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

Percentage Accurate: 100.0% → 100.0%

Time: 2.1s

Alternatives: 6

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

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

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]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) - x \cdot y \]

2. Final simplification 100.0%

   \[\leadsto \left(x + y\right) - x \cdot y \]

Alternative 2: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+280} \lor \neg \left(x \leq -1.9 \cdot 10^{+224}\right) \land \left(x \leq -1.05 \cdot 10^{+198} \lor \neg \left(x \leq -1.26 \cdot 10^{+136}\right) \land \left(x \leq -2.45 \cdot 10^{+100} \lor \neg \left(x \leq -9 \cdot 10^{+62}\right) \land x \leq 1.15 \cdot 10^{+20}\right)\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.5e+280)
         (and (not (<= x -1.9e+224))
              (or (<= x -1.05e+198)
                  (and (not (<= x -1.26e+136))
                       (or (<= x -2.45e+100)
                           (and (not (<= x -9e+62)) (<= x 1.15e+20)))))))
   (+ x y)
   (* x (- y))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.5e+280) || (!(x <= -1.9e+224) && ((x <= -1.05e+198) || (!(x <= -1.26e+136) && ((x <= -2.45e+100) || (!(x <= -9e+62) && (x <= 1.15e+20))))))) {
		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 <= (-3.5d+280)) .or. (.not. (x <= (-1.9d+224))) .and. (x <= (-1.05d+198)) .or. (.not. (x <= (-1.26d+136))) .and. (x <= (-2.45d+100)) .or. (.not. (x <= (-9d+62))) .and. (x <= 1.15d+20)) 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 <= -3.5e+280) || (!(x <= -1.9e+224) && ((x <= -1.05e+198) || (!(x <= -1.26e+136) && ((x <= -2.45e+100) || (!(x <= -9e+62) && (x <= 1.15e+20))))))) {
		tmp = x + y;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3.5e+280) or (not (x <= -1.9e+224) and ((x <= -1.05e+198) or (not (x <= -1.26e+136) and ((x <= -2.45e+100) or (not (x <= -9e+62) and (x <= 1.15e+20)))))):
		tmp = x + y
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3.5e+280) || (!(x <= -1.9e+224) && ((x <= -1.05e+198) || (!(x <= -1.26e+136) && ((x <= -2.45e+100) || (!(x <= -9e+62) && (x <= 1.15e+20)))))))
		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 <= -3.5e+280) || (~((x <= -1.9e+224)) && ((x <= -1.05e+198) || (~((x <= -1.26e+136)) && ((x <= -2.45e+100) || (~((x <= -9e+62)) && (x <= 1.15e+20)))))))
		tmp = x + y;
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3.5e+280], And[N[Not[LessEqual[x, -1.9e+224]], $MachinePrecision], Or[LessEqual[x, -1.05e+198], And[N[Not[LessEqual[x, -1.26e+136]], $MachinePrecision], Or[LessEqual[x, -2.45e+100], And[N[Not[LessEqual[x, -9e+62]], $MachinePrecision], LessEqual[x, 1.15e+20]]]]]]], N[(x + y), $MachinePrecision], N[(x * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5000000000000001e280 or -1.90000000000000013e224 < x < -1.05000000000000006e198 or -1.25999999999999999e136 < x < -2.44999999999999983e100 or -8.99999999999999997e62 < x < 1.15e20

   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. Taylor expanded in y around 0 90.0%

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

   if -3.5000000000000001e280 < x < -1.90000000000000013e224 or -1.05000000000000006e198 < x < -1.25999999999999999e136 or -2.44999999999999983e100 < x < -8.99999999999999997e62 or 1.15e20 < x

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]

   2. Taylor expanded in y around inf 58.8%

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

   3. Taylor expanded in x around inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. distribute-rgt-neg-in 58.8%

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

   5. Simplified 58.8%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+280} \lor \neg \left(x \leq -1.9 \cdot 10^{+224}\right) \land \left(x \leq -1.05 \cdot 10^{+198} \lor \neg \left(x \leq -1.26 \cdot 10^{+136}\right) \land \left(x \leq -2.45 \cdot 10^{+100} \lor \neg \left(x \leq -9 \cdot 10^{+62}\right) \land x \leq 1.15 \cdot 10^{+20}\right)\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]

Alternative 3: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-5}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.8e+17) (* x (- y)) (if (<= y 2e-5) (+ x y) (* y (- 1.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.8e+17) {
		tmp = x * -y;
	} else if (y <= 2e-5) {
		tmp = x + y;
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.8d+17)) then
        tmp = x * -y
    else if (y <= 2d-5) then
        tmp = x + y
    else
        tmp = y * (1.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.8e+17) {
		tmp = x * -y;
	} else if (y <= 2e-5) {
		tmp = x + y;
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.8e+17:
		tmp = x * -y
	elif y <= 2e-5:
		tmp = x + y
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.8e+17)
		tmp = Float64(x * Float64(-y));
	elseif (y <= 2e-5)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.8e+17)
		tmp = x * -y;
	elseif (y <= 2e-5)
		tmp = x + y;
	else
		tmp = y * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.8e+17], N[(x * (-y)), $MachinePrecision], If[LessEqual[y, 2e-5], N[(x + y), $MachinePrecision], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8e17

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]

   2. Taylor expanded in y around inf 100.0%

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

   3. Taylor expanded in x around inf 60.5%

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

      1. mul-1-neg 60.5%

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

      2. distribute-rgt-neg-in 60.5%

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

   5. Simplified 60.5%

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

   if -1.8e17 < y < 2.00000000000000016e-5

   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. Taylor expanded in y around 0 97.6%

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

   if 2.00000000000000016e-5 < y

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]

   2. Taylor expanded in y around inf 98.9%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-5}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 4: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. associate--l+ 100.0%

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

   2. +-commutative 100.0%

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

   3. remove-double-neg 100.0%

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

   4. unsub-neg 100.0%

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

   5. cancel-sign-sub-inv 100.0%

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

   6. associate--l+ 100.0%

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

   7. neg-mul-1 100.0%

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

   8. cancel-sign-sub-inv 100.0%

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

   9. distribute-lft-neg-out 100.0%

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

   10. distribute-rgt-neg-out 100.0%

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

   11. *-commutative 100.0%

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

   12. distribute-rgt-out 100.0%

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

   13. +-commutative 100.0%

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

   14. sub-neg 100.0%

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

   15. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto y + x \cdot \left(1 - y\right) \]

Alternative 5: 74.4% accurate, 2.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. associate--l+ 100.0%

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

   2. +-commutative 100.0%

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

   3. remove-double-neg 100.0%

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

   4. unsub-neg 100.0%

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

   5. cancel-sign-sub-inv 100.0%

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

   6. associate--l+ 100.0%

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

   7. neg-mul-1 100.0%

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

   8. cancel-sign-sub-inv 100.0%

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

   9. distribute-lft-neg-out 100.0%

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

   10. distribute-rgt-neg-out 100.0%

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

   11. *-commutative 100.0%

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

   12. distribute-rgt-out 100.0%

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

   13. +-commutative 100.0%

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

   14. sub-neg 100.0%

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

   15. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in y around 0 71.8%

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

5. Final simplification 71.8%

   \[\leadsto x + y \]

Alternative 6: 38.8% accurate, 7.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 y)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return y

Julia

function code(x, y)
	return y
end

MATLAB

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

Wolfram

code[x_, y_] := y

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) - x \cdot y \]

2. Taylor expanded in x around 0 38.7%

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

3. Final simplification 38.7%

   \[\leadsto y \]

Reproduce

herbie shell --seed 2023322 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))