Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 3.4s

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. distribute-lft1-in 100.0%

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

   2. associate--l+ 100.0%

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 62.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+219}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+135}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+100}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+58}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -5400000000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-32}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-31}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.2e+219)
   (* x y)
   (if (<= x -1.6e+135)
     (- x)
     (if (<= x -3.2e+100)
       (* x y)
       (if (<= x -9e+58)
         (- x)
         (if (<= x -5400000000.0)
           (* x y)
           (if (<= x -4.8e-32) (- x) (if (<= x 6e-31) y (- x)))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.2e+219) {
		tmp = x * y;
	} else if (x <= -1.6e+135) {
		tmp = -x;
	} else if (x <= -3.2e+100) {
		tmp = x * y;
	} else if (x <= -9e+58) {
		tmp = -x;
	} else if (x <= -5400000000.0) {
		tmp = x * y;
	} else if (x <= -4.8e-32) {
		tmp = -x;
	} else if (x <= 6e-31) {
		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 <= (-2.2d+219)) then
        tmp = x * y
    else if (x <= (-1.6d+135)) then
        tmp = -x
    else if (x <= (-3.2d+100)) then
        tmp = x * y
    else if (x <= (-9d+58)) then
        tmp = -x
    else if (x <= (-5400000000.0d0)) then
        tmp = x * y
    else if (x <= (-4.8d-32)) then
        tmp = -x
    else if (x <= 6d-31) 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 <= -2.2e+219) {
		tmp = x * y;
	} else if (x <= -1.6e+135) {
		tmp = -x;
	} else if (x <= -3.2e+100) {
		tmp = x * y;
	} else if (x <= -9e+58) {
		tmp = -x;
	} else if (x <= -5400000000.0) {
		tmp = x * y;
	} else if (x <= -4.8e-32) {
		tmp = -x;
	} else if (x <= 6e-31) {
		tmp = y;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.2e+219:
		tmp = x * y
	elif x <= -1.6e+135:
		tmp = -x
	elif x <= -3.2e+100:
		tmp = x * y
	elif x <= -9e+58:
		tmp = -x
	elif x <= -5400000000.0:
		tmp = x * y
	elif x <= -4.8e-32:
		tmp = -x
	elif x <= 6e-31:
		tmp = y
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.2e+219)
		tmp = Float64(x * y);
	elseif (x <= -1.6e+135)
		tmp = Float64(-x);
	elseif (x <= -3.2e+100)
		tmp = Float64(x * y);
	elseif (x <= -9e+58)
		tmp = Float64(-x);
	elseif (x <= -5400000000.0)
		tmp = Float64(x * y);
	elseif (x <= -4.8e-32)
		tmp = Float64(-x);
	elseif (x <= 6e-31)
		tmp = y;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.2e+219)
		tmp = x * y;
	elseif (x <= -1.6e+135)
		tmp = -x;
	elseif (x <= -3.2e+100)
		tmp = x * y;
	elseif (x <= -9e+58)
		tmp = -x;
	elseif (x <= -5400000000.0)
		tmp = x * y;
	elseif (x <= -4.8e-32)
		tmp = -x;
	elseif (x <= 6e-31)
		tmp = y;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.2e+219], N[(x * y), $MachinePrecision], If[LessEqual[x, -1.6e+135], (-x), If[LessEqual[x, -3.2e+100], N[(x * y), $MachinePrecision], If[LessEqual[x, -9e+58], (-x), If[LessEqual[x, -5400000000.0], N[(x * y), $MachinePrecision], If[LessEqual[x, -4.8e-32], (-x), If[LessEqual[x, 6e-31], y, (-x)]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2000000000000001e219 or -1.59999999999999987e135 < x < -3.1999999999999999e100 or -8.9999999999999996e58 < x < -5.4e9

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 99.4%

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

   3. Taylor expanded in y around inf 76.4%

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

   if -2.2000000000000001e219 < x < -1.59999999999999987e135 or -3.1999999999999999e100 < x < -8.9999999999999996e58 or -5.4e9 < x < -4.8000000000000003e-32 or 5.99999999999999962e-31 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 66.1%

