t_0
    else if (x <= 0.14d0) then
        tmp = (-0.41379310344827586d0) * y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x * 3.0) * y;
	double tmp;
	if (x <= -0.14) {
		tmp = t_0;
	} else if (x <= 0.14) {
		tmp = -0.41379310344827586 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x * 3.0) * y
	tmp = 0
	if x <= -0.14:
		tmp = t_0
	elif x <= 0.14:
		tmp = -0.41379310344827586 * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x * 3.0) * y)
	tmp = 0.0
	if (x <= -0.14)
		tmp = t_0;
	elseif (x <= 0.14)
		tmp = Float64(-0.41379310344827586 * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x * 3.0) * y;
	tmp = 0.0;
	if (x <= -0.14)
		tmp = t_0;
	elseif (x <= 0.14)
		tmp = -0.41379310344827586 * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[x, -0.14], t$95$0, If[LessEqual[x, 0.14], N[(-0.41379310344827586 * y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.14000000000000001 or 0.14000000000000001 < x

   1. Initial program 99.7%

      \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
   2. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(x - \frac{16}{116}\right) \cdot 3\right), \color{blue}{y}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x - \frac{16}{116}\right), 3\right), y\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{16}{116}\right)\right)\right), 3\right), y\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\frac{16}{116}\right)\right)\right), 3\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\frac{4}{29}\right)\right)\right), 3\right), y\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{-4}{29}\right), 3\right), y\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(\left(x + -0.13793103448275862\right) \cdot 3\right) \cdot y} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{x}, 3\right), y\right) \]
   6. Step-by-step derivation

   7. Simplified 97.6%

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

   if -0.14000000000000001 < x < 0.14000000000000001

   1. Initial program 99.9%

      \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
   2. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(x - \frac{16}{116}\right) \cdot 3\right), \color{blue}{y}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x - \frac{16}{116}\right), 3\right), y\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{16}{116}\right)\right)\right), 3\right), y\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\frac{16}{116}\right)\right)\right), 3\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\frac{4}{29}\right)\right)\right), 3\right), y\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{-4}{29}\right), 3\right), y\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(\left(x + -0.13793103448275862\right) \cdot 3\right) \cdot y} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-12}{29} \cdot y} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 97.5%

         \[\leadsto \mathsf{*.f64}\left(\frac{-12}{29}, \color{blue}{y}\right) \]

   7. Simplified 97.5%

      \[\leadsto \color{blue}{-0.41379310344827586 \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 97.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(3 \cdot y\right)\\ \mathbf{if}\;x \leq -0.14:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.14:\\ \;\;\;\;-0.41379310344827586 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (* 3.0 y))))
   (if (<= x -0.14) t_0 (if (<= x 0.14) (* -0.41379310344827586 y) t_0))))

C

double code(double x, double y) {
	double t_0 = x * (3.0 * y);
	double tmp;
	if (x <= -0.14) {
		tmp = t_0;
	} else if (x <= 0.14) {
		tmp = -0.41379310344827586 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (3.0d0 * y)
    if (x <= (-0.14d0)) then
        tmp = t_0
    else if (x <= 0.14d0) then
        tmp = (-0.41379310344827586d0) * y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x * (3.0 * y);
	double tmp;
	if (x <= -0.14) {
		tmp = t_0;
	} else if (x <= 0.14) {
		tmp = -0.41379310344827586 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (3.0 * y)
	tmp = 0
	if x <= -0.14:
		tmp = t_0
	elif x <= 0.14:
		tmp = -0.41379310344827586 * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(3.0 * y))
	tmp = 0.0
	if (x <= -0.14)
		tmp = t_0;
	elseif (x <= 0.14)
		tmp = Float64(-0.41379310344827586 * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * (3.0 * y);
	tmp = 0.0;
	if (x <= -0.14)
		tmp = t_0;
	elseif (x <= 0.14)
		tmp = -0.41379310344827586 * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.14], t$95$0, If[LessEqual[x, 0.14], N[(-0.41379310344827586 * y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.14000000000000001 or 0.14000000000000001 < x

   1. Initial program 99.7%

      \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
   2. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(x - \frac{16}{116}\right) \cdot 3\right), \color{blue}{y}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x - \frac{16}{116}\right), 3\right), y\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{16}{116}\right)\right)\right), 3\right), y\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\frac{16}{116}\right)\right)\right), 3\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\frac{4}{29}\right)\right)\right), 3\right), y\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{-4}{29}\right), 3\right), y\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(\left(x + -0.13793103448275862\right) \cdot 3\right) \cdot y} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{x}, 3\right), y\right) \]
   6. Step-by-step derivation

