Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 3.2s

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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. *-commutative 100.0%

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

   2. distribute-rgt-in 100.0%

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

   3. fma-def 100.0%

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

   4. *-lft-identity 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 63.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+265}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+116}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{-17}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-5}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+178}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.1e+265)
   y
   (if (<= y -2e+116)
     (* x y)
     (if (<= y -5.3e-17)
       y
       (if (<= y 5e-5) (- x) (if (<= y 8.2e+178) y (* x y)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.1e+265) {
		tmp = y;
	} else if (y <= -2e+116) {
		tmp = x * y;
	} else if (y <= -5.3e-17) {
		tmp = y;
	} else if (y <= 5e-5) {
		tmp = -x;
	} else if (y <= 8.2e+178) {
		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 <= (-4.1d+265)) then
        tmp = y
    else if (y <= (-2d+116)) then
        tmp = x * y
    else if (y <= (-5.3d-17)) then
        tmp = y
    else if (y <= 5d-5) then
        tmp = -x
    else if (y <= 8.2d+178) 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 <= -4.1e+265) {
		tmp = y;
	} else if (y <= -2e+116) {
		tmp = x * y;
	} else if (y <= -5.3e-17) {
		tmp = y;
	} else if (y <= 5e-5) {
		tmp = -x;
	} else if (y <= 8.2e+178) {
		tmp = y;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.1e+265:
		tmp = y
	elif y <= -2e+116:
		tmp = x * y
	elif y <= -5.3e-17:
		tmp = y
	elif y <= 5e-5:
		tmp = -x
	elif y <= 8.2e+178:
		tmp = y
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.1e+265)
		tmp = y;
	elseif (y <= -2e+116)
		tmp = Float64(x * y);
	elseif (y <= -5.3e-17)
		tmp = y;
	elseif (y <= 5e-5)
		tmp = Float64(-x);
	elseif (y <= 8.2e+178)
		tmp = y;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.1e+265)
		tmp = y;
	elseif (y <= -2e+116)
		tmp = x * y;
	elseif (y <= -5.3e-17)
		tmp = y;
	elseif (y <= 5e-5)
		tmp = -x;
	elseif (y <= 8.2e+178)
		tmp = y;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.1e+265], y, If[LessEqual[y, -2e+116], N[(x * y), $MachinePrecision], If[LessEqual[y, -5.3e-17], y, If[LessEqual[y, 5e-5], (-x), If[LessEqual[y, 8.2e+178], y, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.1000000000000003e265 or -2.00000000000000003e116 < y < -5.2999999999999998e-17 or 5.00000000000000024e-5 < y < 8.19999999999999993e178

   1. Initial program 99.9%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in x around 0 61.9%

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

   if -4.1000000000000003e265 < y < -2.00000000000000003e116 or 8.19999999999999993e178 < y

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in x around inf 68.7%

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

   if -5.2999999999999998e-17 < y < 5.00000000000000024e-5

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in y around 0 78.8%

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

      1. neg-mul-1 78.8%

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

   4. Simplified 78.8%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+265}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+116}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{-17}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-5}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+178}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.45 \cdot 10^{+264}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+117}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+28}:\\ \;\;\;\;y - x\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+83}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+173}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.45e+264)
   y
   (if (<= y -1.4e+117)
     (* x y)
     (if (<= y 4.5e+28)
       (- y x)
       (if (<= y 8.2e+83) (* x y) (if (<= y 7.8e+173) y (* x y)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.45e+264) {
		tmp = y;
	} else if (y <= -1.4e+117) {
		tmp = x * y;
	} else if (y <= 4.5e+28) {
		tmp = y - x;
	} else if (y <= 8.2e+83) {
		tmp = x * y;
	} else if (y <= 7.8e+173) {
		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 <= (-3.45d+264)) then
        tmp = y
    else if (y <= (-1.4d+117)) then
        tmp = x * y
    else if (y <= 4.5d+28) then
        tmp = y - x
    else if (y <= 8.2d+83) then
        tmp = x * y
    else if (y <= 7.8d+173) 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 <= -3.45e+264) {
		tmp = y;
	} else if (y <= -1.4e+117) {
		tmp = x * y;
	} else if (y <= 4.5e+28) {
		tmp = y - x;
	} else if (y <= 8.2e+83) {
		tmp = x * y;
	} else if (y <= 7.8e+173) {
		tmp = y;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.45e+264:
		tmp = y
	elif y <= -1.4e+117:
		tmp = x * y
	elif y <= 4.5e+28:
		tmp = y - x
	elif y <= 8.2e+83:
		tmp = x * y
	elif y <= 7.8e+173:
		tmp = y
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.45e+264)
		tmp = y;
	elseif (y <= -1.4e+117)
		tmp = Float64(x * y);
	elseif (y <= 4.5e+28)
		tmp = Float64(y - x);
	elseif (y <= 8.2e+83)
		tmp = Float64(x * y);
	elseif (y <= 7.8e+173)
		tmp = y;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.45e+264)
		tmp = y;
	elseif (y <= -1.4e+117)
		tmp = x * y;
	elseif (y <= 4.5e+28)
		tmp = y - x;
	elseif (y <= 8.2e+83)
		tmp = x * y;
	elseif (y <= 7.8e+173)
		tmp = y;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.45e+264], y, If[LessEqual[y, -1.4e+117], N[(x * y), $MachinePrecision], If[LessEqual[y, 4.5e+28], N[(y - x), $MachinePrecision], If[LessEqual[y, 8.2e+83], N[(x * y), $MachinePrecision], If[LessEqual[y, 7.8e+173], y, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4500000000000002e264 or 8.2000000000000002e83 < y < 7.7999999999999996e173

