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

Percentage Accurate: 100.0% → 100.0%

Time: 4.5s

Alternatives: 7

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x - \frac{y}{200} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- x (/ y 200.0)))

C

double code(double x, double y) {
	return x - (y / 200.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x - (y / 200.0d0)
end function

Java

public static double code(double x, double y) {
	return x - (y / 200.0);
}

Python

def code(x, y):
	return x - (y / 200.0)

Julia

function code(x, y)
	return Float64(x - Float64(y / 200.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x - (y / 200.0);
end

Wolfram

code[x_, y_] := N[(x - N[(y / 200.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{y}{200} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- x (/ y 200.0)))

C

double code(double x, double y) {
	return x - (y / 200.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x - (y / 200.0d0)
end function

Java

public static double code(double x, double y) {
	return x - (y / 200.0);
}

Python

def code(x, y):
	return x - (y / 200.0)

Julia

function code(x, y)
	return Float64(x - Float64(y / 200.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x - (y / 200.0);
end

Wolfram

code[x_, y_] := N[(x - N[(y / 200.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{y}{200} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- x (/ y 200.0)))

C

double code(double x, double y) {
	return x - (y / 200.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x - (y / 200.0d0)
end function

Java

public static double code(double x, double y) {
	return x - (y / 200.0);
}

Python

def code(x, y):
	return x - (y / 200.0)

Julia

function code(x, y)
	return Float64(x - Float64(y / 200.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x - (y / 200.0);
end

Wolfram

code[x_, y_] := N[(x - N[(y / 200.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x - \frac{y}{200} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 75.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-10}:\\ \;\;\;\;x - y\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-19}:\\ \;\;\;\;y \cdot -0.005\\ \mathbf{else}:\\ \;\;\;\;x - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.85e-10) (- x y) (if (<= x 3.5e-19) (* y -0.005) (- x y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.85e-10) {
		tmp = x - y;
	} else if (x <= 3.5e-19) {
		tmp = y * -0.005;
	} else {
		tmp = 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 <= (-1.85d-10)) then
        tmp = x - y
    else if (x <= 3.5d-19) then
        tmp = y * (-0.005d0)
    else
        tmp = x - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.85e-10) {
		tmp = x - y;
	} else if (x <= 3.5e-19) {
		tmp = y * -0.005;
	} else {
		tmp = x - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.85e-10:
		tmp = x - y
	elif x <= 3.5e-19:
		tmp = y * -0.005
	else:
		tmp = x - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.85e-10)
		tmp = Float64(x - y);
	elseif (x <= 3.5e-19)
		tmp = Float64(y * -0.005);
	else
		tmp = Float64(x - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.85e-10)
		tmp = x - y;
	elseif (x <= 3.5e-19)
		tmp = y * -0.005;
	else
		tmp = x - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.85e-10], N[(x - y), $MachinePrecision], If[LessEqual[x, 3.5e-19], N[(y * -0.005), $MachinePrecision], N[(x - y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.85000000000000007e-10 or 3.50000000000000015e-19 < x

   1. Initial program 100.0%

      \[x - \frac{y}{200} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf

      \[\leadsto x - \color{blue}{-1 \cdot y} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \]

      2. lower-neg.f64 82.1

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

   5. Simplified 82.1%

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

      1. lift-neg.f64 N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \]

      2. remove-double-div N/A

         \[\leadsto x - \color{blue}{\frac{1}{\frac{1}{\mathsf{neg}\left(y\right)}}} \]

      3. inv-pow N/A

         \[\leadsto x - \frac{1}{\color{blue}{{\left(\mathsf{neg}\left(y\right)\right)}^{-1}}} \]

      4. metadata-eval N/A

         \[\leadsto x - \frac{1}{{\left(\mathsf{neg}\left(y\right)\right)}^{\color{blue}{\left(2 \cdot \frac{-1}{2}\right)}}} \]

      5. metadata-eval N/A

         \[\leadsto x - \frac{1}{{\left(\mathsf{neg}\left(y\right)\right)}^{\left(2 \cdot \color{blue}{\frac{-1}{2}}\right)}} \]

