Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 5.5s

Alternatives: 9

Speedup: 1.0×

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, 1.0× 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]

Derivation

1. Initial program 100.0%

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

Alternative 2: 62.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+168}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-62}:\\ \;\;\;\;0 - x\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-24}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;0 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.75e+168)
   (* x y)
   (if (<= x -1.4e-62) (- 0.0 x) (if (<= x 2.3e-24) y (- 0.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.75e+168) {
		tmp = x * y;
	} else if (x <= -1.4e-62) {
		tmp = 0.0 - x;
	} else if (x <= 2.3e-24) {
		tmp = y;
	} else {
		tmp = 0.0 - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.75d+168)) then
        tmp = x * y
    else if (x <= (-1.4d-62)) then
        tmp = 0.0d0 - x
    else if (x <= 2.3d-24) then
        tmp = y
    else
        tmp = 0.0d0 - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.75e+168) {
		tmp = x * y;
	} else if (x <= -1.4e-62) {
		tmp = 0.0 - x;
	} else if (x <= 2.3e-24) {
		tmp = y;
	} else {
		tmp = 0.0 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.75e+168:
		tmp = x * y
	elif x <= -1.4e-62:
		tmp = 0.0 - x
	elif x <= 2.3e-24:
		tmp = y
	else:
		tmp = 0.0 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.75e+168)
		tmp = Float64(x * y);
	elseif (x <= -1.4e-62)
		tmp = Float64(0.0 - x);
	elseif (x <= 2.3e-24)
		tmp = y;
	else
		tmp = Float64(0.0 - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.75e+168)
		tmp = x * y;
	elseif (x <= -1.4e-62)
		tmp = 0.0 - x;
	elseif (x <= 2.3e-24)
		tmp = y;
	else
		tmp = 0.0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.75e+168], N[(x * y), $MachinePrecision], If[LessEqual[x, -1.4e-62], N[(0.0 - x), $MachinePrecision], If[LessEqual[x, 2.3e-24], y, N[(0.0 - x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.7500000000000001e168

   1. Initial program 100.0%

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

      1. sub-neg N/A

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

      2. distribute-rgt1-in N/A

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

      3. *-commutative N/A

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

      4. associate-+l+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

      7. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

      9. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(1 + x\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(x + \color{blue}{1}\right)\right) \]

      3. +-lowering-+.f64 60.9%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   7. Simplified 60.9%

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

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{x}\right) \]
   9. Step-by-step derivation

   10. Simplified 60.9%

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

   if -1.7500000000000001e168 < x < -1.40000000000000001e-62 or 2.3000000000000001e-24 < x

   1. Initial program 100.0%

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

      1. sub-neg N/A

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

      2. distribute-rgt1-in N/A

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

      3. *-commutative N/A

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

      4. associate-+l+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

      7. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

      9. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{x} \]

      3. --lowering--.f64 59.5%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{x}\right) \]

   7. Simplified 59.5%

      \[\leadsto \color{blue}{0 - x} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 59.5%

         \[\leadsto \mathsf{neg.f64}\left(x\right) \]

