Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.7s

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

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

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: 62.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+240}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+52}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-17}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-91}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+233}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.5e+240)
   y
   (if (<= y -4.5e+52)
     (* y x)
     (if (<= y -3.2e-17)
       y
       (if (<= y 9.5e-91) (- x) (if (<= y 3.5e+233) y (* y x)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.5e+240) {
		tmp = y;
	} else if (y <= -4.5e+52) {
		tmp = y * x;
	} else if (y <= -3.2e-17) {
		tmp = y;
	} else if (y <= 9.5e-91) {
		tmp = -x;
	} else if (y <= 3.5e+233) {
		tmp = 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 <= (-1.5d+240)) then
        tmp = y
    else if (y <= (-4.5d+52)) then
        tmp = y * x
    else if (y <= (-3.2d-17)) then
        tmp = y
    else if (y <= 9.5d-91) then
        tmp = -x
    else if (y <= 3.5d+233) then
        tmp = y
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.5e+240) {
		tmp = y;
	} else if (y <= -4.5e+52) {
		tmp = y * x;
	} else if (y <= -3.2e-17) {
		tmp = y;
	} else if (y <= 9.5e-91) {
		tmp = -x;
	} else if (y <= 3.5e+233) {
		tmp = y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.5e+240:
		tmp = y
	elif y <= -4.5e+52:
		tmp = y * x
	elif y <= -3.2e-17:
		tmp = y
	elif y <= 9.5e-91:
		tmp = -x
	elif y <= 3.5e+233:
		tmp = y
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.5e+240)
		tmp = y;
	elseif (y <= -4.5e+52)
		tmp = Float64(y * x);
	elseif (y <= -3.2e-17)
		tmp = y;
	elseif (y <= 9.5e-91)
		tmp = Float64(-x);
	elseif (y <= 3.5e+233)
		tmp = y;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.5e+240)
		tmp = y;
	elseif (y <= -4.5e+52)
		tmp = y * x;
	elseif (y <= -3.2e-17)
		tmp = y;
	elseif (y <= 9.5e-91)
		tmp = -x;
	elseif (y <= 3.5e+233)
		tmp = y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.5e+240], y, If[LessEqual[y, -4.5e+52], N[(y * x), $MachinePrecision], If[LessEqual[y, -3.2e-17], y, If[LessEqual[y, 9.5e-91], (-x), If[LessEqual[y, 3.5e+233], y, N[(y * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4999999999999999e240 or -4.5e52 < y < -3.2000000000000002e-17 or 9.5e-91 < y < 3.4999999999999998e233

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 64.5%

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

   if -1.4999999999999999e240 < y < -4.5e52 or 3.4999999999999998e233 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in x around inf 69.9%

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

   if -3.2000000000000002e-17 < y < 9.5e-91

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.1%

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

      1. neg-mul-1 82.1%

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

   5. Simplified 82.1%

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

Alternative 3: 74.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+231} \lor \neg \left(y \leq -5.8 \cdot 10^{+51}\right) \land y \leq 1.25 \cdot 10^{+233}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.4e+231) (and (not (<= y -5.8e+51)) (<= y 1.25e+233)))
   (- y x)
   (* y x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.4e+231) || (!(y <= -5.8e+51) && (y <= 1.25e+233))) {
		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 ((y <= (-1.4d+231)) .or. (.not. (y <= (-5.8d+51))) .and. (y <= 1.25d+233)) 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 ((y <= -1.4e+231) || (!(y <= -5.8e+51) && (y <= 1.25e+233))) {
		tmp = y - x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.4e+231) or (not (y <= -5.8e+51) and (y <= 1.25e+233)):
		tmp = y - x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.4e+231) || (!(y <= -5.8e+51) && (y <= 1.25e+233)))
		tmp = Float64(y - x);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.4e+231) || (~((y <= -5.8e+51)) && (y <= 1.25e+233)))
		tmp = y - x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.4e+231], And[N[Not[LessEqual[y, -5.8e+51]], $MachinePrecision], LessEqual[y, 1.25e+233]]], N[(y - x), $MachinePrecision], N[(y * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e231 or -5.7999999999999997e51 < y < 1.25000000000000002e233

