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

Percentage Accurate: 100.0% → 100.0%

Time: 4.3s

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. associate--l+ 100.0%

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

   2. +-commutative 100.0%

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

   3. remove-double-neg 100.0%

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

   4. unsub-neg 100.0%

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

   5. cancel-sign-sub-inv 100.0%

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

   6. associate--l+ 100.0%

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

   7. neg-mul-1 100.0%

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

   8. cancel-sign-sub-inv 100.0%

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

   9. distribute-lft-neg-out 100.0%

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

   10. distribute-rgt-neg-out 100.0%

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

   11. *-commutative 100.0%

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

   12. distribute-rgt-out 100.0%

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

   13. +-commutative 100.0%

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

   14. sub-neg 100.0%

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

   15. metadata-eval 100.0%

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

3. Simplified 100.0%

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

Alternative 2: 86.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -21:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 3.35 \cdot 10^{-18}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -21.0) (* y (- x)) (if (<= y 3.35e-18) (+ y x) (- y (* y x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -21.0) {
		tmp = y * -x;
	} else if (y <= 3.35e-18) {
		tmp = y + x;
	} else {
		tmp = y - (y * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-21.0d0)) then
        tmp = y * -x
    else if (y <= 3.35d-18) then
        tmp = y + x
    else
        tmp = y - (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -21.0) {
		tmp = y * -x;
	} else if (y <= 3.35e-18) {
		tmp = y + x;
	} else {
		tmp = y - (y * x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -21.0:
		tmp = y * -x
	elif y <= 3.35e-18:
		tmp = y + x
	else:
		tmp = y - (y * x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -21.0)
		tmp = Float64(y * Float64(-x));
	elseif (y <= 3.35e-18)
		tmp = Float64(y + x);
	else
		tmp = Float64(y - Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -21.0)
		tmp = y * -x;
	elseif (y <= 3.35e-18)
		tmp = y + x;
	else
		tmp = y - (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -21.0], N[(y * (-x)), $MachinePrecision], If[LessEqual[y, 3.35e-18], N[(y + x), $MachinePrecision], N[(y - N[(y * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -21

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. remove-double-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate--l+ 100.0%

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

      7. neg-mul-1 100.0%

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

      8. cancel-sign-sub-inv 100.0%

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

      9. distribute-lft-neg-out 100.0%

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

      10. distribute-rgt-neg-out 100.0%

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

      11. *-commutative 100.0%

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

      12. distribute-rgt-out 100.0%

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

      13. +-commutative 100.0%

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

      14. sub-neg 100.0%

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

      15. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 99.1%

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

      1. neg-mul-1 99.1%

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

      2. sub-neg 99.1%

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

   7. Simplified 99.1%

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

   8. Taylor expanded in x around inf 44.9%

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

      1. mul-1-neg 44.9%

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

      2. *-commutative 44.9%

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

      3. distribute-rgt-neg-in 44.9%

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

   10. Simplified 44.9%

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

   if -21 < y < 3.3499999999999999e-18

   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 99.9%

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

   if 3.3499999999999999e-18 < 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 98.4%

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

      1. neg-mul-1 98.4%

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

      2. sub-neg 98.4%

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

   7. Simplified 98.4%

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

   8. Taylor expanded in x around 0 98.4%

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

      1. mul-1-neg 98.4%

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

      2. *-commutative 98.4%

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

      3. sub-neg 98.4%

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

   10. Simplified 98.4%

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

Alternative 3: 86.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -21:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 3.35 \cdot 10^{-18}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -21.0) (* y (- x)) (if (<= y 3.35e-18) (+ y x) (* y (- 1.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -21.0) {
		tmp = y * -x;
	} else if (y <= 3.35e-18) {
		tmp = y + x;
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-21.0d0)) then
        tmp = y * -x
    else if (y <= 3.35d-18) then
        tmp = y + x
    else
        tmp = y * (1.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -21.0) {
		tmp = y * -x;
	} else if (y <= 3.35e-18) {
		tmp = y + x;
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -21.0:
		tmp = y * -x
	elif y <= 3.35e-18:
		tmp = y + x
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -21.0)
		tmp = Float64(y * Float64(-x));
	elseif (y <= 3.35e-18)
		tmp = Float64(y + x);
	else
		tmp = Float64(y * Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -21.0)
		tmp = y * -x;
	elseif (y <= 3.35e-18)
		tmp = y + x;
	else
		tmp = y * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -21.0], N[(y * (-x)), $MachinePrecision], If[LessEqual[y, 3.35e-18], N[(y + x), $MachinePrecision], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -21

