Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 3.1s

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, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(N[(y + N[(y * x), $MachinePrecision]), $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. *-commutative 100.0%

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

   2. distribute-lft-in 100.0%

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

   3. *-commutative 100.0%

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

   4. *-un-lft-identity 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+284} \lor \neg \left(x \leq 2.35 \cdot 10^{+104} \lor \neg \left(x \leq 1.65 \cdot 10^{+139}\right) \land x \leq 8.5 \cdot 10^{+260}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.5e+284)
         (not
          (or (<= x 2.35e+104) (and (not (<= x 1.65e+139)) (<= x 8.5e+260)))))
   (* y x)
   (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.5e+284) || !((x <= 2.35e+104) || (!(x <= 1.65e+139) && (x <= 8.5e+260)))) {
		tmp = y * x;
	} 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 <= (-1.5d+284)) .or. (.not. (x <= 2.35d+104) .or. (.not. (x <= 1.65d+139)) .and. (x <= 8.5d+260))) then
        tmp = y * x
    else
        tmp = y - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.5e+284) || !((x <= 2.35e+104) || (!(x <= 1.65e+139) && (x <= 8.5e+260)))) {
		tmp = y * x;
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.5e+284) or not ((x <= 2.35e+104) or (not (x <= 1.65e+139) and (x <= 8.5e+260))):
		tmp = y * x
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.5e+284) || !((x <= 2.35e+104) || (!(x <= 1.65e+139) && (x <= 8.5e+260))))
		tmp = Float64(y * x);
	else
		tmp = Float64(y - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.5e+284) || ~(((x <= 2.35e+104) || (~((x <= 1.65e+139)) && (x <= 8.5e+260)))))
		tmp = y * x;
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.5e+284], N[Not[Or[LessEqual[x, 2.35e+104], And[N[Not[LessEqual[x, 1.65e+139]], $MachinePrecision], LessEqual[x, 8.5e+260]]]], $MachinePrecision]], N[(y * x), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.50000000000000004e284 or 2.35000000000000008e104 < x < 1.6500000000000001e139 or 8.5e260 < x

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around inf 76.7%

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

   6. Taylor expanded in x around inf 76.7%

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

      1. *-commutative 76.7%

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

   8. Simplified 76.7%

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

   if -1.50000000000000004e284 < x < 2.35000000000000008e104 or 1.6500000000000001e139 < x < 8.5e260

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 85.1%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+284} \lor \neg \left(x \leq 2.35 \cdot 10^{+104} \lor \neg \left(x \leq 1.65 \cdot 10^{+139}\right) \land x \leq 8.5 \cdot 10^{+260}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -10000000000000 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -10000000000000.0) (not (<= x 1.0))) (* x (+ y -1.0)) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -10000000000000.0) || !(x <= 1.0)) {
		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 <= (-10000000000000.0d0)) .or. (.not. (x <= 1.0d0))) 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 <= -10000000000000.0) || !(x <= 1.0)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -10000000000000.0) or not (x <= 1.0):
		tmp = x * (y + -1.0)
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -10000000000000.0) || !(x <= 1.0))
		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 <= -10000000000000.0) || ~((x <= 1.0)))
		tmp = x * (y + -1.0);
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -10000000000000.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1e13 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 99.8%

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

   if -1e13 < x < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 98.9%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -10000000000000 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -10000000000000:\\ \;\;\;\;y \cdot x - x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -10000000000000.0)
   (- (* y x) x)
   (if (<= x 1.0) (- y x) (* x (+ y -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -10000000000000.0) {
		tmp = (y * x) - x;
	} else if (x <= 1.0) {
		tmp = y - x;
	} else {
		tmp = x * (y + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-10000000000000.0d0)) then
        tmp = (y * x) - x
    else if (x <= 1.0d0) then
        tmp = y - x
    else
        tmp = x * (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -10000000000000.0) {
		tmp = (y * x) - x;
	} else if (x <= 1.0) {
		tmp = y - x;
	} else {
		tmp = x * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -10000000000000.0:
		tmp = (y * x) - x
	elif x <= 1.0:
		tmp = y - x
	else:
		tmp = x * (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -10000000000000.0)
		tmp = Float64(Float64(y * x) - x);
	elseif (x <= 1.0)
		tmp = Float64(y - x);
	else
		tmp = Float64(x * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -10000000000000.0)
		tmp = (y * x) - x;
	elseif (x <= 1.0)
		tmp = y - x;
	else
		tmp = x * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -10000000000000.0], N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[x, 1.0], N[(y - x), $MachinePrecision], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1e13

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -1e13 < x < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 98.9%

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

   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 99.7%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -10000000000000:\\ \;\;\;\;y \cdot x - x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-15}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1e-15) y (if (<= y 1.0) (- x) (* y x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1e-15) {
		tmp = y;
	} else if (y <= 1.0) {
		tmp = -x;
	} 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 <= (-1d-15)) then
        tmp = y
    else if (y <= 1.0d0) then
        tmp = -x
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1e-15) {
		tmp = y;
	} else if (y <= 1.0) {
		tmp = -x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1e-15:
		tmp = y
	elif y <= 1.0:
		tmp = -x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1e-15)
		tmp = y;
	elseif (y <= 1.0)
		tmp = Float64(-x);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1e-15)
		tmp = y;
	elseif (y <= 1.0)
		tmp = -x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1e-15], y, If[LessEqual[y, 1.0], (-x), N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0000000000000001e-15

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around 0 59.1%

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

   if -1.0000000000000001e-15 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.6%

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

      1. neg-mul-1 82.6%

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

   5. Simplified 82.6%

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

   if 1 < y

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. distribute-lft-in 100.0%

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

      3. *-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around inf 96.3%

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

   6. Taylor expanded in x around inf 49.7%

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

      1. *-commutative 49.7%

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

   8. Simplified 49.7%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-15}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 7: 62.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-16}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-6}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.5e-16) y (if (<= y 6.1e-6) (- x) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.5e-16) {
		tmp = y;
	} else if (y <= 6.1e-6) {
		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 <= (-2.5d-16)) then
        tmp = y
    else if (y <= 6.1d-6) 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 <= -2.5e-16) {
		tmp = y;
	} else if (y <= 6.1e-6) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.5e-16:
		tmp = y
	elif y <= 6.1e-6:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.5e-16)
		tmp = y;
	elseif (y <= 6.1e-6)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.5e-16)
		tmp = y;
	elseif (y <= 6.1e-6)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.5e-16], y, If[LessEqual[y, 6.1e-6], (-x), y]]

Derivation

1. Split input into 2 regimes

2. if y < -2.5000000000000002e-16 or 6.10000000000000004e-6 < y

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around 0 54.7%

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

   if -2.5000000000000002e-16 < y < 6.10000000000000004e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.6%

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

      1. neg-mul-1 82.6%

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

   5. Simplified 82.6%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-16}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-6}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.3% 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. Add Preprocessing
3. Step-by-step derivation

   1. *-commutative 100.0%

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

   2. distribute-lft-in 100.0%

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

   3. *-commutative 100.0%

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

   4. *-un-lft-identity 100.0%

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

4. Applied egg-rr 100.0%

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

5. Taylor expanded in x around 0 38.2%

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

6. Final simplification 38.2%

   \[\leadsto y \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024011 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))