Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A

Percentage Accurate: 100.0% → 100.0%

Time: 8.2s

Alternatives: 8

Speedup: 0.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, 1 - y, y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma x (- 1.0 y) y))

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) - x \cdot y \]
2. Step-by-step derivation

   1. +-commutative 100.0%

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

   2. *-commutative 100.0%

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

   3. associate--l+ 100.0%

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

   4. +-commutative 100.0%

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

   5. *-lft-identity 100.0%

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

   6. metadata-eval 100.0%

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

   7. distribute-rgt-out-- 100.0%

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

   8. fma-define 100.0%

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

   9. metadata-eval 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, 1 - y, y\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 86.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8500:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-14}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -8500.0) (* x (- y)) (if (<= y 1.22e-14) (+ x y) (* y (- 1.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -8500.0) {
		tmp = x * -y;
	} else if (y <= 1.22e-14) {
		tmp = x + y;
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-8500.0d0)) then
        tmp = x * -y
    else if (y <= 1.22d-14) then
        tmp = x + y
    else
        tmp = y * (1.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -8500.0) {
		tmp = x * -y;
	} else if (y <= 1.22e-14) {
		tmp = x + y;
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -8500.0:
		tmp = x * -y
	elif y <= 1.22e-14:
		tmp = x + y
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -8500.0)
		tmp = Float64(x * Float64(-y));
	elseif (y <= 1.22e-14)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -8500.0)
		tmp = x * -y;
	elseif (y <= 1.22e-14)
		tmp = x + y;
	else
		tmp = y * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -8500.0], N[(x * (-y)), $MachinePrecision], If[LessEqual[y, 1.22e-14], N[(x + y), $MachinePrecision], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8500

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. remove-double-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate--l+ 100.0%

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

      7. neg-mul-1 100.0%

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

      8. cancel-sign-sub-inv 100.0%

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

      9. distribute-lft-neg-out 100.0%

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

      10. distribute-rgt-neg-out 100.0%

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

      11. *-commutative 100.0%

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

      12. distribute-rgt-out 100.0%

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

      13. +-commutative 100.0%

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

      14. sub-neg 100.0%

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

      15. metadata-eval 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{y + x \cdot \left(1 - y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 99.1%

      \[\leadsto \color{blue}{y \cdot \left(1 + -1 \cdot x\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 99.1%

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

      2. sub-neg 99.1%

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

   7. Simplified 99.1%

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

   8. Taylor expanded in x around inf 45.5%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot y\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 45.5%

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

      2. distribute-lft-neg-out 45.5%

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

      3. *-commutative 45.5%

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

   10. Simplified 45.5%

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

   if -8500 < y < 1.21999999999999994e-14

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. remove-double-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate--l+ 100.0%

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

      7. neg-mul-1 100.0%

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

      8. cancel-sign-sub-inv 100.0%

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

      9. distribute-lft-neg-out 100.0%

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

      10. distribute-rgt-neg-out 100.0%

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

      11. *-commutative 100.0%

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

      12. distribute-rgt-out 100.0%

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

      13. +-commutative 100.0%

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

      14. sub-neg 100.0%

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

      15. metadata-eval 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{y + x \cdot \left(1 - y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 98.4%

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

   if 1.21999999999999994e-14 < y

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. remove-double-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate--l+ 100.0%

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

      7. neg-mul-1 100.0%

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

      8. cancel-sign-sub-inv 100.0%

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

      9. distribute-lft-neg-out 100.0%

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

      10. distribute-rgt-neg-out 100.0%

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

      11. *-commutative 100.0%

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

      12. distribute-rgt-out 100.0%

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

      13. +-commutative 100.0%

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

      14. sub-neg 100.0%

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

      15. metadata-eval 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{y + x \cdot \left(1 - y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 99.0%

      \[\leadsto \color{blue}{y \cdot \left(1 + -1 \cdot x\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 99.0%

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

      2. sub-neg 99.0%

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

   7. Simplified 99.0%

      \[\leadsto \color{blue}{y \cdot \left(1 - x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8500:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-14}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 18000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x 18000.0) (+ x y) (* x (- y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 18000.0) {
		tmp = x + y;
	} 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 <= 18000.0d0) then
        tmp = x + y
    else
        tmp = x * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 18000.0) {
		tmp = x + y;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 18000.0:
		tmp = x + y
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 18000.0)
		tmp = Float64(x + y);
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 18000.0)
		tmp = x + y;
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 18000.0], N[(x + y), $MachinePrecision], N[(x * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 18000

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. remove-double-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate--l+ 100.0%

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

      7. neg-mul-1 100.0%

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

      8. cancel-sign-sub-inv 100.0%

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

      9. distribute-lft-neg-out 100.0%

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

      10. distribute-rgt-neg-out 100.0%

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

      11. *-commutative 100.0%

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

      12. distribute-rgt-out 100.0%

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

      13. +-commutative 100.0%

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

      14. sub-neg 100.0%

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

      15. metadata-eval 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{y + x \cdot \left(1 - y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 84.2%