   7. Simplified 97.6%

      \[\leadsto \left(\color{blue}{x} \cdot 3\right) \cdot y \]
   8. Step-by-step derivation

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(3 \cdot y\right), \color{blue}{x}\right) \]

      4. *-lowering-*.f64 97.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(3, y\right), x\right) \]

   9. Applied egg-rr 97.5%

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

   if -0.14000000000000001 < x < 0.14000000000000001

   1. Initial program 99.9%

      \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
   2. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(x - \frac{16}{116}\right) \cdot 3\right), \color{blue}{y}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x - \frac{16}{116}\right), 3\right), y\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{16}{116}\right)\right)\right), 3\right), y\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\frac{16}{116}\right)\right)\right), 3\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\frac{4}{29}\right)\right)\right), 3\right), y\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{-4}{29}\right), 3\right), y\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(\left(x + -0.13793103448275862\right) \cdot 3\right) \cdot y} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-12}{29} \cdot y} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 97.5%

         \[\leadsto \mathsf{*.f64}\left(\frac{-12}{29}, \color{blue}{y}\right) \]

   7. Simplified 97.5%

      \[\leadsto \color{blue}{-0.41379310344827586 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.5%

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

Alternative 5: 99.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ y \cdot \left(3 \cdot \left(x + -0.13793103448275862\right)\right) \end{array} \]

FPCore

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

C

double code(double x, double y) {
	return y * (3.0 * (x + -0.13793103448275862));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y * (3.0d0 * (x + (-0.13793103448275862d0)))
end function

Java

public static double code(double x, double y) {
	return y * (3.0 * (x + -0.13793103448275862));
}

Python

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

Julia

function code(x, y)
	return Float64(y * Float64(3.0 * Float64(x + -0.13793103448275862)))
end

MATLAB

function tmp = code(x, y)
	tmp = y * (3.0 * (x + -0.13793103448275862));
end

Wolfram

code[x_, y_] := N[(y * N[(3.0 * N[(x + -0.13793103448275862), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
2. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\left(x - \frac{16}{116}\right) \cdot 3\right), \color{blue}{y}\right) \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x - \frac{16}{116}\right), 3\right), y\right) \]

   3. sub-neg N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{16}{116}\right)\right)\right), 3\right), y\right) \]

   4. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\frac{16}{116}\right)\right)\right), 3\right), y\right) \]

   5. metadata-eval N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\frac{4}{29}\right)\right)\right), 3\right), y\right) \]

   6. metadata-eval 99.8%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{-4}{29}\right), 3\right), y\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\left(\left(x + -0.13793103448275862\right) \cdot 3\right) \cdot y} \]
4. Add Preprocessing

5. Final simplification 99.8%

   \[\leadsto y \cdot \left(3 \cdot \left(x + -0.13793103448275862\right)\right) \]
6. Add Preprocessing

Alternative 6: 50.4% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ -0.41379310344827586 \cdot y \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
2. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\left(x - \frac{16}{116}\right) \cdot 3\right), \color{blue}{y}\right) \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x - \frac{16}{116}\right), 3\right), y\right) \]

   3. sub-neg N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{16}{116}\right)\right)\right), 3\right), y\right) \]

   4. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\frac{16}{116}\right)\right)\right), 3\right), y\right) \]

   5. metadata-eval N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\frac{4}{29}\right)\right)\right), 3\right), y\right) \]

   6. metadata-eval 99.8%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{-4}{29}\right), 3\right), y\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\left(\left(x + -0.13793103448275862\right) \cdot 3\right) \cdot y} \]
4. Add Preprocessing

5. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{-12}{29} \cdot y} \]
6. Step-by-step derivation

   1. *-lowering-*.f64 46.1%

      \[\leadsto \mathsf{*.f64}\left(\frac{-12}{29}, \color{blue}{y}\right) \]

7. Simplified 46.1%

   \[\leadsto \color{blue}{-0.41379310344827586 \cdot y} \]
8. Add Preprocessing

Developer Target 1: 99.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ y \cdot \left(x \cdot 3 - 0.41379310344827586\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024150 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (* y (- (* x 3) 20689655172413793/50000000000000000)))

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