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

Percentage Accurate: 100.0% → 100.0%

Time: 6.9s

Alternatives: 10

Speedup: 1.2×

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, 1.2× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (fma (- 1.0 y) x y))

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. lift--.f64 N/A

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

   2. sub-neg N/A

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

   3. +-commutative N/A

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

   4. lift-+.f64 N/A

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

   5. associate-+r+ N/A

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

   6. +-commutative N/A

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

   7. lift-*.f64 N/A

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

   8. *-commutative N/A

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

   9. distribute-lft-neg-in N/A

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

   10. distribute-rgt1-in N/A

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

   11. lower-fma.f64 N/A

       \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\mathsf{neg}\left(y\right)\right) + 1, x, y\right)} \]

   12. neg-mul-1 N/A

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

   13. lower-fma.f64 100.0

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

4. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-1, y, 1\right), x, y\right)} \]
5. Step-by-step derivation

   1. lift-fma.f64 N/A

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

   2. +-commutative N/A

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

   3. mul-1-neg N/A

      \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}, x, y\right) \]

   4. sub-neg N/A

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

   5. lift--.f64 100.0

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

6. Applied rewrites 100.0%

   \[\leadsto \mathsf{fma}\left(\color{blue}{1 - y}, x, y\right) \]
7. Add Preprocessing

Alternative 2: 87.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + y\right) - x \cdot y\\ t_1 := \left(-y\right) \cdot x\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 10^{+307}:\\ \;\;\;\;\mathsf{fma}\left(1, x, y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (+ x y) (* x y))) (t_1 (* (- y) x)))
   (if (<= t_0 (- INFINITY)) t_1 (if (<= t_0 1e+307) (fma 1.0 x y) t_1))))

C

double code(double x, double y) {
	double t_0 = (x + y) - (x * y);
	double t_1 = -y * x;
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_0 <= 1e+307) {
		tmp = fma(1.0, x, y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(Float64(x + y) - Float64(x * y))
	t_1 = Float64(Float64(-y) * x)
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_0 <= 1e+307)
		tmp = fma(1.0, x, y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[((-y) * x), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], t$95$1, If[LessEqual[t$95$0, 1e+307], N[(1.0 * x + y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (*.f64 x y)) < -inf.0 or 9.99999999999999986e306 < (-.f64 (+.f64 x y) (*.f64 x y))

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around inf

      \[\leadsto \left(-1 \cdot y\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 100.0%

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

   if -inf.0 < (-.f64 (+.f64 x y) (*.f64 x y)) < 9.99999999999999986e306

   1. Initial program 100.0%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-+.f64 N/A

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

      5. associate-+r+ N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. distribute-rgt1-in N/A

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

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\mathsf{neg}\left(y\right)\right) + 1, x, y\right)} \]

      12. neg-mul-1 N/A

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

      13. lower-fma.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 86.0%

      \[\leadsto \mathsf{fma}\left(\color{blue}{1}, x, y\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 63.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x + y\right) - x \cdot y \leq -1 \cdot 10^{-221}:\\ \;\;\;\;\mathsf{fma}\left(-y, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, x, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (- (+ x y) (* x y)) -1e-221) (fma (- y) x x) (fma (- y) x y)))

C

double code(double x, double y) {
	double tmp;
	if (((x + y) - (x * y)) <= -1e-221) {
		tmp = fma(-y, x, x);
	} else {
		tmp = fma(-y, x, y);
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(x + y) - Float64(x * y)) <= -1e-221)
		tmp = fma(Float64(-y), x, x);
	else
		tmp = fma(Float64(-y), x, y);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(x + y), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision], -1e-221], N[((-y) * x + x), $MachinePrecision], N[((-y) * x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (*.f64 x y)) < -1.00000000000000002e-221

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. lower--.f64 64.1

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

   5. Applied rewrites 64.1%

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

   7. Applied rewrites 64.1%

      \[\leadsto \mathsf{fma}\left(-y, \color{blue}{x}, x\right) \]

   if -1.00000000000000002e-221 < (-.f64 (+.f64 x y) (*.f64 x y))

   1. Initial program 100.0%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-+.f64 N/A

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

      5. associate-+r+ N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. distribute-rgt1-in N/A