      6. pow-pow N/A

         \[\leadsto x - \frac{1}{\color{blue}{{\left({\left(\mathsf{neg}\left(y\right)\right)}^{2}\right)}^{\left(\frac{-1}{2}\right)}}} \]

      7. pow2 N/A

         \[\leadsto x - \frac{1}{{\color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}}^{\left(\frac{-1}{2}\right)}} \]

      8. lift-neg.f64 N/A

         \[\leadsto x - \frac{1}{{\left(\color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}^{\left(\frac{-1}{2}\right)}} \]

      9. lift-neg.f64 N/A

         \[\leadsto x - \frac{1}{{\left(\left(\mathsf{neg}\left(y\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)}^{\left(\frac{-1}{2}\right)}} \]

      10. sqr-neg N/A

          \[\leadsto x - \frac{1}{{\color{blue}{\left(y \cdot y\right)}}^{\left(\frac{-1}{2}\right)}} \]

      11. pow-prod-down N/A

          \[\leadsto x - \frac{1}{\color{blue}{{y}^{\left(\frac{-1}{2}\right)} \cdot {y}^{\left(\frac{-1}{2}\right)}}} \]

      12. sqr-pow N/A

          \[\leadsto x - \frac{1}{\color{blue}{{y}^{-1}}} \]

      13. inv-pow N/A

          \[\leadsto x - \frac{1}{\color{blue}{\frac{1}{y}}} \]

      14. remove-double-div N/A

          \[\leadsto x - \color{blue}{y} \]

      15. lower--.f64 84.1

          \[\leadsto \color{blue}{x - y} \]

   7. Applied egg-rr 84.1%

      \[\leadsto \color{blue}{x - y} \]

   if -1.85000000000000007e-10 < x < 3.50000000000000015e-19

   1. Initial program 100.0%

      \[x - \frac{y}{200} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1}{200} \cdot y} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{y \cdot \frac{-1}{200}} \]

      2. lower-*.f64 74.5

         \[\leadsto \color{blue}{y \cdot -0.005} \]

   5. Simplified 74.5%

      \[\leadsto \color{blue}{y \cdot -0.005} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 99.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, -0.005, x\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma y -0.005 x))

C

double code(double x, double y) {
	return fma(y, -0.005, x);
}

Julia

function code(x, y)
	return fma(y, -0.005, x)
end

Wolfram

code[x_, y_] := N[(y * -0.005 + x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x - \frac{y}{200} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto x - \color{blue}{\frac{y}{200}} \]

   2. sub-neg N/A

      \[\leadsto \color{blue}{x + \left(\mathsf{neg}\left(\frac{y}{200}\right)\right)} \]

   3. +-commutative N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{y}{200}\right)\right) + x} \]

   4. lift-/.f64 N/A

      \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\frac{y}{200}}\right)\right) + x \]

   5. distribute-neg-frac2 N/A

      \[\leadsto \color{blue}{\frac{y}{\mathsf{neg}\left(200\right)}} + x \]

   6. div-inv N/A

      \[\leadsto \color{blue}{y \cdot \frac{1}{\mathsf{neg}\left(200\right)}} + x \]

   7. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{1}{\mathsf{neg}\left(200\right)}, x\right)} \]

   8. metadata-eval N/A

      \[\leadsto \mathsf{fma}\left(y, \frac{1}{\color{blue}{-200}}, x\right) \]

   9. metadata-eval 99.9

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{-0.005}, x\right) \]

4. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, -0.005, x\right)} \]
5. Add Preprocessing

Alternative 4: 56.0% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ x - y \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x - \frac{y}{200} \]
2. Add Preprocessing

3. Taylor expanded in y around -inf

   \[\leadsto x - \color{blue}{-1 \cdot y} \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \]

   2. lower-neg.f64 54.1

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

5. Simplified 54.1%

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

   1. lift-neg.f64 N/A

      \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \]

   2. remove-double-div N/A

      \[\leadsto x - \color{blue}{\frac{1}{\frac{1}{\mathsf{neg}\left(y\right)}}} \]

