Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.3s

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. fma-neg 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 84.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + -1\right)\\ \mathbf{if}\;x \leq -8 \cdot 10^{-18}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-27}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-120}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-57}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (+ y -1.0))))
   (if (<= x -8e-18)
     t_0
     (if (<= x -2.9e-27)
       y
       (if (<= x -7.8e-120) (- x) (if (<= x 2.5e-57) y t_0))))))

C

double code(double x, double y) {
	double t_0 = x * (y + -1.0);
	double tmp;
	if (x <= -8e-18) {
		tmp = t_0;
	} else if (x <= -2.9e-27) {
		tmp = y;
	} else if (x <= -7.8e-120) {
		tmp = -x;
	} else if (x <= 2.5e-57) {
		tmp = y;
	} 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 <= (-8d-18)) then
        tmp = t_0
    else if (x <= (-2.9d-27)) then
        tmp = y
    else if (x <= (-7.8d-120)) then
        tmp = -x
    else if (x <= 2.5d-57) then
        tmp = y
    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 <= -8e-18) {
		tmp = t_0;
	} else if (x <= -2.9e-27) {
		tmp = y;
	} else if (x <= -7.8e-120) {
		tmp = -x;
	} else if (x <= 2.5e-57) {
		tmp = y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (y + -1.0)
	tmp = 0
	if x <= -8e-18:
		tmp = t_0
	elif x <= -2.9e-27:
		tmp = y
	elif x <= -7.8e-120:
		tmp = -x
	elif x <= 2.5e-57:
		tmp = y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(y + -1.0))
	tmp = 0.0
	if (x <= -8e-18)
		tmp = t_0;
	elseif (x <= -2.9e-27)
		tmp = y;
	elseif (x <= -7.8e-120)
		tmp = Float64(-x);
	elseif (x <= 2.5e-57)
		tmp = y;
	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 <= -8e-18)
		tmp = t_0;
	elseif (x <= -2.9e-27)
		tmp = y;
	elseif (x <= -7.8e-120)
		tmp = -x;
	elseif (x <= 2.5e-57)
		tmp = y;
	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, -8e-18], t$95$0, If[LessEqual[x, -2.9e-27], y, If[LessEqual[x, -7.8e-120], (-x), If[LessEqual[x, 2.5e-57], y, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.0000000000000006e-18 or 2.5000000000000001e-57 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 94.5%

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

   if -8.0000000000000006e-18 < x < -2.90000000000000004e-27 or -7.8000000000000003e-120 < x < 2.5000000000000001e-57

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 85.7%

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

   if -2.90000000000000004e-27 < x < -7.8000000000000003e-120

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 62.8%

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

      1. mul-1-neg 62.8%

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

   5. Simplified 62.8%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-27}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-120}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-57}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-92}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+63}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+157}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   (* x y)
   (if (<= y 2.65e-92)
     (- x)
     (if (<= y 2.9e+63) y (if (<= y 2.2e+157) (* x y) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x * y;
	} else if (y <= 2.65e-92) {
		tmp = -x;
	} else if (y <= 2.9e+63) {
		tmp = y;
	} else if (y <= 2.2e+157) {
		tmp = x * y;
	} 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 <= (-1.0d0)) then
        tmp = x * y
    else if (y <= 2.65d-92) then
        tmp = -x
    else if (y <= 2.9d+63) then
        tmp = y
    else if (y <= 2.2d+157) then
        tmp = x * y
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x * y;
	} else if (y <= 2.65e-92) {
		tmp = -x;
	} else if (y <= 2.9e+63) {
		tmp = y;
	} else if (y <= 2.2e+157) {
		tmp = x * y;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x * y
	elif y <= 2.65e-92:
		tmp = -x
	elif y <= 2.9e+63:
		tmp = y
	elif y <= 2.2e+157:
		tmp = x * y
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(x * y);
	elseif (y <= 2.65e-92)
		tmp = Float64(-x);
	elseif (y <= 2.9e+63)
		tmp = y;
	elseif (y <= 2.2e+157)
		tmp = Float64(x * y);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = x * y;
	elseif (y <= 2.65e-92)
		tmp = -x;
	elseif (y <= 2.9e+63)
		tmp = y;
	elseif (y <= 2.2e+157)
		tmp = x * y;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], N[(x * y), $MachinePrecision], If[LessEqual[y, 2.65e-92], (-x), If[LessEqual[y, 2.9e+63], y, If[LessEqual[y, 2.2e+157], N[(x * y), $MachinePrecision], y]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 2.8999999999999999e63 < y < 2.2000000000000001e157

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 58.1%

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

      1. *-commutative 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in y around inf 57.2%

