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

Percentage Accurate: 100.0% → 100.0%

Time: 3.4s

Alternatives: 6

Speedup: N/A×

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, 1.0× speedup

Math

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

FPCore

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

C

assert(x < y);
double code(double x, double y) {
	return x + (y * (1.0 - 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 + (y * (1.0d0 - x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := N[(x + N[(y * N[(1.0 - x), $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%

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

3. Simplified 100.0%

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

5. Taylor expanded in y around 0 100.0%

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

6. Final simplification 100.0%

   \[\leadsto x + y \cdot \left(1 - x\right) \]
7. Add Preprocessing

Alternative 2: 99.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

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

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = x * (1.0 - y);
	} else if (x <= 1.0) {
		tmp = x + y;
	} else {
		tmp = x * -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 <= (-1.0d0)) then
        tmp = x * (1.0d0 - y)
    else if (x <= 1.0d0) then
        tmp = x + y
    else
        tmp = x * -y
    end if
    code = tmp
end function

Java

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

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if x <= -1.0:
		tmp = x * (1.0 - y)
	elif x <= 1.0:
		tmp = x + y
	else:
		tmp = x * -y
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (x <= 1.0)
		tmp = Float64(x + y);
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = x * (1.0 - y);
	elseif (x <= 1.0)
		tmp = x + y;
	else
		tmp = x * -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[x, -1.0], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0], N[(x + y), $MachinePrecision], N[(x * (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1

   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. Taylor expanded in x around inf 98.9%

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

   if -1 < x < 1

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 99.5%

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

   if 1 < x

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. associate--l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      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. Taylor expanded in x around inf 96.3%

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

      1. sub-neg 96.3%

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

      2. distribute-rgt-in 96.3%

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

      3. *-un-lft-identity 96.3%

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

      4. distribute-lft-neg-in 96.3%

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

      5. unsub-neg 96.3%

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

   7. Applied egg-rr 96.3%

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

   8. Taylor expanded in y around inf 48.3%

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

      1. mul-1-neg 48.3%

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

      2. distribute-rgt-neg-out 48.3%

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

   10. Simplified 48.3%

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

4. Final simplification 88.9%

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

Alternative 3: 99.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

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

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = x - (x * y);
	} else if (x <= 1.0) {
		tmp = x + y;
	} else {
		tmp = x * -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 <= (-1.0d0)) then
        tmp = x - (x * y)
    else if (x <= 1.0d0) then
        tmp = x + y
    else
        tmp = x * -y
    end if
    code = tmp
end function

Java

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

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if x <= -1.0:
		tmp = x - (x * y)
	elif x <= 1.0:
		tmp = x + y
	else:
		tmp = x * -y
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(x - Float64(x * y));
	elseif (x <= 1.0)
		tmp = Float64(x + y);
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = x - (x * y);
	elseif (x <= 1.0)
		tmp = x + y;
	else
		tmp = x * -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[x, -1.0], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0], N[(x + y), $MachinePrecision], N[(x * (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1

   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. Taylor expanded in x around inf 98.9%

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

      1. sub-neg 98.9%

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

      2. distribute-rgt-in 98.9%

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

      3. *-un-lft-identity 98.9%

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

      4. distribute-lft-neg-in 98.9%

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

      5. unsub-neg 98.9%

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

   7. Applied egg-rr 98.9%

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

   if -1 < x < 1

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 99.5%

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

   if 1 < x

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. associate--l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      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. Taylor expanded in x around inf 96.3%

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

      1. sub-neg 96.3%

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

      2. distribute-rgt-in 96.3%

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

      3. *-un-lft-identity 96.3%

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

      4. distribute-lft-neg-in 96.3%

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

      5. unsub-neg 96.3%

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

   7. Applied egg-rr 96.3%

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

   8. Taylor expanded in y around inf 48.3%

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

      1. mul-1-neg 48.3%

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

      2. distribute-rgt-neg-out 48.3%

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

   10. Simplified 48.3%

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

4. Final simplification 88.9%

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

Alternative 4: 81.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -860:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 (if (<= y -860.0) (* x (- y)) (+ x y)))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (y <= -860.0) {
		tmp = x * -y;
	} else {
		tmp = x + 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 <= (-860.0d0)) then
        tmp = x * -y
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y) {
	double tmp;
	if (y <= -860.0) {
		tmp = x * -y;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if y <= -860.0:
		tmp = x * -y
	else:
		tmp = x + y
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (y <= -860.0)
		tmp = Float64(x * Float64(-y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -860.0)
		tmp = x * -y;
	else
		tmp = x + 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, -860.0], N[(x * (-y)), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -860

   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. Taylor expanded in x around inf 42.4%

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

      1. sub-neg 42.4%

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

      2. distribute-rgt-in 42.4%

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

      3. *-un-lft-identity 42.4%

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

      4. distribute-lft-neg-in 42.4%

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

      5. unsub-neg 42.4%

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

   7. Applied egg-rr 42.4%

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

   8. Taylor expanded in y around inf 42.0%

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

      1. mul-1-neg 42.0%

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

      2. distribute-rgt-neg-out 42.0%

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

   10. Simplified 42.0%

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

   if -860 < y

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 83.8%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -860:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.2% accurate, 2.3× speedup

Math

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

FPCore

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

C

assert(x < y);
double code(double x, double y) {
	return x + 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 = x + y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

3. Simplified 100.0%

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

5. Taylor expanded in x around 0 76.9%

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

6. Final simplification 76.9%

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

Alternative 6: 38.9% 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. +-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. Taylor expanded in y around 0 39.4%

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

6. Final simplification 39.4%

   \[\leadsto x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024076 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))