   3. inv-pow N/A

      \[\leadsto x - \frac{1}{\color{blue}{{\left(\mathsf{neg}\left(y\right)\right)}^{-1}}} \]

   4. metadata-eval N/A

      \[\leadsto x - \frac{1}{{\left(\mathsf{neg}\left(y\right)\right)}^{\color{blue}{\left(2 \cdot \frac{-1}{2}\right)}}} \]

   5. metadata-eval N/A

      \[\leadsto x - \frac{1}{{\left(\mathsf{neg}\left(y\right)\right)}^{\left(2 \cdot \color{blue}{\frac{-1}{2}}\right)}} \]

   6. pow-pow N/A

      \[\leadsto x - \frac{1}{\color{blue}{{\left({\left(\mathsf{neg}\left(y\right)\right)}^{2}\right)}^{\left(\frac{-1}{2}\right)}}} \]

   7. pow2 N/A

      \[\leadsto x - \frac{1}{{\color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}}^{\left(\frac{-1}{2}\right)}} \]

   8. lift-neg.f64 N/A

      \[\leadsto x - \frac{1}{{\left(\color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}^{\left(\frac{-1}{2}\right)}} \]

   9. lift-neg.f64 N/A

      \[\leadsto x - \frac{1}{{\left(\left(\mathsf{neg}\left(y\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)}^{\left(\frac{-1}{2}\right)}} \]

   10. sqr-neg N/A

       \[\leadsto x - \frac{1}{{\color{blue}{\left(y \cdot y\right)}}^{\left(\frac{-1}{2}\right)}} \]

   11. pow-prod-down N/A

       \[\leadsto x - \frac{1}{\color{blue}{{y}^{\left(\frac{-1}{2}\right)} \cdot {y}^{\left(\frac{-1}{2}\right)}}} \]

   12. sqr-pow N/A

       \[\leadsto x - \frac{1}{\color{blue}{{y}^{-1}}} \]

   13. inv-pow N/A

       \[\leadsto x - \frac{1}{\color{blue}{\frac{1}{y}}} \]

   14. remove-double-div N/A

       \[\leadsto x - \color{blue}{y} \]

   15. lower--.f64 59.8

       \[\leadsto \color{blue}{x - y} \]

7. Applied egg-rr 59.8%

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

Alternative 5: 49.6% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ x + y \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x - \frac{y}{200} \]
2. Add Preprocessing

3. Taylor expanded in y around -inf

   \[\leadsto x - \color{blue}{-1 \cdot y} \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \]

   2. lower-neg.f64 54.1

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

5. Simplified 54.1%

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

   1. lift-neg.f64 N/A

      \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \]

   2. sub-neg N/A

      \[\leadsto \color{blue}{x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right)} \]

   3. lift-neg.f64 N/A

      \[\leadsto x + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

   4. remove-double-neg N/A

      \[\leadsto x + \color{blue}{y} \]

   5. +-commutative N/A

      \[\leadsto \color{blue}{y + x} \]

   6. lower-+.f64 54.1

      \[\leadsto \color{blue}{y + x} \]

7. Applied egg-rr 54.1%

   \[\leadsto \color{blue}{y + x} \]

8. Final simplification 54.1%

   \[\leadsto x + y \]
9. Add Preprocessing

Alternative 6: 8.8% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return -y

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := (-y)

Derivation

1. Initial program 100.0%

   \[x - \frac{y}{200} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{-1}{200} \cdot y} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{y \cdot \frac{-1}{200}} \]

   2. lower-*.f64 44.4

      \[\leadsto \color{blue}{y \cdot -0.005} \]

5. Simplified 44.4%

   \[\leadsto \color{blue}{y \cdot -0.005} \]

6. Taylor expanded in y around -inf

   \[\leadsto \color{blue}{-1 \cdot y} \]
7. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(y\right)} \]

   2. lower-neg.f64 8.3

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

8. Simplified 8.3%

   \[\leadsto \color{blue}{-y} \]
9. Add Preprocessing

Alternative 7: 2.3% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 y)

