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

Percentage Accurate: 100.0% → 100.0%

Time: 5.3s

Alternatives: 7

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, 1.0× speedup

Math

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

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(x + Float64(y - Float64(x * y)))
end

MATLAB

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

Wolfram

code[x_, y_] := N[(x + N[(y - N[(x * 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%

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

3. Simplified 100.0%

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

Alternative 2: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -900:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-86}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -900.0) (* x (- 1.0 y)) (if (<= x 2.8e-86) (+ x y) (- y (* x y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -900.0) {
		tmp = x * (1.0 - y);
	} else if (x <= 2.8e-86) {
		tmp = x + y;
	} else {
		tmp = y - (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-900.0d0)) then
        tmp = x * (1.0d0 - y)
    else if (x <= 2.8d-86) then
        tmp = x + y
    else
        tmp = y - (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -900.0) {
		tmp = x * (1.0 - y);
	} else if (x <= 2.8e-86) {
		tmp = x + y;
	} else {
		tmp = y - (x * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -900.0:
		tmp = x * (1.0 - y)
	elif x <= 2.8e-86:
		tmp = x + y
	else:
		tmp = y - (x * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -900.0)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (x <= 2.8e-86)
		tmp = Float64(x + y);
	else
		tmp = Float64(y - Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -900.0)
		tmp = x * (1.0 - y);
	elseif (x <= 2.8e-86)
		tmp = x + y;
	else
		tmp = y - (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -900.0], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e-86], N[(x + y), $MachinePrecision], N[(y - N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -900

   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 inf 98.7%

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

   if -900 < x < 2.80000000000000009e-86

   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 99.6%

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

   if 2.80000000000000009e-86 < x

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. remove-double-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate--l+ 100.0%

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

      7. neg-mul-1 100.0%

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

      8. cancel-sign-sub-inv 100.0%

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

      9. distribute-lft-neg-out 100.0%

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

      10. distribute-rgt-neg-out 100.0%

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

      11. *-commutative 100.0%

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

      12. distribute-rgt-out 100.0%

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

      13. +-commutative 100.0%

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

      14. sub-neg 100.0%

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

      15. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 53.9%

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

      1. neg-mul-1 53.9%

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

   7. Simplified 53.9%

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

   8. Taylor expanded in y around 0 53.9%

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

      1. mul-1-neg 53.9%

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

      2. unsub-neg 53.9%

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

      3. distribute-lft-out-- 53.9%

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

      4. *-rgt-identity 53.9%

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

   10. Simplified 53.9%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -900:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-86}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+283} \lor \neg \left(x \leq 2 \cdot 10^{+18}\right):\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.85e+283) (not (<= x 2e+18))) (* x (- y)) (+ x y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.85e+283) || !(x <= 2e+18)) {
		tmp = x * -y;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.85d+283)) .or. (.not. (x <= 2d+18))) then
        tmp = x * -y
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.85e+283) || !(x <= 2e+18)) {
		tmp = x * -y;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.85e+283) or not (x <= 2e+18):
		tmp = x * -y
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.85e+283) || !(x <= 2e+18))
		tmp = Float64(x * Float64(-y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.85e+283) || ~((x <= 2e+18)))
		tmp = x * -y;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.85e+283], N[Not[LessEqual[x, 2e+18]], $MachinePrecision]], N[(x * (-y)), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.85e283 or 2e18 < x

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

      3. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around inf 54.2%

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

      1. neg-mul-1 54.2%

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

      2. *-commutative 54.2%

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

      3. distribute-rgt-neg-in 54.2%

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

   10. Simplified 54.2%

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

   if -1.85e283 < x < 2e18

   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 83.4%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+283} \lor \neg \left(x \leq 2 \cdot 10^{+18}\right):\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -900:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+23}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -900.0) (* x (- 1.0 y)) (if (<= x 4.8e+23) (+ x y) (* x (- y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -900.0) {
		tmp = x * (1.0 - y);
	} else if (x <= 4.8e+23) {
		tmp = x + y;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-900.0d0)) then
        tmp = x * (1.0d0 - y)
    else if (x <= 4.8d+23) then
        tmp = x + y
    else
        tmp = x * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -900.0) {
		tmp = x * (1.0 - y);
	} else if (x <= 4.8e+23) {
		tmp = x + y;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -900.0:
		tmp = x * (1.0 - y)
	elif x <= 4.8e+23:
		tmp = x + y
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -900.0)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (x <= 4.8e+23)
		tmp = Float64(x + y);
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -900.0)
		tmp = x * (1.0 - y);
	elseif (x <= 4.8e+23)
		tmp = x + y;
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -900.0], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.8e+23], N[(x + y), $MachinePrecision], N[(x * (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -900

   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 inf 98.7%

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

   if -900 < x < 4.8e23

   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 97.7%

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

   if 4.8e23 < x

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

      3. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around inf 53.7%

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

      1. neg-mul-1 53.7%

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

      2. *-commutative 53.7%

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

      3. distribute-rgt-neg-in 53.7%

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

   10. Simplified 53.7%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -900:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+23}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.3 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 1.3e-92) x y))

C

double code(double x, double y) {
	double tmp;
	if (y <= 1.3e-92) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 1.3d-92) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 1.3e-92) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 1.3e-92:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 1.3e-92)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 1.3e-92)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 1.3e-92], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 1.3e-92

   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 53.9%

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

   if 1.3e-92 < 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 53.3%

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

   6. Taylor expanded in x around 0 44.8%

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

Alternative 6: 74.7% accurate, 2.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. associate--l+ 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in x around 0 72.6%

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

Alternative 7: 38.6% accurate, 7.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

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

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 100.0%

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

   1. associate--l+ 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in y around 0 40.8%

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

Reproduce

herbie shell --seed 2024145 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))