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

Percentage Accurate: 100.0% → 100.0%

Time: 4.4s

Alternatives: 10

Speedup: 1.0×

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

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

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 (fma x (- 1.0 y) y))

C

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

Julia

x, y = sort([x, y])
function code(x, y)
	return fma(x, Float64(1.0 - y), y)
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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: 69.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-174}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-162}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+266}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (- y))))
   (if (<= y -1.0)
     t_0
     (if (<= y 2.9e-174)
       x
       (if (<= y 8.5e-162)
         y
         (if (<= y 7.5e-48) x (if (<= y 5.6e+266) y t_0)))))))

C

assert(x < y);
double code(double x, double y) {
	double t_0 = x * -y;
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 2.9e-174) {
		tmp = x;
	} else if (y <= 8.5e-162) {
		tmp = y;
	} else if (y <= 7.5e-48) {
		tmp = x;
	} else if (y <= 5.6e+266) {
		tmp = y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 * -y
    if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 2.9d-174) then
        tmp = x
    else if (y <= 8.5d-162) then
        tmp = y
    else if (y <= 7.5d-48) then
        tmp = x
    else if (y <= 5.6d+266) then
        tmp = y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y) {
	double t_0 = x * -y;
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 2.9e-174) {
		tmp = x;
	} else if (y <= 8.5e-162) {
		tmp = y;
	} else if (y <= 7.5e-48) {
		tmp = x;
	} else if (y <= 5.6e+266) {
		tmp = y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	t_0 = x * -y
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= 2.9e-174:
		tmp = x
	elif y <= 8.5e-162:
		tmp = y
	elif y <= 7.5e-48:
		tmp = x
	elif y <= 5.6e+266:
		tmp = y
	else:
		tmp = t_0
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	t_0 = Float64(x * Float64(-y))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 2.9e-174)
		tmp = x;
	elseif (y <= 8.5e-162)
		tmp = y;
	elseif (y <= 7.5e-48)
		tmp = x;
	elseif (y <= 5.6e+266)
		tmp = y;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	t_0 = x * -y;
	tmp = 0.0;
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 2.9e-174)
		tmp = x;
	elseif (y <= 8.5e-162)
		tmp = y;
	elseif (y <= 7.5e-48)
		tmp = x;
	elseif (y <= 5.6e+266)
		tmp = y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := Block[{t$95$0 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 2.9e-174], x, If[LessEqual[y, 8.5e-162], y, If[LessEqual[y, 7.5e-48], x, If[LessEqual[y, 5.6e+266], y, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 5.5999999999999999e266 < 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 98.2%

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

      1. mul-1-neg 98.2%

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

      2. unsub-neg 98.2%

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

   7. Simplified 98.2%

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

   8. Taylor expanded in x around inf 49.2%

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

      1. mul-1-neg 49.2%

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

      2. distribute-lft-neg-out 49.2%

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

      3. *-commutative 49.2%

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

   10. Simplified 49.2%

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

   if -1 < y < 2.9000000000000001e-174 or 8.49999999999999955e-162 < y < 7.50000000000000042e-48

   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 78.2%

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

   if 2.9000000000000001e-174 < y < 8.49999999999999955e-162 or 7.50000000000000042e-48 < y < 5.5999999999999999e266