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

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\mathsf{neg}\left(y\right)\right) + 1, x, y\right)} \]

      12. neg-mul-1 N/A

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

      13. lower-fma.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y\right)}, x, y\right) \]

      2. lower-neg.f64 61.2

         \[\leadsto \mathsf{fma}\left(\color{blue}{-y}, x, y\right) \]

   7. Applied rewrites 61.2%

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

Alternative 4: 63.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x + y\right) - x \cdot y \leq -1 \cdot 10^{-221}:\\ \;\;\;\;\mathsf{fma}\left(-y, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - x\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (- (+ x y) (* x y)) -1e-221) (fma (- y) x x) (* (- 1.0 x) y)))

C

double code(double x, double y) {
	double tmp;
	if (((x + y) - (x * y)) <= -1e-221) {
		tmp = fma(-y, x, x);
	} else {
		tmp = (1.0 - x) * y;
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(x + y) - Float64(x * y)) <= -1e-221)
		tmp = fma(Float64(-y), x, x);
	else
		tmp = Float64(Float64(1.0 - x) * y);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(x + y), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision], -1e-221], N[((-y) * x + x), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (*.f64 x y)) < -1.00000000000000002e-221

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. lower--.f64 64.1

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

   5. Applied rewrites 64.1%

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

   7. Applied rewrites 64.1%

      \[\leadsto \mathsf{fma}\left(-y, \color{blue}{x}, x\right) \]

   if -1.00000000000000002e-221 < (-.f64 (+.f64 x y) (*.f64 x y))

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. lower--.f64 61.1

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

   5. Applied rewrites 61.1%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 63.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x + y\right) - x \cdot y \leq -1 \cdot 10^{-221}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - x\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (- (+ x y) (* x y)) -1e-221) (* x (- 1.0 y)) (* (- 1.0 x) y)))

C

double code(double x, double y) {
	double tmp;
	if (((x + y) - (x * y)) <= -1e-221) {
		tmp = x * (1.0 - y);
	} else {
		tmp = (1.0 - 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 + y) - (x * y)) <= (-1d-221)) then
        tmp = x * (1.0d0 - y)
    else
        tmp = (1.0d0 - x) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((x + y) - (x * y)) <= -1e-221) {
		tmp = x * (1.0 - y);
	} else {
		tmp = (1.0 - x) * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((x + y) - (x * y)) <= -1e-221:
		tmp = x * (1.0 - y)
	else:
		tmp = (1.0 - x) * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(x + y) - Float64(x * y)) <= -1e-221)
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(Float64(1.0 - x) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((x + y) - (x * y)) <= -1e-221)
		tmp = x * (1.0 - y);
	else
		tmp = (1.0 - x) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(x + y), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision], -1e-221], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (*.f64 x y)) < -1.00000000000000002e-221

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. lower--.f64 64.1

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

   5. Applied rewrites 64.1%

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

   if -1.00000000000000002e-221 < (-.f64 (+.f64 x y) (*.f64 x y))

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. lower--.f64 61.1

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

   5. Applied rewrites 61.1%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - x \cdot y \leq -1 \cdot 10^{-221}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 39.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x + y\right) - x \cdot y \leq -1 \cdot 10^{-221}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (- (+ x y) (* x y)) -1e-221) (* 1.0 x) (* 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if (((x + y) - (x * y)) <= -1e-221) {
		tmp = 1.0 * x;
	} else {
		tmp = 1.0 * 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 + y) - (x * y)) <= (-1d-221)) then
        tmp = 1.0d0 * x
    else
        tmp = 1.0d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((x + y) - (x * y)) <= -1e-221) {
		tmp = 1.0 * x;
	} else {
		tmp = 1.0 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((x + y) - (x * y)) <= -1e-221:
		tmp = 1.0 * x
	else:
		tmp = 1.0 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(x + y) - Float64(x * y)) <= -1e-221)
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(1.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((x + y) - (x * y)) <= -1e-221)
		tmp = 1.0 * x;
	else
		tmp = 1.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(x + y), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision], -1e-221], N[(1.0 * x), $MachinePrecision], N[(1.0 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (*.f64 x y)) < -1.00000000000000002e-221