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in x around 0 72.7%

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

   if -3.4500000000000002e264 < y < -1.39999999999999999e117 or 4.4999999999999997e28 < y < 8.2000000000000002e83 or 7.7999999999999996e173 < y

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in x around inf 68.0%

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

   if -1.39999999999999999e117 < y < 4.4999999999999997e28

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 91.9%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.45 \cdot 10^{+264}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+117}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+28}:\\ \;\;\;\;y - x\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+83}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+173}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 4: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1200000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1200000.0) (not (<= y 1.0))) (* y (+ x 1.0)) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1200000.0) || !(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 <= (-1200000.0d0)) .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 <= -1200000.0) || !(y <= 1.0)) {
		tmp = y * (x + 1.0);
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1200000.0) 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 <= -1200000.0) || !(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 <= -1200000.0) || ~((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, -1200000.0], 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 < -1.2e6 or 1 < y

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in y around inf 99.0%

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

   if -1.2e6 < y < 1

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 98.8%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1200000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]

Alternative 5: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1200000:\\ \;\;\;\;y + x \cdot y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1200000.0) (+ y (* x y)) (if (<= y 1.0) (- y x) (* y (+ x 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1200000.0) {
		tmp = y + (x * y);
	} 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 <= (-1200000.0d0)) then
        tmp = y + (x * y)
    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 <= -1200000.0) {
		tmp = y + (x * y);
	} 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 <= -1200000.0:
		tmp = y + (x * y)
	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 <= -1200000.0)
		tmp = Float64(y + Float64(x * y));
	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 <= -1200000.0)
		tmp = y + (x * y);
	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, -1200000.0], N[(y + N[(x * y), $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 < -1.2e6

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in y around inf 99.3%

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

   4. Taylor expanded in x around 0 99.3%

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

   if -1.2e6 < y < 1

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 98.8%

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

   if 1 < y

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in y around inf 98.8%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1200000:\\ \;\;\;\;y + x \cdot y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \end{array} \]

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. Final simplification 100.0%

   \[\leadsto y \cdot \left(x + 1\right) - x \]

Alternative 7: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]

2. Taylor expanded in x around 0 100.0%

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

3. Final simplification 100.0%

   \[\leadsto \left(y + x \cdot y\right) - x \]

Alternative 8: 63.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-52}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-22}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6.5e-52) (- x) (if (<= x 4.2e-22) y (- x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.5e-52) {
		tmp = -x;
	} else if (x <= 4.2e-22) {
		tmp = y;
	} else {
		tmp = -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 <= (-6.5d-52)) then
        tmp = -x
    else if (x <= 4.2d-22) then
        tmp = y
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -6.5e-52) {
		tmp = -x;
	} else if (x <= 4.2e-22) {
		tmp = y;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.5e-52:
		tmp = -x
	elif x <= 4.2e-22:
		tmp = y
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.5e-52)
		tmp = Float64(-x);
	elseif (x <= 4.2e-22)
		tmp = y;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6.5e-52)
		tmp = -x;
	elseif (x <= 4.2e-22)
		tmp = y;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.5e-52], (-x), If[LessEqual[x, 4.2e-22], y, (-x)]]

Derivation

1. Split input into 2 regimes

2. if x < -6.5e-52 or 4.20000000000000016e-22 < x

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in y around 0 51.8%

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

      1. neg-mul-1 51.8%

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

   4. Simplified 51.8%

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

   if -6.5e-52 < x < 4.20000000000000016e-22

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in x around 0 79.7%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-52}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-22}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 9: 38.9% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 y)

C

double code(double x, double y) {
	return y;
}

Fortran

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

Java

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

Python

def code(x, y):
	return y

Julia

function code(x, y)
	return y
end

MATLAB

function tmp = code(x, y)
	tmp = y;
end

Wolfram

code[x_, y_] := y

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]

2. Taylor expanded in x around 0 100.0%

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

3. Taylor expanded in x around 0 37.0%

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

4. Final simplification 37.0%

   \[\leadsto y \]

Reproduce

herbie shell --seed 2023242 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))