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

   if -1 < y < 2.65000000000000015e-92

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 81.2%

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

      1. mul-1-neg 81.2%

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

   5. Simplified 81.2%

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

   if 2.65000000000000015e-92 < y < 2.8999999999999999e63 or 2.2000000000000001e157 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 72.8%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-92}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+63}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+157}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-7} \lor \neg \left(y \leq 5.7 \cdot 10^{-92}\right):\\ \;\;\;\;\left(x + 1\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -7.5e-7) (not (<= y 5.7e-92)))
   (* (+ x 1.0) y)
   (* x (+ y -1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -7.5e-7) || !(y <= 5.7e-92)) {
		tmp = (x + 1.0) * y;
	} 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 ((y <= (-7.5d-7)) .or. (.not. (y <= 5.7d-92))) then
        tmp = (x + 1.0d0) * y
    else
        tmp = x * (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -7.5e-7) || !(y <= 5.7e-92)) {
		tmp = (x + 1.0) * y;
	} else {
		tmp = x * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -7.5e-7) or not (y <= 5.7e-92):
		tmp = (x + 1.0) * y
	else:
		tmp = x * (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -7.5e-7) || !(y <= 5.7e-92))
		tmp = Float64(Float64(x + 1.0) * y);
	else
		tmp = Float64(x * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -7.5e-7) || ~((y <= 5.7e-92)))
		tmp = (x + 1.0) * y;
	else
		tmp = x * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -7.5e-7], N[Not[LessEqual[y, 5.7e-92]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] * y), $MachinePrecision], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5000000000000002e-7 or 5.70000000000000009e-92 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 95.9%

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

   if -7.5000000000000002e-7 < y < 5.70000000000000009e-92

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.0%

      \[\leadsto \color{blue}{x \cdot \left(y - 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-7} \lor \neg \left(y \leq 5.7 \cdot 10^{-92}\right):\\ \;\;\;\;\left(x + 1\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{-7} \lor \neg \left(y \leq 5.7 \cdot 10^{-92}\right):\\ \;\;\;\;\left(x + 1\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -7.6e-7) (not (<= y 5.7e-92))) (* (+ x 1.0) y) (- (* x y) x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -7.6e-7) || !(y <= 5.7e-92)) {
		tmp = (x + 1.0) * y;
	} 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 ((y <= (-7.6d-7)) .or. (.not. (y <= 5.7d-92))) then
        tmp = (x + 1.0d0) * y
    else
        tmp = (x * y) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -7.6e-7) || !(y <= 5.7e-92)) {
		tmp = (x + 1.0) * y;
	} else {
		tmp = (x * y) - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -7.6e-7) or not (y <= 5.7e-92):
		tmp = (x + 1.0) * y
	else:
		tmp = (x * y) - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -7.6e-7) || !(y <= 5.7e-92))
		tmp = Float64(Float64(x + 1.0) * y);
	else
		tmp = Float64(Float64(x * y) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -7.6e-7) || ~((y <= 5.7e-92)))
		tmp = (x + 1.0) * y;
	else
		tmp = (x * y) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -7.6e-7], N[Not[LessEqual[y, 5.7e-92]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] * y), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.60000000000000029e-7 or 5.70000000000000009e-92 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 95.9%

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

   if -7.60000000000000029e-7 < y < 5.70000000000000009e-92

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.0%

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

      1. *-commutative 83.0%

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

   5. Simplified 83.0%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{-7} \lor \neg \left(y \leq 5.7 \cdot 10^{-92}\right):\\ \;\;\;\;\left(x + 1\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-7}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-92}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.4e-7) y (if (<= y 5.7e-92) (- x) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.4e-7) {
		tmp = y;
	} else if (y <= 5.7e-92) {
		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 <= (-5.4d-7)) then
        tmp = y
    else if (y <= 5.7d-92) 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 <= -5.4e-7) {
		tmp = y;
	} else if (y <= 5.7e-92) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.4e-7:
		tmp = y
	elif y <= 5.7e-92:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.4e-7)
		tmp = y;
	elseif (y <= 5.7e-92)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5.4e-7)
		tmp = y;
	elseif (y <= 5.7e-92)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.4e-7], y, If[LessEqual[y, 5.7e-92], (-x), y]]

Derivation

1. Split input into 2 regimes

2. if y < -5.40000000000000018e-7 or 5.70000000000000009e-92 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 54.4%

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

   if -5.40000000000000018e-7 < y < 5.70000000000000009e-92

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.4%

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

      1. mul-1-neg 82.4%

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

   5. Simplified 82.4%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-7}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-92}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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. Final simplification 100.0%

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

Alternative 8: 38.2% 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 36.8%

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

4. Final simplification 36.8%

   \[\leadsto y \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024066 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))