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

   if 18000 < x

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. remove-double-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate--l+ 100.0%

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

      7. neg-mul-1 100.0%

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

      8. cancel-sign-sub-inv 100.0%

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

      9. distribute-lft-neg-out 100.0%

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

      10. distribute-rgt-neg-out 100.0%

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

      11. *-commutative 100.0%

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

      12. distribute-rgt-out 100.0%

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

      13. +-commutative 100.0%

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

      14. sub-neg 100.0%

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

      15. metadata-eval 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{y + x \cdot \left(1 - y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 44.3%

      \[\leadsto \color{blue}{y \cdot \left(1 + -1 \cdot x\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 44.3%

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

      2. sub-neg 44.3%

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

   7. Simplified 44.3%

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

   8. Taylor expanded in x around inf 42.7%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot y\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 42.7%

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

      2. distribute-lft-neg-out 42.7%

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

      3. *-commutative 42.7%

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

   10. Simplified 42.7%

       \[\leadsto \color{blue}{y \cdot \left(-x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 18000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ y + x \cdot \left(1 - y\right) \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y + (x * (1.0d0 - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) - x \cdot y \]
2. Step-by-step derivation

   1. associate--l+ 100.0%

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

   2. +-commutative 100.0%

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

   3. remove-double-neg 100.0%

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

   4. unsub-neg 100.0%

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

   5. cancel-sign-sub-inv 100.0%

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

   6. associate--l+ 100.0%

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

   7. neg-mul-1 100.0%

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

   8. cancel-sign-sub-inv 100.0%

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

   9. distribute-lft-neg-out 100.0%

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

   10. distribute-rgt-neg-out 100.0%

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

   11. *-commutative 100.0%

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

   12. distribute-rgt-out 100.0%

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

   13. +-commutative 100.0%

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

   14. sub-neg 100.0%

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

   15. metadata-eval 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{y + x \cdot \left(1 - y\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 5: 48.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-146}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x -1.35e-146) x y))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.35e-146) {
		tmp = x;
	} else {
		tmp = 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 <= (-1.35d-146)) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.35e-146) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.35e-146:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.35e-146)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.35e-146)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.35e-146], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -1.34999999999999997e-146

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. remove-double-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate--l+ 100.0%

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

      7. neg-mul-1 100.0%

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

      8. cancel-sign-sub-inv 100.0%

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

      9. distribute-lft-neg-out 100.0%

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

      10. distribute-rgt-neg-out 100.0%

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

      11. *-commutative 100.0%

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

      12. distribute-rgt-out 100.0%

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

      13. +-commutative 100.0%

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

      14. sub-neg 100.0%

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

      15. metadata-eval 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{y + x \cdot \left(1 - y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 67.6%

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

   6. Taylor expanded in y around 0 43.0%

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

   if -1.34999999999999997e-146 < x

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. remove-double-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate--l+ 100.0%

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

      7. neg-mul-1 100.0%

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

      8. cancel-sign-sub-inv 100.0%

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

      9. distribute-lft-neg-out 100.0%

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

      10. distribute-rgt-neg-out 100.0%

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

      11. *-commutative 100.0%

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

      12. distribute-rgt-out 100.0%

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

      13. +-commutative 100.0%

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

      14. sub-neg 100.0%

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

      15. metadata-eval 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{y + x \cdot \left(1 - y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 46.8%

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

Alternative 6: 75.0% accurate, 2.3× 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%

   \[\left(x + y\right) - x \cdot y \]
2. Step-by-step derivation

   1. associate--l+ 100.0%

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

   2. +-commutative 100.0%

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

   3. remove-double-neg 100.0%

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

   4. unsub-neg 100.0%

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

   5. cancel-sign-sub-inv 100.0%

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

   6. associate--l+ 100.0%

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

   7. neg-mul-1 100.0%

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

   8. cancel-sign-sub-inv 100.0%

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

   9. distribute-lft-neg-out 100.0%

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

   10. distribute-rgt-neg-out 100.0%

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

   11. *-commutative 100.0%

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

   12. distribute-rgt-out 100.0%

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

   13. +-commutative 100.0%

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

   14. sub-neg 100.0%

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

   15. metadata-eval 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{y + x \cdot \left(1 - y\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 75.7%

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

6. Final simplification 75.7%

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

Alternative 7: 37.6% accurate, 7.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

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

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) - x \cdot y \]
2. Step-by-step derivation

   1. associate--l+ 100.0%

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

   2. +-commutative 100.0%

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

   3. remove-double-neg 100.0%

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

   4. unsub-neg 100.0%

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

   5. cancel-sign-sub-inv 100.0%

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

   6. associate--l+ 100.0%

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

   7. neg-mul-1 100.0%

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

   8. cancel-sign-sub-inv 100.0%

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

   9. distribute-lft-neg-out 100.0%

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

   10. distribute-rgt-neg-out 100.0%

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

   11. *-commutative 100.0%

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

   12. distribute-rgt-out 100.0%

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

   13. +-commutative 100.0%

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

   14. sub-neg 100.0%

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

   15. metadata-eval 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{y + x \cdot \left(1 - y\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 75.7%

