Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.8s

Alternatives: 8

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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. sub-neg 100.0%

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

   2. *-commutative 100.0%

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

   3. +-commutative 100.0%

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

   4. distribute-lft-in 100.0%

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

   5. *-rgt-identity 100.0%

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

   6. associate-+l+ 100.0%

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

   7. *-commutative 100.0%

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

   8. +-commutative 100.0%

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

   9. *-commutative 100.0%

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

   10. neg-mul-1 100.0%

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

   11. distribute-rgt-out 100.0%

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

   12. fma-define 100.0%

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

3. Simplified 100.0%

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

Alternative 2: 62.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.04 \cdot 10^{-10}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{-21}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+84} \lor \neg \left(y \leq 1.45 \cdot 10^{+149}\right) \land y \leq 1.12 \cdot 10^{+229}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.04e-10)
   y
   (if (<= y 3.25e-21)
     (- x)
     (if (or (<= y 2.05e+84) (and (not (<= y 1.45e+149)) (<= y 1.12e+229)))
       y
       (* x y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.04e-10) {
		tmp = y;
	} else if (y <= 3.25e-21) {
		tmp = -x;
	} else if ((y <= 2.05e+84) || (!(y <= 1.45e+149) && (y <= 1.12e+229))) {
		tmp = y;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.04d-10)) then
        tmp = y
    else if (y <= 3.25d-21) then
        tmp = -x
    else if ((y <= 2.05d+84) .or. (.not. (y <= 1.45d+149)) .and. (y <= 1.12d+229)) then
        tmp = y
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.04e-10) {
		tmp = y;
	} else if (y <= 3.25e-21) {
		tmp = -x;
	} else if ((y <= 2.05e+84) || (!(y <= 1.45e+149) && (y <= 1.12e+229))) {
		tmp = y;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.04e-10:
		tmp = y
	elif y <= 3.25e-21:
		tmp = -x
	elif (y <= 2.05e+84) or (not (y <= 1.45e+149) and (y <= 1.12e+229)):
		tmp = y
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.04e-10)
		tmp = y;
	elseif (y <= 3.25e-21)
		tmp = Float64(-x);
	elseif ((y <= 2.05e+84) || (!(y <= 1.45e+149) && (y <= 1.12e+229)))
		tmp = y;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.04e-10)
		tmp = y;
	elseif (y <= 3.25e-21)
		tmp = -x;
	elseif ((y <= 2.05e+84) || (~((y <= 1.45e+149)) && (y <= 1.12e+229)))
		tmp = y;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.04e-10], y, If[LessEqual[y, 3.25e-21], (-x), If[Or[LessEqual[y, 2.05e+84], And[N[Not[LessEqual[y, 1.45e+149]], $MachinePrecision], LessEqual[y, 1.12e+229]]], y, N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.04e-10 or 3.24999999999999993e-21 < y < 2.05000000000000015e84 or 1.4500000000000001e149 < y < 1.12e229

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. +-commutative 100.0%

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

      4. distribute-lft-in 100.0%

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

      5. *-rgt-identity 100.0%

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

      6. associate-+l+ 100.0%

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

      7. *-commutative 100.0%

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

      8. +-commutative 100.0%

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

      9. *-commutative 100.0%

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

      10. neg-mul-1 100.0%

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

      11. distribute-rgt-out 100.0%

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

      12. fma-define 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 59.7%

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

   if -1.04e-10 < y < 3.24999999999999993e-21

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 86.3%

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

      1. neg-mul-1 86.3%

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

   5. Simplified 86.3%

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

   if 2.05000000000000015e84 < y < 1.4500000000000001e149 or 1.12e229 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. +-commutative 100.0%

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

      4. distribute-lft-in 100.0%

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

      5. *-rgt-identity 100.0%

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

      6. associate-+l+ 100.0%

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

      7. *-commutative 100.0%

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

      8. +-commutative 100.0%

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

      9. *-commutative 100.0%

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

      10. neg-mul-1 100.0%

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

      11. distribute-rgt-out 100.0%

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

      12. fma-define 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around inf 100.0%

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

   8. Taylor expanded in x around inf 70.8%

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

      1. *-commutative 70.8%

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

   10. Simplified 70.8%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.04 \cdot 10^{-10}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{-21}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+84} \lor \neg \left(y \leq 1.45 \cdot 10^{+149}\right) \land y \leq 1.12 \cdot 10^{+229}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 4 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 4e-7))) (* x (+ y -1.0)) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 4e-7)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = y - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.0d0)) .or. (.not. (x <= 4d-7))) then
        tmp = x * (y + (-1.0d0))
    else
        tmp = y - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 4e-7)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.0) or not (x <= 4e-7):
		tmp = x * (y + -1.0)
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 4e-7))
		tmp = Float64(x * Float64(y + -1.0));
	else
		tmp = Float64(y - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 4e-7)))
		tmp = x * (y + -1.0);
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 4e-7]], $MachinePrecision]], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 3.9999999999999998e-7 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 98.7%