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. remove-double-neg 99.9%

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

      4. unsub-neg 99.9%

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

      5. cancel-sign-sub-inv 99.9%

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

      6. associate--l+ 99.9%

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

      7. neg-mul-1 99.9%

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

      8. cancel-sign-sub-inv 99.9%

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

      9. distribute-lft-neg-out 99.9%

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

      10. distribute-rgt-neg-out 99.9%

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

      11. *-commutative 99.9%

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

      12. distribute-rgt-out 99.9%

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

      13. +-commutative 99.9%

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

      14. sub-neg 99.9%

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

      15. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 50.3%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-174}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-162}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+266}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-162} \lor \neg \left(y \leq 5.2 \cdot 10^{-47}\right):\\ \;\;\;\;y - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= y 2.9e-174)
   (* x (- 1.0 y))
   (if (or (<= y 8.5e-162) (not (<= y 5.2e-47))) (- y (* x y)) x)))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (y <= 2.9e-174) {
		tmp = x * (1.0 - y);
	} else if ((y <= 8.5e-162) || !(y <= 5.2e-47)) {
		tmp = y - (x * y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 2.9d-174) then
        tmp = x * (1.0d0 - y)
    else if ((y <= 8.5d-162) .or. (.not. (y <= 5.2d-47))) then
        tmp = y - (x * y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y) {
	double tmp;
	if (y <= 2.9e-174) {
		tmp = x * (1.0 - y);
	} else if ((y <= 8.5e-162) || !(y <= 5.2e-47)) {
		tmp = y - (x * y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if y <= 2.9e-174:
		tmp = x * (1.0 - y)
	elif (y <= 8.5e-162) or not (y <= 5.2e-47):
		tmp = y - (x * y)
	else:
		tmp = x
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (y <= 2.9e-174)
		tmp = Float64(x * Float64(1.0 - y));
	elseif ((y <= 8.5e-162) || !(y <= 5.2e-47))
		tmp = Float64(y - Float64(x * y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 2.9e-174)
		tmp = x * (1.0 - y);
	elseif ((y <= 8.5e-162) || ~((y <= 5.2e-47)))
		tmp = y - (x * y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := If[LessEqual[y, 2.9e-174], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 8.5e-162], N[Not[LessEqual[y, 5.2e-47]], $MachinePrecision]], N[(y - N[(x * y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if y < 2.9000000000000001e-174

   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 inf 66.4%

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

   if 2.9000000000000001e-174 < y < 8.49999999999999955e-162 or 5.2e-47 < y

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. remove-double-neg 99.9%

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

      4. unsub-neg 99.9%

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

      5. cancel-sign-sub-inv 99.9%

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

      6. associate--l+ 99.9%

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

      7. neg-mul-1 99.9%

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

      8. cancel-sign-sub-inv 99.9%

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

      9. distribute-lft-neg-out 99.9%

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

      10. distribute-rgt-neg-out 99.9%

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

      11. *-commutative 99.9%

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

      12. distribute-rgt-out 99.9%

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

      13. +-commutative 99.9%

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

      14. sub-neg 99.9%

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

      15. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 90.2%

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

      1. mul-1-neg 90.2%

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

      2. unsub-neg 90.2%

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

   7. Simplified 90.2%

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

      1. sub-neg 90.2%

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

      2. distribute-rgt-in 90.3%

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

      3. *-un-lft-identity 90.3%

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

   9. Applied egg-rr 90.3%

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

   if 8.49999999999999955e-162 < y < 5.2e-47

   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 84.9%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-162} \lor \neg \left(y \leq 5.2 \cdot 10^{-47}\right):\\ \;\;\;\;y - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-162} \lor \neg \left(y \leq 2.9 \cdot 10^{-46}\right):\\ \;\;\;\;y - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= y 2.9e-174)
   (* x (- 1.0 y))
   (if (or (<= y 8.5e-162) (not (<= y 2.9e-46))) (- y (* x y)) x)))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (y <= 2.9e-174) {
		tmp = x * (1.0 - y);
	} else if ((y <= 8.5e-162) || !(y <= 2.9e-46)) {
		tmp = y - (x * y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 2.9d-174) then
        tmp = x * (1.0d0 - y)
    else if ((y <= 8.5d-162) .or. (.not. (y <= 2.9d-46))) then
        tmp = y - (x * y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y) {
	double tmp;
	if (y <= 2.9e-174) {
		tmp = x * (1.0 - y);
	} else if ((y <= 8.5e-162) || !(y <= 2.9e-46)) {
		tmp = y - (x * y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if y <= 2.9e-174:
		tmp = x * (1.0 - y)
	elif (y <= 8.5e-162) or not (y <= 2.9e-46):
		tmp = y - (x * y)
	else:
		tmp = x
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (y <= 2.9e-174)
		tmp = Float64(x * Float64(1.0 - y));
	elseif ((y <= 8.5e-162) || !(y <= 2.9e-46))
		tmp = Float64(y - Float64(x * y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 2.9e-174)
		tmp = x * (1.0 - y);
	elseif ((y <= 8.5e-162) || ~((y <= 2.9e-46)))
		tmp = y - (x * y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := If[LessEqual[y, 2.9e-174], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 8.5e-162], N[Not[LessEqual[y, 2.9e-46]], $MachinePrecision]], N[(y - N[(x * y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if y < 2.9000000000000001e-174