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

6. Taylor expanded in y around 0 38.0%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Alternative 8: 2.6% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.0)

C

double code(double x, double y) {
	return 0.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.0d0
end function

Java

public static double code(double x, double y) {
	return 0.0;
}

Python

def code(x, y):
	return 0.0

Julia

function code(x, y)
	return 0.0
end

MATLAB

function tmp = code(x, y)
	tmp = 0.0;
end

Wolfram

code[x_, y_] := 0.0

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) - x \cdot y \]
2. Step-by-step derivation

   1. associate--l+ 100.0%

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

   2. +-commutative 100.0%

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

   3. remove-double-neg 100.0%

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

   4. unsub-neg 100.0%

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

   5. cancel-sign-sub-inv 100.0%

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

   6. associate--l+ 100.0%

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

   7. neg-mul-1 100.0%

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

   8. cancel-sign-sub-inv 100.0%

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

   9. distribute-lft-neg-out 100.0%

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

   10. distribute-rgt-neg-out 100.0%

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

   11. *-commutative 100.0%

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

   12. distribute-rgt-out 100.0%

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

   13. +-commutative 100.0%

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

   14. sub-neg 100.0%

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

   15. metadata-eval 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{y + x \cdot \left(1 - y\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around inf 63.7%

   \[\leadsto \color{blue}{y \cdot \left(1 + -1 \cdot x\right)} \]
6. Step-by-step derivation

   1. neg-mul-1 63.7%

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

   2. sub-neg 63.7%

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

7. Simplified 63.7%

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

8. Taylor expanded in x around inf 25.9%

   \[\leadsto \color{blue}{-1 \cdot \left(x \cdot y\right)} \]
9. Step-by-step derivation

   1. mul-1-neg 25.9%

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

   2. distribute-lft-neg-out 25.9%

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

   3. *-commutative 25.9%

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

10. Simplified 25.9%

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

    1. add-log-exp 12.9%

       \[\leadsto \color{blue}{\log \left(e^{y \cdot \left(-x\right)}\right)} \]

    2. add-sqr-sqrt 12.9%

       \[\leadsto \log \color{blue}{\left(\sqrt{e^{y \cdot \left(-x\right)}} \cdot \sqrt{e^{y \cdot \left(-x\right)}}\right)} \]

    3. sqrt-unprod 12.9%

       \[\leadsto \log \color{blue}{\left(\sqrt{e^{y \cdot \left(-x\right)} \cdot e^{y \cdot \left(-x\right)}}\right)} \]

    4. exp-prod 12.9%

       \[\leadsto \log \left(\sqrt{e^{y \cdot \left(-x\right)} \cdot \color{blue}{{\left(e^{y}\right)}^{\left(-x\right)}}}\right) \]

    5. add-sqr-sqrt 8.0%

       \[\leadsto \log \left(\sqrt{e^{y \cdot \left(-x\right)} \cdot {\left(e^{y}\right)}^{\left(-\color{blue}{\sqrt{x} \cdot \sqrt{x}}\right)}}\right) \]

    6. sqrt-unprod 8.2%

       \[\leadsto \log \left(\sqrt{e^{y \cdot \left(-x\right)} \cdot {\left(e^{y}\right)}^{\left(-\color{blue}{\sqrt{x \cdot x}}\right)}}\right) \]

    7. sqr-neg 8.2%

       \[\leadsto \log \left(\sqrt{e^{y \cdot \left(-x\right)} \cdot {\left(e^{y}\right)}^{\left(-\sqrt{\color{blue}{\left(-x\right) \cdot \left(-x\right)}}\right)}}\right) \]

    8. sqrt-unprod 1.6%

       \[\leadsto \log \left(\sqrt{e^{y \cdot \left(-x\right)} \cdot {\left(e^{y}\right)}^{\left(-\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}\right)}}\right) \]

    9. add-sqr-sqrt 1.8%

       \[\leadsto \log \left(\sqrt{e^{y \cdot \left(-x\right)} \cdot {\left(e^{y}\right)}^{\left(-\color{blue}{\left(-x\right)}\right)}}\right) \]

    10. pow-flip 1.8%

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

    11. exp-prod 1.6%

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

    12. rgt-mult-inverse 2.6%

        \[\leadsto \log \left(\sqrt{\color{blue}{1}}\right) \]

    13. metadata-eval 2.6%

        \[\leadsto \log \color{blue}{1} \]

    14. metadata-eval 2.6%

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

12. Applied egg-rr 2.6%

    \[\leadsto \color{blue}{0} \]
13. Add Preprocessing

Reproduce

herbie shell --seed 2024135 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))