Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 5.4s

Alternatives: 7

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-+.f64 N/A

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

   4. distribute-lft-in N/A

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

   5. *-rgt-identity N/A

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

   6. lower-fma.f64 100.0

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

4. Applied rewrites 100.0%

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

Alternative 2: 97.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(y, x, -x\right)\\ \mathbf{if}\;x \leq -8.8 \cdot 10^{+36}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;1 \cdot y - x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (fma y x (- x))))
   (if (<= x -8.8e+36) t_0 (if (<= x 1.0) (- (* 1.0 y) x) t_0))))

C

double code(double x, double y) {
	double t_0 = fma(y, x, -x);
	double tmp;
	if (x <= -8.8e+36) {
		tmp = t_0;
	} else if (x <= 1.0) {
		tmp = (1.0 * y) - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = fma(y, x, Float64(-x))
	tmp = 0.0
	if (x <= -8.8e+36)
		tmp = t_0;
	elseif (x <= 1.0)
		tmp = Float64(Float64(1.0 * y) - x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y * x + (-x)), $MachinePrecision]}, If[LessEqual[x, -8.8e+36], t$95$0, If[LessEqual[x, 1.0], N[(N[(1.0 * y), $MachinePrecision] - x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.80000000000000002e36 or 1 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. distribute-lft-out-- N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. *-commutative N/A

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

      4. *-rgt-identity N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 100.0

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

   5. Applied rewrites 100.0%

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

   if -8.80000000000000002e36 < x < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 98.7%

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

Alternative 3: 87.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(y, x, -x\right)\\ \mathbf{if}\;x \leq -1.06 \cdot 10^{-28}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-33}:\\ \;\;\;\;\mathsf{fma}\left(y, x, y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (fma y x (- x))))
   (if (<= x -1.06e-28) t_0 (if (<= x 1.6e-33) (fma y x y) t_0))))

C

double code(double x, double y) {
	double t_0 = fma(y, x, -x);
	double tmp;
	if (x <= -1.06e-28) {
		tmp = t_0;
	} else if (x <= 1.6e-33) {
		tmp = fma(y, x, y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = fma(y, x, Float64(-x))
	tmp = 0.0
	if (x <= -1.06e-28)
		tmp = t_0;
	elseif (x <= 1.6e-33)
		tmp = fma(y, x, y);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y * x + (-x)), $MachinePrecision]}, If[LessEqual[x, -1.06e-28], t$95$0, If[LessEqual[x, 1.6e-33], N[(y * x + y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.06e-28 or 1.59999999999999988e-33 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. distribute-lft-out-- N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. *-commutative N/A

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

      4. *-rgt-identity N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 97.0

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

   5. Applied rewrites 97.0%

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

   if -1.06e-28 < x < 1.59999999999999988e-33

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-+.f64 N/A

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

      4. distribute-lft-in N/A

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

      5. *-rgt-identity N/A

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

      6. lower-fma.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-in N/A

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

      6. +-commutative N/A

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

      7. remove-double-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-lft-in N/A

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

      10. *-rgt-identity N/A

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

      11. lower-fma.f64 82.2

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

   7. Applied rewrites 82.2%

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

Alternative 4: 86.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-38}:\\ \;\;\;\;\mathsf{fma}\left(y, x, y\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-10}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.8e-38) (fma y x y) (if (<= y 8e-10) (- x) (fma y x y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.8e-38) {
		tmp = fma(y, x, y);
	} else if (y <= 8e-10) {
		tmp = -x;
	} else {
		tmp = fma(y, x, y);
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.8e-38)
		tmp = fma(y, x, y);
	elseif (y <= 8e-10)
		tmp = Float64(-x);
	else
		tmp = fma(y, x, y);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.8e-38], N[(y * x + y), $MachinePrecision], If[LessEqual[y, 8e-10], (-x), N[(y * x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8e-38 or 8.00000000000000029e-10 < y

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-+.f64 N/A

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

      4. distribute-lft-in N/A

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

      5. *-rgt-identity N/A

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

      6. lower-fma.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-in N/A

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

      6. +-commutative N/A

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

      7. remove-double-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-lft-in N/A

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

      10. *-rgt-identity N/A

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

      11. lower-fma.f64 94.4

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

   7. Applied rewrites 94.4%

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

   if -1.8e-38 < y < 8.00000000000000029e-10

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{-1 \cdot x} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lower-neg.f64 79.3

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

   5. Applied rewrites 79.3%

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

Alternative 5: 62.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) (* x y) (if (<= y 1.0) (- x) (* x y))))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-+.f64 N/A

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

      4. distribute-lft-in N/A

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

      5. *-rgt-identity N/A

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

      6. lower-fma.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-in N/A

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

      6. +-commutative N/A

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

      7. remove-double-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-lft-in N/A

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

      10. *-rgt-identity N/A

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

      11. lower-fma.f64 96.2

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

   7. Applied rewrites 96.2%

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

   8. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{y} \]
   9. Step-by-step derivation

   10. Applied rewrites 42.9%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{-1 \cdot x} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lower-neg.f64 75.7

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

   5. Applied rewrites 75.7%

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

4. Final simplification 60.3%

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

Alternative 6: 38.4% accurate, 4.0× 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 Float64(-x)
end

MATLAB

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

Wolfram

code[x_, y_] := (-x)

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{-1 \cdot x} \]
4. Step-by-step derivation

   1. mul-1-neg N/A

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

   2. lower-neg.f64 41.6

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

5. Applied rewrites 41.6%

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

Alternative 7: 2.7% accurate, 12.0× 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%

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

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{-1 \cdot x} \]
4. Step-by-step derivation

   1. mul-1-neg N/A

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

   2. lower-neg.f64 41.6

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

5. Applied rewrites 41.6%

   \[\leadsto \color{blue}{-x} \]
6. Step-by-step derivation

7. Applied rewrites 2.5%

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

Reproduce

herbie shell --seed 2024331 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))