   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 inf 66.4%

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

   if 2.9000000000000001e-174 < y < 8.49999999999999955e-162 or 2.90000000000000005e-46 < y

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. remove-double-neg 99.9%

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

      4. unsub-neg 99.9%

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

      5. cancel-sign-sub-inv 99.9%

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

      6. associate--l+ 99.9%

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

      7. neg-mul-1 99.9%

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

      8. cancel-sign-sub-inv 99.9%

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

      9. distribute-lft-neg-out 99.9%

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

      10. distribute-rgt-neg-out 99.9%

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

      11. *-commutative 99.9%

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

      12. distribute-rgt-out 99.9%

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

      13. +-commutative 99.9%

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

      14. sub-neg 99.9%

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

      15. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 90.3%

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

      1. mul-1-neg 90.3%

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

      2. distribute-rgt-neg-out 90.3%

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

   7. Simplified 90.3%

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

   if 8.49999999999999955e-162 < y < 2.90000000000000005e-46

   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 84.9%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-162} \lor \neg \left(y \leq 2.9 \cdot 10^{-46}\right):\\ \;\;\;\;y - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-162} \lor \neg \left(y \leq 2.95 \cdot 10^{-46}\right):\\ \;\;\;\;y - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= y 2.9e-174)
   (* x (- 1.0 y))
   (if (or (<= y 8.5e-162) (not (<= y 2.95e-46))) (- y (* x y)) x)))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (y <= 2.9e-174) {
		tmp = x * (1.0 - y);
	} else if ((y <= 8.5e-162) || !(y <= 2.95e-46)) {
		tmp = y - (x * y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 2.9d-174) then
        tmp = x * (1.0d0 - y)
    else if ((y <= 8.5d-162) .or. (.not. (y <= 2.95d-46))) then
        tmp = y - (x * y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y) {
	double tmp;
	if (y <= 2.9e-174) {
		tmp = x * (1.0 - y);
	} else if ((y <= 8.5e-162) || !(y <= 2.95e-46)) {
		tmp = y - (x * y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if y <= 2.9e-174:
		tmp = x * (1.0 - y)
	elif (y <= 8.5e-162) or not (y <= 2.95e-46):
		tmp = y - (x * y)
	else:
		tmp = x
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (y <= 2.9e-174)
		tmp = Float64(x * Float64(1.0 - y));
	elseif ((y <= 8.5e-162) || !(y <= 2.95e-46))
		tmp = Float64(y - Float64(x * y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 2.9e-174)
		tmp = x * (1.0 - y);
	elseif ((y <= 8.5e-162) || ~((y <= 2.95e-46)))
		tmp = y - (x * y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := If[LessEqual[y, 2.9e-174], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 8.5e-162], N[Not[LessEqual[y, 2.95e-46]], $MachinePrecision]], N[(y - N[(x * y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if y < 2.9000000000000001e-174