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

      1. neg-mul-1 66.1%

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

   4. Simplified 66.1%

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

   if -4.8000000000000003e-32 < x < 5.99999999999999962e-31

   1. Initial program 100.0%

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

      1. distribute-lft1-in 100.0%

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

      2. associate--l+ 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around 0 83.7%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+219}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+135}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+100}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+58}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -5400000000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-32}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-31}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 3: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+219}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{+135}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{+99}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+57}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -58000000000:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.35e+219)
   (* x y)
   (if (<= x -2.05e+135)
     (- x)
     (if (<= x -8.2e+99)
       (* x y)
       (if (<= x -5e+57) (- x) (if (<= x -58000000000.0) (* x y) (- y x)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.35e+219) {
		tmp = x * y;
	} else if (x <= -2.05e+135) {
		tmp = -x;
	} else if (x <= -8.2e+99) {
		tmp = x * y;
	} else if (x <= -5e+57) {
		tmp = -x;
	} else if (x <= -58000000000.0) {
		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 <= (-2.35d+219)) then
        tmp = x * y
    else if (x <= (-2.05d+135)) then
        tmp = -x
    else if (x <= (-8.2d+99)) then
        tmp = x * y
    else if (x <= (-5d+57)) then
        tmp = -x
    else if (x <= (-58000000000.0d0)) 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 <= -2.35e+219) {
		tmp = x * y;
	} else if (x <= -2.05e+135) {
		tmp = -x;
	} else if (x <= -8.2e+99) {
		tmp = x * y;
	} else if (x <= -5e+57) {
		tmp = -x;
	} else if (x <= -58000000000.0) {
		tmp = x * y;
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.35e+219:
		tmp = x * y
	elif x <= -2.05e+135:
		tmp = -x
	elif x <= -8.2e+99:
		tmp = x * y
	elif x <= -5e+57:
		tmp = -x
	elif x <= -58000000000.0:
		tmp = x * y
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.35e+219)
		tmp = Float64(x * y);
	elseif (x <= -2.05e+135)
		tmp = Float64(-x);
	elseif (x <= -8.2e+99)
		tmp = Float64(x * y);
	elseif (x <= -5e+57)
		tmp = Float64(-x);
	elseif (x <= -58000000000.0)
		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 <= -2.35e+219)
		tmp = x * y;
	elseif (x <= -2.05e+135)
		tmp = -x;
	elseif (x <= -8.2e+99)
		tmp = x * y;
	elseif (x <= -5e+57)
		tmp = -x;
	elseif (x <= -58000000000.0)
		tmp = x * y;
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.35e+219], N[(x * y), $MachinePrecision], If[LessEqual[x, -2.05e+135], (-x), If[LessEqual[x, -8.2e+99], N[(x * y), $MachinePrecision], If[LessEqual[x, -5e+57], (-x), If[LessEqual[x, -58000000000.0], N[(x * y), $MachinePrecision], N[(y - x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.35000000000000007e219 or -2.05e135 < x < -8.19999999999999959e99 or -4.99999999999999972e57 < x < -5.8e10

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 99.4%

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

   3. Taylor expanded in y around inf 76.4%

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

   if -2.35000000000000007e219 < x < -2.05e135 or -8.19999999999999959e99 < x < -4.99999999999999972e57

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 73.8%

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

      1. neg-mul-1 73.8%

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

   4. Simplified 73.8%

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

   if -5.8e10 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 85.1%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+219}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{+135}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{+99}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+57}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -58000000000:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]

Alternative 4: 98.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+20} \lor \neg \left(y \leq 1.7 \cdot 10^{-7}\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3e+20) (not (<= y 1.7e-7))) (* y (+ x 1.0)) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3e+20) || !(y <= 1.7e-7)) {
		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 <= (-3d+20)) .or. (.not. (y <= 1.7d-7))) 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 <= -3e+20) || !(y <= 1.7e-7)) {
		tmp = y * (x + 1.0);
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3e+20) or not (y <= 1.7e-7):
		tmp = y * (x + 1.0)
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -3e+20) || !(y <= 1.7e-7))
		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 <= -3e+20) || ~((y <= 1.7e-7)))
		tmp = y * (x + 1.0);
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3e+20], N[Not[LessEqual[y, 1.7e-7]], $MachinePrecision]], N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3e20 or 1.69999999999999987e-7 < y