   9. Applied egg-rr 59.5%

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

   if -1.40000000000000001e-62 < x < 2.3000000000000001e-24

   1. Initial program 100.0%

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

      1. sub-neg N/A

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

      2. distribute-rgt1-in N/A

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

      3. *-commutative N/A

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

      4. associate-+l+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

      7. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

      9. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 80.7%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+168}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-62}:\\ \;\;\;\;0 - x\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-24}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;0 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -12500000:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -12500000.0)
   (* x (+ y -1.0))
   (if (<= x 1.0) (- y x) (- (* x y) x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -12500000.0) {
		tmp = x * (y + -1.0);
	} else if (x <= 1.0) {
		tmp = y - x;
	} else {
		tmp = (x * 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 <= (-12500000.0d0)) then
        tmp = x * (y + (-1.0d0))
    else if (x <= 1.0d0) then
        tmp = y - x
    else
        tmp = (x * y) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -12500000.0) {
		tmp = x * (y + -1.0);
	} else if (x <= 1.0) {
		tmp = y - x;
	} else {
		tmp = (x * y) - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -12500000.0:
		tmp = x * (y + -1.0)
	elif x <= 1.0:
		tmp = y - x
	else:
		tmp = (x * y) - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -12500000.0)
		tmp = Float64(x * Float64(y + -1.0));
	elseif (x <= 1.0)
		tmp = Float64(y - x);
	else
		tmp = Float64(Float64(x * y) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -12500000.0)
		tmp = x * (y + -1.0);
	elseif (x <= 1.0)
		tmp = y - x;
	else
		tmp = (x * y) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -12500000.0], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0], N[(y - x), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.25e7

   1. Initial program 100.0%

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

      1. sub-neg N/A

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

      2. distribute-rgt1-in N/A

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

      3. *-commutative N/A

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

      4. associate-+l+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

      7. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

      9. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y - 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(y + -1\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-1 + \color{blue}{y}\right)\right) \]

      5. +-lowering-+.f64 99.9%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(-1, \color{blue}{y}\right)\right) \]

   7. Simplified 99.9%

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

   if -1.25e7 < x < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{y}, x\right) \]
   4. Step-by-step derivation

   5. Simplified 98.7%

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

   if 1 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(x \cdot y\right)}, x\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 98.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), x\right) \]

   5. Simplified 98.7%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -12500000:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + -1\right)\\ \mathbf{if}\;x \leq -12500000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (+ y -1.0))))
   (if (<= x -12500000.0) t_0 (if (<= x 1.0) (- y x) t_0))))

C

double code(double x, double y) {
	double t_0 = x * (y + -1.0);
	double tmp;
	if (x <= -12500000.0) {
		tmp = t_0;
	} else if (x <= 1.0) {
		tmp = y - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (y + (-1.0d0))
    if (x <= (-12500000.0d0)) then
        tmp = t_0
    else if (x <= 1.0d0) then
        tmp = y - x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x * (y + -1.0);
	double tmp;
	if (x <= -12500000.0) {
		tmp = t_0;
	} else if (x <= 1.0) {
		tmp = y - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (y + -1.0)
	tmp = 0
	if x <= -12500000.0:
		tmp = t_0
	elif x <= 1.0:
		tmp = y - x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(y + -1.0))
	tmp = 0.0
	if (x <= -12500000.0)
		tmp = t_0;
	elseif (x <= 1.0)
		tmp = Float64(y - x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * (y + -1.0);
	tmp = 0.0;
	if (x <= -12500000.0)
		tmp = t_0;
	elseif (x <= 1.0)
		tmp = y - x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -12500000.0], t$95$0, If[LessEqual[x, 1.0], N[(y - x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.25e7 or 1 < x

   1. Initial program 100.0%

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

      1. sub-neg N/A

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

      2. distribute-rgt1-in N/A

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

      3. *-commutative N/A

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

      4. associate-+l+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

      7. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

      9. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y - 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(y + -1\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-1 + \color{blue}{y}\right)\right) \]

      5. +-lowering-+.f64 99.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(-1, \color{blue}{y}\right)\right) \]

   7. Simplified 99.3%

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

   if -1.25e7 < x < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{y}, x\right) \]
   4. Step-by-step derivation