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 87.8%

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

   4. Taylor expanded in y around 0 87.8%

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

   if -1.4e231 < y < -5.7999999999999997e51 or 1.25000000000000002e233 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in x around inf 71.5%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+231} \lor \neg \left(y \leq -5.8 \cdot 10^{+51}\right) \land y \leq 1.25 \cdot 10^{+233}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -210000000 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;y \cdot x - x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -210000000.0) (not (<= x 1.0))) (- (* y x) x) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -210000000.0) || !(x <= 1.0)) {
		tmp = (y * x) - 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 <= (-210000000.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = (y * x) - x
    else
        tmp = y - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -210000000.0) || !(x <= 1.0)) {
		tmp = (y * x) - x;
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -210000000.0) or not (x <= 1.0):
		tmp = (y * x) - x
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -210000000.0) || !(x <= 1.0))
		tmp = Float64(Float64(y * x) - x);
	else
		tmp = Float64(y - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -210000000.0) || ~((x <= 1.0)))
		tmp = (y * x) - x;
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -210000000.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1e8 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 99.5%

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

   if -2.1e8 < x < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 99.0%

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

   4. Taylor expanded in y around 0 99.0%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -210000000 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;y \cdot x - x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3500000000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3500000000.0) (not (<= y 1.0))) (* y (+ x 1.0)) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3500000000.0) || !(y <= 1.0)) {
		tmp = y * (x + 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 ((y <= (-3500000000.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = y * (x + 1.0d0)
    else
        tmp = y - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -3500000000.0) || !(y <= 1.0)) {
		tmp = y * (x + 1.0);
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3500000000.0) or not (y <= 1.0):
		tmp = y * (x + 1.0)
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -3500000000.0) || !(y <= 1.0))
		tmp = Float64(y * Float64(x + 1.0));
	else
		tmp = Float64(y - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -3500000000.0) || ~((y <= 1.0)))
		tmp = y * (x + 1.0);
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3500000000.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5e9 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.4%

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

   if -3.5e9 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 98.2%

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

   4. Taylor expanded in y around 0 98.2%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3500000000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3500000000:\\ \;\;\;\;y + y \cdot x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3500000000.0)
   (+ y (* y x))
   (if (<= y 1.0) (- y x) (* y (+ x 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3500000000.0) {
		tmp = y + (y * x);
	} else if (y <= 1.0) {
		tmp = y - x;
	} else {
		tmp = y * (x + 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 (y <= (-3500000000.0d0)) then
        tmp = y + (y * x)
    else if (y <= 1.0d0) then
        tmp = y - x
    else
        tmp = y * (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3500000000.0) {
		tmp = y + (y * x);
	} else if (y <= 1.0) {
		tmp = y - x;
	} else {
		tmp = y * (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3500000000.0:
		tmp = y + (y * x)
	elif y <= 1.0:
		tmp = y - x
	else:
		tmp = y * (x + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3500000000.0)
		tmp = Float64(y + Float64(y * x));
	elseif (y <= 1.0)
		tmp = Float64(y - x);
	else
		tmp = Float64(y * Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3500000000.0)
		tmp = y + (y * x);
	elseif (y <= 1.0)
		tmp = y - x;
	else
		tmp = y * (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3500000000.0], N[(y + N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.0], N[(y - x), $MachinePrecision], N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5e9

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

      1. distribute-rgt-in 100.0%

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

      2. *-un-lft-identity 100.0%

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

      3. *-commutative 100.0%

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

      4. +-commutative 100.0%

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

   5. Applied egg-rr 100.0%

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

   if -3.5e9 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 98.2%

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

   4. Taylor expanded in y around 0 98.2%

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

   if 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 98.8%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3500000000:\\ \;\;\;\;y + y \cdot x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-16}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-91}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.3e-16) y (if (<= y 8e-91) (- x) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.3e-16) {
		tmp = y;
	} else if (y <= 8e-91) {
		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 <= (-1.3d-16)) then
        tmp = y
    else if (y <= 8d-91) 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 <= -1.3e-16) {
		tmp = y;
	} else if (y <= 8e-91) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.3e-16:
		tmp = y
	elif y <= 8e-91:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.3e-16)
		tmp = y;
	elseif (y <= 8e-91)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.3e-16)
		tmp = y;
	elseif (y <= 8e-91)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.3e-16], y, If[LessEqual[y, 8e-91], (-x), y]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2999999999999999e-16 or 8.00000000000000018e-91 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 52.8%

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

   if -1.2999999999999999e-16 < y < 8.00000000000000018e-91

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.1%

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

      1. neg-mul-1 82.1%

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

   5. Simplified 82.1%

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

Alternative 8: 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 9: 38.8% 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. Taylor expanded in x around 0 38.2%

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

Reproduce

herbie shell --seed 2024170 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))