   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 inf 66.4%

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

   if 2.9000000000000001e-174 < y < 8.49999999999999955e-162 or 2.95e-46 < y

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. remove-double-neg 99.9%

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

      4. unsub-neg 99.9%

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

      5. cancel-sign-sub-inv 99.9%

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

      6. associate--l+ 99.9%

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

      7. neg-mul-1 99.9%

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

      8. cancel-sign-sub-inv 99.9%

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

      9. distribute-lft-neg-out 99.9%

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

      10. distribute-rgt-neg-out 99.9%

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

      11. *-commutative 99.9%

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

      12. distribute-rgt-out 99.9%

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

      13. +-commutative 99.9%

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

      14. sub-neg 99.9%

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

      15. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 90.2%

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

      1. mul-1-neg 90.2%

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

      2. unsub-neg 90.2%

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

   7. Simplified 90.2%

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

      1. sub-neg 90.2%

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

      2. distribute-rgt-in 90.3%

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

      3. *-un-lft-identity 90.3%

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

   9. Applied egg-rr 90.3%

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

       1. distribute-lft-neg-out 90.3%

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

       2. unsub-neg 90.3%

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

       3. *-commutative 90.3%

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

   11. Applied egg-rr 90.3%

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

   if 8.49999999999999955e-162 < y < 2.95e-46

   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 84.9%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-162} \lor \neg \left(y \leq 2.95 \cdot 10^{-46}\right):\\ \;\;\;\;y - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-162} \lor \neg \left(y \leq 7.8 \cdot 10^{-47}\right):\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= y 2.9e-174)
   (* x (- 1.0 y))
   (if (or (<= y 8.5e-162) (not (<= y 7.8e-47))) (* y (- 1.0 x)) x)))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (y <= 2.9e-174) {
		tmp = x * (1.0 - y);
	} else if ((y <= 8.5e-162) || !(y <= 7.8e-47)) {
		tmp = y * (1.0 - x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 2.9d-174) then
        tmp = x * (1.0d0 - y)
    else if ((y <= 8.5d-162) .or. (.not. (y <= 7.8d-47))) then
        tmp = y * (1.0d0 - x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y) {
	double tmp;
	if (y <= 2.9e-174) {
		tmp = x * (1.0 - y);
	} else if ((y <= 8.5e-162) || !(y <= 7.8e-47)) {
		tmp = y * (1.0 - x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if y <= 2.9e-174:
		tmp = x * (1.0 - y)
	elif (y <= 8.5e-162) or not (y <= 7.8e-47):
		tmp = y * (1.0 - x)
	else:
		tmp = x
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (y <= 2.9e-174)
		tmp = Float64(x * Float64(1.0 - y));
	elseif ((y <= 8.5e-162) || !(y <= 7.8e-47))
		tmp = Float64(y * Float64(1.0 - x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 2.9e-174)
		tmp = x * (1.0 - y);
	elseif ((y <= 8.5e-162) || ~((y <= 7.8e-47)))
		tmp = y * (1.0 - x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := If[LessEqual[y, 2.9e-174], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 8.5e-162], N[Not[LessEqual[y, 7.8e-47]], $MachinePrecision]], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if y < 2.9000000000000001e-174

   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 inf 66.4%

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

   if 2.9000000000000001e-174 < y < 8.49999999999999955e-162 or 7.79999999999999956e-47 < y