   5. Simplified 98.7%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -12500000:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-62}:\\ \;\;\;\;0 - x\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-25}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;0 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.5e-62) (- 0.0 x) (if (<= x 7e-25) y (- 0.0 x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.5e-62) {
		tmp = 0.0 - x;
	} else if (x <= 7e-25) {
		tmp = y;
	} else {
		tmp = 0.0 - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.5d-62)) then
        tmp = 0.0d0 - x
    else if (x <= 7d-25) then
        tmp = y
    else
        tmp = 0.0d0 - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.5e-62) {
		tmp = 0.0 - x;
	} else if (x <= 7e-25) {
		tmp = y;
	} else {
		tmp = 0.0 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.5e-62:
		tmp = 0.0 - x
	elif x <= 7e-25:
		tmp = y
	else:
		tmp = 0.0 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.5e-62)
		tmp = Float64(0.0 - x);
	elseif (x <= 7e-25)
		tmp = y;
	else
		tmp = Float64(0.0 - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.5e-62)
		tmp = 0.0 - x;
	elseif (x <= 7e-25)
		tmp = y;
	else
		tmp = 0.0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.5e-62], N[(0.0 - x), $MachinePrecision], If[LessEqual[x, 7e-25], y, N[(0.0 - x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5000000000000001e-62 or 7.0000000000000004e-25 < x

   1. Initial program 100.0%

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

      1. sub-neg N/A

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

      2. distribute-rgt1-in N/A

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

      3. *-commutative N/A

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

      4. associate-+l+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

      7. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

      9. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{x} \]

      3. --lowering--.f64 55.4%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{x}\right) \]

   7. Simplified 55.4%

      \[\leadsto \color{blue}{0 - x} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 55.4%

         \[\leadsto \mathsf{neg.f64}\left(x\right) \]

   9. Applied egg-rr 55.4%

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

   if -2.5000000000000001e-62 < x < 7.0000000000000004e-25

   1. Initial program 100.0%

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

      1. sub-neg N/A

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

      2. distribute-rgt1-in N/A

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

      3. *-commutative N/A

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

      4. associate-+l+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

      7. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

      9. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 80.7%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-62}:\\ \;\;\;\;0 - x\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-25}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;0 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1260000000:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1260000000.0) (* x y) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1260000000.0) {
		tmp = x * y;
	} 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 (y <= (-1260000000.0d0)) then
        tmp = x * y
    else
        tmp = y - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1260000000.0) {
		tmp = x * y;
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1260000000.0:
		tmp = x * y
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1260000000.0)
		tmp = Float64(x * y);
	else
		tmp = Float64(y - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1260000000.0)
		tmp = x * y;
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1260000000.0], N[(x * y), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.26e9

   1. Initial program 100.0%

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

      1. sub-neg N/A

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

      2. distribute-rgt1-in N/A

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

      3. *-commutative N/A

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

      4. associate-+l+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

      7. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

      9. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(1 + x\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(x + \color{blue}{1}\right)\right) \]

      3. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{x}\right) \]
   9. Step-by-step derivation

   10. Simplified 57.7%

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

   if -1.26e9 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{y}, x\right) \]
   4. Step-by-step derivation

   5. Simplified 85.1%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1260000000:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. sub-neg N/A

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

   2. distribute-rgt1-in N/A

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

   3. *-commutative N/A

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

   4. associate-+l+ N/A

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

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

   6. neg-mul-1 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

   7. distribute-rgt-out N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

   9. +-lowering-+.f64 100.0%

      \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

3. Simplified 100.0%

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

Alternative 8: 38.9% 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%

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

   1. sub-neg N/A

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

   2. distribute-rgt1-in N/A

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

   3. *-commutative N/A

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

   4. associate-+l+ N/A

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

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

   6. neg-mul-1 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

   7. distribute-rgt-out N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

   9. +-lowering-+.f64 100.0%

      \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

3. Simplified 100.0%

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

5. Taylor expanded in x around 0

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

7. Simplified 36.4%

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

Alternative 9: 2.7% 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%

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

   1. sub-neg N/A

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

   2. distribute-rgt1-in N/A

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

   3. *-commutative N/A

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

   4. associate-+l+ N/A

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

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

   6. neg-mul-1 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

   7. distribute-rgt-out N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

   9. +-lowering-+.f64 100.0%

      \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

3. Simplified 100.0%

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

5. Taylor expanded in y around 0

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

   1. mul-1-neg N/A

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

   2. neg-sub0 N/A

      \[\leadsto 0 - \color{blue}{x} \]