C

double code(double x, double y) {
	return y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y
end function

Java

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

Python

def code(x, y):
	return y

Julia

function code(x, y)
	return y
end

MATLAB

function tmp = code(x, y)
	tmp = y;
end

Wolfram

code[x_, y_] := y

Derivation

1. Initial program 100.0%

   \[x - \frac{y}{200} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{-1}{200} \cdot y} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{y \cdot \frac{-1}{200}} \]

   2. lower-*.f64 44.4

      \[\leadsto \color{blue}{y \cdot -0.005} \]

5. Simplified 44.4%

   \[\leadsto \color{blue}{y \cdot -0.005} \]

6. Taylor expanded in y around -inf

   \[\leadsto \color{blue}{-1 \cdot y} \]
7. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(y\right)} \]

   2. lower-neg.f64 8.3

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

8. Simplified 8.3%

   \[\leadsto \color{blue}{-y} \]
9. Step-by-step derivation

   1. neg-sub0 N/A

      \[\leadsto \color{blue}{0 - y} \]

   2. flip3-- N/A

      \[\leadsto \color{blue}{\frac{{0}^{3} - {y}^{3}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)}} \]

   3. metadata-eval N/A

      \[\leadsto \frac{\color{blue}{0} - {y}^{3}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   4. neg-sub0 N/A

      \[\leadsto \frac{\color{blue}{\mathsf{neg}\left({y}^{3}\right)}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   5. cube-neg N/A

      \[\leadsto \frac{\color{blue}{{\left(\mathsf{neg}\left(y\right)\right)}^{3}}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   6. lift-neg.f64 N/A

      \[\leadsto \frac{{\color{blue}{\left(\mathsf{neg}\left(y\right)\right)}}^{3}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   7. sqr-pow N/A

      \[\leadsto \frac{\color{blue}{{\left(\mathsf{neg}\left(y\right)\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(\mathsf{neg}\left(y\right)\right)}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   8. unpow-prod-down N/A

      \[\leadsto \frac{\color{blue}{{\left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   9. lift-neg.f64 N/A

      \[\leadsto \frac{{\left(\color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   10. lift-neg.f64 N/A

       \[\leadsto \frac{{\left(\left(\mathsf{neg}\left(y\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   11. sqr-neg N/A

       \[\leadsto \frac{{\color{blue}{\left(y \cdot y\right)}}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   12. pow-prod-down N/A

       \[\leadsto \frac{\color{blue}{{y}^{\left(\frac{3}{2}\right)} \cdot {y}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   13. sqr-pow N/A

       \[\leadsto \frac{\color{blue}{{y}^{3}}}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   14. metadata-eval N/A

       \[\leadsto \frac{{y}^{3}}{\color{blue}{0} + \left(y \cdot y + 0 \cdot y\right)} \]

   15. +-lft-identity N/A

       \[\leadsto \frac{{y}^{3}}{\color{blue}{y \cdot y + 0 \cdot y}} \]

   16. distribute-rgt-out N/A

       \[\leadsto \frac{{y}^{3}}{\color{blue}{y \cdot \left(y + 0\right)}} \]

   17. +-commutative N/A

       \[\leadsto \frac{{y}^{3}}{y \cdot \color{blue}{\left(0 + y\right)}} \]

   18. +-lft-identity N/A

       \[\leadsto \frac{{y}^{3}}{y \cdot \color{blue}{y}} \]

   19. pow2 N/A

       \[\leadsto \frac{{y}^{3}}{\color{blue}{{y}^{2}}} \]

   20. pow-div N/A

       \[\leadsto \color{blue}{{y}^{\left(3 - 2\right)}} \]

   21. metadata-eval N/A

       \[\leadsto {y}^{\color{blue}{1}} \]

   22. unpow1 2.5

       \[\leadsto \color{blue}{y} \]

10. Applied egg-rr 2.5%

    \[\leadsto \color{blue}{y} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024214 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, D"
  :precision binary64
  (- x (/ y 200.0)))