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. remove-double-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate--l+ 100.0%

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

      7. neg-mul-1 100.0%

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

      8. cancel-sign-sub-inv 100.0%

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

      9. distribute-lft-neg-out 100.0%

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

      10. distribute-rgt-neg-out 100.0%

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

      11. *-commutative 100.0%

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

      12. distribute-rgt-out 100.0%

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

      13. +-commutative 100.0%

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

      14. sub-neg 100.0%

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

      15. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 99.1%

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

      1. neg-mul-1 99.1%

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

      2. sub-neg 99.1%

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

   7. Simplified 99.1%

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

   8. Taylor expanded in x around inf 44.9%

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

      1. mul-1-neg 44.9%

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

      2. *-commutative 44.9%

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

      3. distribute-rgt-neg-in 44.9%

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

   10. Simplified 44.9%

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

   if -21 < y < 3.3499999999999999e-18

   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 99.9%

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

   if 3.3499999999999999e-18 < 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 98.4%

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

      1. neg-mul-1 98.4%

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

      2. sub-neg 98.4%

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

   7. Simplified 98.4%

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

Alternative 4: 74.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 850:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x 850.0) (+ y x) (* y (- x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 850.0) {
		tmp = y + x;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 850.0d0) then
        tmp = y + x
    else
        tmp = y * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 850.0) {
		tmp = y + x;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 850.0:
		tmp = y + x
	else:
		tmp = y * -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 850.0)
		tmp = Float64(y + x);
	else
		tmp = Float64(y * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 850.0)
		tmp = y + x;
	else
		tmp = y * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 850.0], N[(y + x), $MachinePrecision], N[(y * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 850

   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 82.7%

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

   if 850 < 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 48.7%

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

      1. neg-mul-1 48.7%

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

      2. sub-neg 48.7%

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

   7. Simplified 48.7%

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

   8. Taylor expanded in x around inf 46.8%

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

      1. mul-1-neg 46.8%

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

      2. *-commutative 46.8%

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

      3. distribute-rgt-neg-in 46.8%

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

   10. Simplified 46.8%

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

Alternative 5: 49.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x -1.6e-67) x y))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.6e-67) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.6d-67)) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.6e-67) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.6e-67:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.6e-67)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.6e-67)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.6e-67], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -1.60000000000000011e-67

   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 58.3%

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

   6. Taylor expanded in y around 0 49.2%

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

   if -1.60000000000000011e-67 < x

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. remove-double-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate--l+ 100.0%

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

      7. neg-mul-1 100.0%

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

      8. cancel-sign-sub-inv 100.0%

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

      9. distribute-lft-neg-out 100.0%

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

      10. distribute-rgt-neg-out 100.0%

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

      11. *-commutative 100.0%

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

      12. distribute-rgt-out 100.0%

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

      13. +-commutative 100.0%

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

      14. sub-neg 100.0%

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

      15. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 50.4%

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

Alternative 6: 74.8% accurate, 2.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. associate--l+ 100.0%

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

   2. +-commutative 100.0%

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

   3. remove-double-neg 100.0%

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

   4. unsub-neg 100.0%

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

   5. cancel-sign-sub-inv 100.0%

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

   6. associate--l+ 100.0%

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

   7. neg-mul-1 100.0%

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

   8. cancel-sign-sub-inv 100.0%

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

   9. distribute-lft-neg-out 100.0%

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

   10. distribute-rgt-neg-out 100.0%

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

   11. *-commutative 100.0%

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

   12. distribute-rgt-out 100.0%

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

   13. +-commutative 100.0%

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

   14. sub-neg 100.0%

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

   15. metadata-eval 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in y around 0 75.6%

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

Alternative 7: 38.9% accurate, 7.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

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

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 100.0%

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

   1. associate--l+ 100.0%

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

   2. +-commutative 100.0%

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

   3. remove-double-neg 100.0%

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

   4. unsub-neg 100.0%

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

   5. cancel-sign-sub-inv 100.0%

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

   6. associate--l+ 100.0%

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

   7. neg-mul-1 100.0%

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

   8. cancel-sign-sub-inv 100.0%

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

   9. distribute-lft-neg-out 100.0%

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

   10. distribute-rgt-neg-out 100.0%

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

   11. *-commutative 100.0%

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

   12. distribute-rgt-out 100.0%

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

   13. +-commutative 100.0%

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

   14. sub-neg 100.0%

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

   15. metadata-eval 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in y around 0 75.6%

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

6. Taylor expanded in y around 0 39.7%

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

Reproduce

herbie shell --seed 2024132 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))