   1. Initial program 100.0%

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

      1. distribute-lft1-in 100.0%

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

      2. associate--l+ 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in y around inf 99.5%

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

   if -3e20 < y < 1.69999999999999987e-7

   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 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+20} \lor \neg \left(y \leq 1.7 \cdot 10^{-7}\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]

Alternative 5: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -32 \lor \neg \left(x \leq 0.000285\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -32.0) (not (<= x 0.000285))) (* x (+ y -1.0)) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -32.0) || !(x <= 0.000285)) {
		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 <= (-32.0d0)) .or. (.not. (x <= 0.000285d0))) 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 <= -32.0) || !(x <= 0.000285)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -32.0) or not (x <= 0.000285):
		tmp = x * (y + -1.0)
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -32.0) || !(x <= 0.000285))
		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 <= -32.0) || ~((x <= 0.000285)))
		tmp = x * (y + -1.0);
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -32.0], N[Not[LessEqual[x, 0.000285]], $MachinePrecision]], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -32 or 2.8499999999999999e-4 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 99.1%

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

   if -32 < x < 2.8499999999999999e-4

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 99.3%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -32 \lor \neg \left(x \leq 0.000285\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]

Alternative 6: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -32:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{elif}\;x \leq 0.000285:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -32.0) (* x (+ y -1.0)) (if (<= x 0.000285) (- y x) (- (* x y) x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -32.0) {
		tmp = x * (y + -1.0);
	} else if (x <= 0.000285) {
		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 <= (-32.0d0)) then
        tmp = x * (y + (-1.0d0))
    else if (x <= 0.000285d0) 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 <= -32.0) {
		tmp = x * (y + -1.0);
	} else if (x <= 0.000285) {
		tmp = y - x;
	} else {
		tmp = (x * y) - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -32.0:
		tmp = x * (y + -1.0)
	elif x <= 0.000285:
		tmp = y - x
	else:
		tmp = (x * y) - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -32.0)
		tmp = Float64(x * Float64(y + -1.0));
	elseif (x <= 0.000285)
		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 <= -32.0)
		tmp = x * (y + -1.0);
	elseif (x <= 0.000285)
		tmp = y - x;
	else
		tmp = (x * y) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -32.0], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.000285], N[(y - x), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -32

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 99.1%

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

   if -32 < x < 2.8499999999999999e-4

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 99.3%

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

   if 2.8499999999999999e-4 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 99.2%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -32:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{elif}\;x \leq 0.000285:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - x\\ \end{array} \]

Alternative 7: 62.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-31}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-36}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9.5e-31) (- x) (if (<= x 6.5e-36) y (- x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9.5e-31) {
		tmp = -x;
	} else if (x <= 6.5e-36) {
		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 <= (-9.5d-31)) then
        tmp = -x
    else if (x <= 6.5d-36) 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 <= -9.5e-31) {
		tmp = -x;
	} else if (x <= 6.5e-36) {
		tmp = y;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9.5e-31:
		tmp = -x
	elif x <= 6.5e-36:
		tmp = y
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9.5e-31)
		tmp = Float64(-x);
	elseif (x <= 6.5e-36)
		tmp = y;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -9.5e-31)
		tmp = -x;
	elseif (x <= 6.5e-36)
		tmp = y;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9.5e-31], (-x), If[LessEqual[x, 6.5e-36], y, (-x)]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5000000000000008e-31 or 6.50000000000000012e-36 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 55.9%

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

      1. neg-mul-1 55.9%

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

   4. Simplified 55.9%

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

   if -9.5000000000000008e-31 < x < 6.50000000000000012e-36

   1. Initial program 100.0%

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

      1. distribute-lft1-in 100.0%

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

      2. associate--l+ 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around 0 83.7%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-31}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-36}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 8: 38.6% 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. distribute-lft1-in 100.0%

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

   2. associate--l+ 100.0%

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

3. Applied egg-rr 100.0%

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

4. Taylor expanded in x around 0 37.3%

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

5. Final simplification 37.3%

   \[\leadsto y \]

Reproduce

herbie shell --seed 2023230 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))