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

   if -1 < x < 3.9999999999999998e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 99.7%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 4 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-7}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.0) (* x (+ y -1.0)) (if (<= x 4e-7) (- y x) (- (* x y) x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = x * (y + -1.0);
	} else if (x <= 4e-7) {
		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 <= (-1.0d0)) then
        tmp = x * (y + (-1.0d0))
    else if (x <= 4d-7) 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 <= -1.0) {
		tmp = x * (y + -1.0);
	} else if (x <= 4e-7) {
		tmp = y - x;
	} else {
		tmp = (x * y) - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.0:
		tmp = x * (y + -1.0)
	elif x <= 4e-7:
		tmp = y - x
	else:
		tmp = (x * y) - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(x * Float64(y + -1.0));
	elseif (x <= 4e-7)
		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 <= -1.0)
		tmp = x * (y + -1.0);
	elseif (x <= 4e-7)
		tmp = y - x;
	else
		tmp = (x * y) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.0], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4e-7], N[(y - x), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 98.5%

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

   if -1 < x < 3.9999999999999998e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 99.7%

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

   if 3.9999999999999998e-7 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.0%

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

      1. *-commutative 99.0%

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

   5. Simplified 99.0%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-7}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{-17}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-26}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.65e-17) y (if (<= y 2.2e-26) (- x) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.65e-17) {
		tmp = y;
	} else if (y <= 2.2e-26) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-2.65d-17)) then
        tmp = y
    else if (y <= 2.2d-26) then
        tmp = -x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.65e-17) {
		tmp = y;
	} else if (y <= 2.2e-26) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.65e-17:
		tmp = y
	elif y <= 2.2e-26:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.65e-17)
		tmp = y;
	elseif (y <= 2.2e-26)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.65e-17)
		tmp = y;
	elseif (y <= 2.2e-26)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.65e-17], y, If[LessEqual[y, 2.2e-26], (-x), y]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6499999999999999e-17 or 2.2000000000000001e-26 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. +-commutative 100.0%

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

      4. distribute-lft-in 100.0%

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

      5. *-rgt-identity 100.0%

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

      6. associate-+l+ 100.0%

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

      7. *-commutative 100.0%

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

      8. +-commutative 100.0%

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

      9. *-commutative 100.0%

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

      10. neg-mul-1 100.0%

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

      11. distribute-rgt-out 100.0%

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

      12. fma-define 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 52.9%

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

   if -2.6499999999999999e-17 < y < 2.2000000000000001e-26

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 86.3%

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

      1. neg-mul-1 86.3%

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

   5. Simplified 86.3%

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

Alternative 6: 75.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+72}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x -2.6e+72) (* x y) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.6e+72) {
		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 (x <= (-2.6d+72)) 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 (x <= -2.6e+72) {
		tmp = x * y;
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.6e+72:
		tmp = x * y
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.6e+72)
		tmp = Float64(x * y);
	else
		tmp = Float64(y - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.6e+72)
		tmp = x * y;
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.6e+72], N[(x * y), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.59999999999999981e72

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. +-commutative 100.0%

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

      4. distribute-lft-in 100.0%

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

      5. *-rgt-identity 100.0%

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

      6. associate-+l+ 100.0%

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

      7. *-commutative 100.0%

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

      8. +-commutative 100.0%

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

      9. *-commutative 100.0%

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

      10. neg-mul-1 100.0%

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

      11. distribute-rgt-out 100.0%

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

      12. fma-define 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around inf 54.8%

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

   8. Taylor expanded in x around inf 54.8%

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

      1. *-commutative 54.8%

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

   10. Simplified 54.8%

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

   if -2.59999999999999981e72 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 85.7%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+72}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]
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 100.0%

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

   2. *-commutative 100.0%

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

   3. +-commutative 100.0%

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

   4. distribute-lft-in 100.0%

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

   5. *-rgt-identity 100.0%

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

   6. associate-+l+ 100.0%

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

   7. *-commutative 100.0%

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

   8. +-commutative 100.0%

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

   9. *-commutative 100.0%

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

   10. neg-mul-1 100.0%

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

   11. distribute-rgt-out 100.0%

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

   12. fma-define 100.0%

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

3. Simplified 100.0%

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

   1. fma-undefine 100.0%

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

6. Applied egg-rr 100.0%

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

7. Final simplification 100.0%

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

Alternative 8: 39.1% 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 100.0%

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

   2. *-commutative 100.0%

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

   3. +-commutative 100.0%

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

   4. distribute-lft-in 100.0%

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

   5. *-rgt-identity 100.0%

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

   6. associate-+l+ 100.0%

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

   7. *-commutative 100.0%

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

   8. +-commutative 100.0%

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

   9. *-commutative 100.0%

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

   10. neg-mul-1 100.0%

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

   11. distribute-rgt-out 100.0%

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

   12. fma-define 100.0%

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

3. Simplified 100.0%

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

   1. fma-undefine 100.0%

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

6. Applied egg-rr 100.0%

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

7. Taylor expanded in x around 0 34.7%

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

Reproduce

herbie shell --seed 2024108 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))