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. remove-double-neg 99.9%

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

      4. unsub-neg 99.9%

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

      5. cancel-sign-sub-inv 99.9%

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

      6. associate--l+ 99.9%

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

      7. neg-mul-1 99.9%

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

      8. cancel-sign-sub-inv 99.9%

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

      9. distribute-lft-neg-out 99.9%

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

      10. distribute-rgt-neg-out 99.9%

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

      11. *-commutative 99.9%

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

      12. distribute-rgt-out 99.9%

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

      13. +-commutative 99.9%

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

      14. sub-neg 99.9%

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

      15. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 90.2%

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

      1. mul-1-neg 90.2%

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

      2. unsub-neg 90.2%

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

   7. Simplified 90.2%

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

   if 8.49999999999999955e-162 < y < 7.79999999999999956e-47

   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 84.9%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-162} \lor \neg \left(y \leq 7.8 \cdot 10^{-47}\right):\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{-174}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-162}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= y 2.9e-174) x (if (<= y 8.5e-162) y (if (<= y 2.95e-46) x y))))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (y <= 2.9e-174) {
		tmp = x;
	} else if (y <= 8.5e-162) {
		tmp = y;
	} else if (y <= 2.95e-46) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 2.9d-174) then
        tmp = x
    else if (y <= 8.5d-162) then
        tmp = y
    else if (y <= 2.95d-46) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y) {
	double tmp;
	if (y <= 2.9e-174) {
		tmp = x;
	} else if (y <= 8.5e-162) {
		tmp = y;
	} else if (y <= 2.95e-46) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if y <= 2.9e-174:
		tmp = x
	elif y <= 8.5e-162:
		tmp = y
	elif y <= 2.95e-46:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (y <= 2.9e-174)
		tmp = x;
	elseif (y <= 8.5e-162)
		tmp = y;
	elseif (y <= 2.95e-46)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 2.9e-174)
		tmp = x;
	elseif (y <= 8.5e-162)
		tmp = y;
	elseif (y <= 2.95e-46)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := If[LessEqual[y, 2.9e-174], x, If[LessEqual[y, 8.5e-162], y, If[LessEqual[y, 2.95e-46], x, y]]]

Derivation

1. Split input into 2 regimes

2. if y < 2.9000000000000001e-174 or 8.49999999999999955e-162 < y < 2.95e-46

   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 53.1%

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

   if 2.9000000000000001e-174 < y < 8.49999999999999955e-162 or 2.95e-46 < y

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. remove-double-neg 99.9%

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

      4. unsub-neg 99.9%

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

      5. cancel-sign-sub-inv 99.9%

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

      6. associate--l+ 99.9%

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

      7. neg-mul-1 99.9%

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

      8. cancel-sign-sub-inv 99.9%

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

      9. distribute-lft-neg-out 99.9%

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

      10. distribute-rgt-neg-out 99.9%

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

      11. *-commutative 99.9%

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

      12. distribute-rgt-out 99.9%

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

      13. +-commutative 99.9%

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

      14. sub-neg 99.9%

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

      15. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 49.2%

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

Alternative 8: 87.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-19} \lor \neg \left(x \leq 0.046\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (or (<= x -1e-19) (not (<= x 0.046))) (* x (- 1.0 y)) y))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if ((x <= -1e-19) || !(x <= 0.046)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1d-19)) .or. (.not. (x <= 0.046d0))) then
        tmp = x * (1.0d0 - y)
    else
        tmp = y
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y) {
	double tmp;
	if ((x <= -1e-19) || !(x <= 0.046)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if (x <= -1e-19) or not (x <= 0.046):
		tmp = x * (1.0 - y)
	else:
		tmp = y
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if ((x <= -1e-19) || !(x <= 0.046))
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1e-19) || ~((x <= 0.046)))
		tmp = x * (1.0 - y);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := If[Or[LessEqual[x, -1e-19], N[Not[LessEqual[x, 0.046]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -9.9999999999999998e-20 or 0.045999999999999999 < 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 inf 94.8%

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

   if -9.9999999999999998e-20 < x < 0.045999999999999999

   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 75.9%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-19} \lor \neg \left(x \leq 0.046\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 100.0% accurate, 1.0× speedup

Math

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

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 (+ y (* x (- 1.0 y))))

C

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

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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

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

Python

[x, y] = sort([x, y])
def code(x, y):
	return y + (x * (1.0 - y))

Julia

x, y = sort([x, y])
function code(x, y)
	return Float64(y + Float64(x * Float64(1.0 - y)))
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y)
	tmp = y + (x * (1.0 - y));
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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 10: 38.8% accurate, 7.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ x \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 x)

C

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

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x
end function

Java

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

Python

[x, y] = sort([x, y])
def code(x, y):
	return x

Julia

x, y = sort([x, y])
function code(x, y)
	return x
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y)
	tmp = x;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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 36.5%

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

Reproduce

herbie shell --seed 2024103 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))