   3. --lowering--.f64 41.0%

      \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{x}\right) \]

7. Simplified 41.0%

   \[\leadsto \color{blue}{0 - x} \]
8. Step-by-step derivation

   1. sub0-neg N/A

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

   2. neg-lowering-neg.f64 41.0%

      \[\leadsto \mathsf{neg.f64}\left(x\right) \]

9. Applied egg-rr 41.0%

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

    1. neg-sub0 N/A

       \[\leadsto 0 - \color{blue}{x} \]

    2. flip3-- N/A

       \[\leadsto \frac{{0}^{3} - {x}^{3}}{\color{blue}{0 \cdot 0 + \left(x \cdot x + 0 \cdot x\right)}} \]

    3. metadata-eval N/A

       \[\leadsto \frac{0 - {x}^{3}}{\color{blue}{0} \cdot 0 + \left(x \cdot x + 0 \cdot x\right)} \]

    4. neg-sub0 N/A

       \[\leadsto \frac{\mathsf{neg}\left({x}^{3}\right)}{\color{blue}{0 \cdot 0} + \left(x \cdot x + 0 \cdot x\right)} \]

    5. cube-neg N/A

       \[\leadsto \frac{{\left(\mathsf{neg}\left(x\right)\right)}^{3}}{\color{blue}{0 \cdot 0} + \left(x \cdot x + 0 \cdot x\right)} \]

    6. sqr-pow N/A

       \[\leadsto \frac{{\left(\mathsf{neg}\left(x\right)\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(\mathsf{neg}\left(x\right)\right)}^{\left(\frac{3}{2}\right)}}{\color{blue}{0 \cdot 0} + \left(x \cdot x + 0 \cdot x\right)} \]

    7. unpow-prod-down N/A

       \[\leadsto \frac{{\left(\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\mathsf{neg}\left(x\right)\right)\right)}^{\left(\frac{3}{2}\right)}}{\color{blue}{0 \cdot 0} + \left(x \cdot x + 0 \cdot x\right)} \]

    8. sqr-neg N/A

       \[\leadsto \frac{{\left(x \cdot x\right)}^{\left(\frac{3}{2}\right)}}{\color{blue}{0} \cdot 0 + \left(x \cdot x + 0 \cdot x\right)} \]

    9. pow-prod-down N/A

       \[\leadsto \frac{{x}^{\left(\frac{3}{2}\right)} \cdot {x}^{\left(\frac{3}{2}\right)}}{\color{blue}{0 \cdot 0} + \left(x \cdot x + 0 \cdot x\right)} \]

    10. sqr-pow N/A

        \[\leadsto \frac{{x}^{3}}{\color{blue}{0 \cdot 0} + \left(x \cdot x + 0 \cdot x\right)} \]

    11. metadata-eval N/A

        \[\leadsto \frac{{x}^{3}}{0 + \left(\color{blue}{x \cdot x} + 0 \cdot x\right)} \]

    12. +-lft-identity N/A

        \[\leadsto \frac{{x}^{3}}{x \cdot x + \color{blue}{0 \cdot x}} \]

    13. distribute-rgt-out N/A

        \[\leadsto \frac{{x}^{3}}{x \cdot \color{blue}{\left(x + 0\right)}} \]

    14. +-commutative N/A

        \[\leadsto \frac{{x}^{3}}{x \cdot \left(0 + \color{blue}{x}\right)} \]

    15. +-lft-identity N/A

        \[\leadsto \frac{{x}^{3}}{x \cdot x} \]

    16. pow2 N/A

        \[\leadsto \frac{{x}^{3}}{{x}^{\color{blue}{2}}} \]

    17. pow-div N/A

        \[\leadsto {x}^{\color{blue}{\left(3 - 2\right)}} \]

    18. metadata-eval N/A

        \[\leadsto {x}^{1} \]

    19. unpow1 2.7%

        \[\leadsto x \]

11. Applied egg-rr 2.7%

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

Reproduce

herbie shell --seed 2024161 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))