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. lower--.f64 64.1

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

   5. Applied rewrites 64.1%

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

   6. Taylor expanded in y around 0

      \[\leadsto 1 \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 40.6%

      \[\leadsto 1 \cdot x \]

   if -1.00000000000000002e-221 < (-.f64 (+.f64 x y) (*.f64 x y))

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. lower--.f64 61.1

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

   5. Applied rewrites 61.1%

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

   6. Taylor expanded in x around 0

      \[\leadsto 1 \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 39.3%

      \[\leadsto 1 \cdot y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 86.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -13000:\\ \;\;\;\;\left(-y\right) \cdot x\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(1, x, y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - x\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -13000.0)
   (* (- y) x)
   (if (<= y 1.55e-8) (fma 1.0 x y) (* (- 1.0 x) y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -13000.0) {
		tmp = -y * x;
	} else if (y <= 1.55e-8) {
		tmp = fma(1.0, x, y);
	} else {
		tmp = (1.0 - x) * y;
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -13000.0)
		tmp = Float64(Float64(-y) * x);
	elseif (y <= 1.55e-8)
		tmp = fma(1.0, x, y);
	else
		tmp = Float64(Float64(1.0 - x) * y);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[y, -13000.0], N[((-y) * x), $MachinePrecision], If[LessEqual[y, 1.55e-8], N[(1.0 * x + y), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -13000

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. lower--.f64 57.4

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

   5. Applied rewrites 57.4%

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

   6. Taylor expanded in y around inf

      \[\leadsto \left(-1 \cdot y\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 55.7%

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

   if -13000 < y < 1.55e-8

   1. Initial program 100.0%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-+.f64 N/A

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

      5. associate-+r+ N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. distribute-rgt1-in N/A

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

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\mathsf{neg}\left(y\right)\right) + 1, x, y\right)} \]

      12. neg-mul-1 N/A

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

      13. lower-fma.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 99.6%

      \[\leadsto \mathsf{fma}\left(\color{blue}{1}, x, y\right) \]

   if 1.55e-8 < y

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. lower--.f64 98.0

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

   5. Applied rewrites 98.0%

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

Alternative 8: 100.0% accurate, 1.2× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (fma (- 1.0 x) y x))

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) - x \cdot y \]
2. Add Preprocessing

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. sub-neg N/A

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

   4. mul-1-neg N/A

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

   5. lower-fma.f64 N/A

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

   6. mul-1-neg N/A

      \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}, y, x\right) \]

   7. sub-neg N/A

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

   8. lower--.f64 100.0

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

5. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(1 - x, y, x\right)} \]
6. Add Preprocessing

Alternative 9: 75.4% accurate, 1.7× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (fma 1.0 x y))

C

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

Julia

function code(x, y)
	return fma(1.0, x, y)
end

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. lift--.f64 N/A

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

   2. sub-neg N/A

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

   3. +-commutative N/A

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

   4. lift-+.f64 N/A

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

   5. associate-+r+ N/A

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

   6. +-commutative N/A

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

   7. lift-*.f64 N/A

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

   8. *-commutative N/A

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

   9. distribute-lft-neg-in N/A

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

   10. distribute-rgt1-in N/A

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

   11. lower-fma.f64 N/A

       \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\mathsf{neg}\left(y\right)\right) + 1, x, y\right)} \]

   12. neg-mul-1 N/A

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

   13. lower-fma.f64 100.0

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

4. Applied rewrites 100.0%

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

5. Taylor expanded in y around 0

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

7. Applied rewrites 77.1%

   \[\leadsto \mathsf{fma}\left(\color{blue}{1}, x, y\right) \]
8. Add Preprocessing

Alternative 10: 39.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ 1 \cdot y \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) - x \cdot y \]
2. Add Preprocessing

3. Taylor expanded in y around inf

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

   1. *-commutative N/A

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

   2. sub-neg N/A

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

   3. mul-1-neg N/A

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

   4. lower-*.f64 N/A

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

   5. mul-1-neg N/A

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

   6. sub-neg N/A

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

   7. lower--.f64 61.5

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

5. Applied rewrites 61.5%

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

6. Taylor expanded in x around 0

   \[\leadsto 1 \cdot y \]
7. Step-by-step derivation

8. Applied rewrites 38.9%

   \[\leadsto 1 \cdot y \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024244 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))