Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 3.0s

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. Taylor expanded in x around 0 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 61.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+126}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-116}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-97}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-84}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+23}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+197}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+224}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.5e+126)
   y
   (if (<= y -1.0)
     (* y x)
     (if (<= y 1.7e-116)
       (- x)
       (if (<= y 2.4e-97)
         y
         (if (<= y 3.4e-84)
           (- x)
           (if (<= y 6.8e+23)
             y
             (if (<= y 9.8e+197) (* y x) (if (<= y 5.2e+224) y (* y x))))))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.5e+126) {
		tmp = y;
	} else if (y <= -1.0) {
		tmp = y * x;
	} else if (y <= 1.7e-116) {
		tmp = -x;
	} else if (y <= 2.4e-97) {
		tmp = y;
	} else if (y <= 3.4e-84) {
		tmp = -x;
	} else if (y <= 6.8e+23) {
		tmp = y;
	} else if (y <= 9.8e+197) {
		tmp = y * x;
	} else if (y <= 5.2e+224) {
		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+126)) then
        tmp = y
    else if (y <= (-1.0d0)) then
        tmp = y * x
    else if (y <= 1.7d-116) then
        tmp = -x
    else if (y <= 2.4d-97) then
        tmp = y
    else if (y <= 3.4d-84) then
        tmp = -x
    else if (y <= 6.8d+23) then
        tmp = y
    else if (y <= 9.8d+197) then
        tmp = y * x
    else if (y <= 5.2d+224) 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+126) {
		tmp = y;
	} else if (y <= -1.0) {
		tmp = y * x;
	} else if (y <= 1.7e-116) {
		tmp = -x;
	} else if (y <= 2.4e-97) {
		tmp = y;
	} else if (y <= 3.4e-84) {
		tmp = -x;
	} else if (y <= 6.8e+23) {
		tmp = y;
	} else if (y <= 9.8e+197) {
		tmp = y * x;
	} else if (y <= 5.2e+224) {
		tmp = y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.5e+126:
		tmp = y
	elif y <= -1.0:
		tmp = y * x
	elif y <= 1.7e-116:
		tmp = -x
	elif y <= 2.4e-97:
		tmp = y
	elif y <= 3.4e-84:
		tmp = -x
	elif y <= 6.8e+23:
		tmp = y
	elif y <= 9.8e+197:
		tmp = y * x
	elif y <= 5.2e+224:
		tmp = y
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.5e+126)
		tmp = y;
	elseif (y <= -1.0)
		tmp = Float64(y * x);
	elseif (y <= 1.7e-116)
		tmp = Float64(-x);
	elseif (y <= 2.4e-97)
		tmp = y;
	elseif (y <= 3.4e-84)
		tmp = Float64(-x);
	elseif (y <= 6.8e+23)
		tmp = y;
	elseif (y <= 9.8e+197)
		tmp = Float64(y * x);
	elseif (y <= 5.2e+224)
		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+126)
		tmp = y;
	elseif (y <= -1.0)
		tmp = y * x;
	elseif (y <= 1.7e-116)
		tmp = -x;
	elseif (y <= 2.4e-97)
		tmp = y;
	elseif (y <= 3.4e-84)
		tmp = -x;
	elseif (y <= 6.8e+23)
		tmp = y;
	elseif (y <= 9.8e+197)
		tmp = y * x;
	elseif (y <= 5.2e+224)
		tmp = y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.5e+126], y, If[LessEqual[y, -1.0], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.7e-116], (-x), If[LessEqual[y, 2.4e-97], y, If[LessEqual[y, 3.4e-84], (-x), If[LessEqual[y, 6.8e+23], y, If[LessEqual[y, 9.8e+197], N[(y * x), $MachinePrecision], If[LessEqual[y, 5.2e+224], y, N[(y * x), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5000000000000001e126 or 1.69999999999999996e-116 < y < 2.4e-97 or 3.40000000000000021e-84 < y < 6.79999999999999983e23 or 9.80000000000000052e197 < y < 5.2000000000000001e224

   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 65.4%

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

   if -1.5000000000000001e126 < y < -1 or 6.79999999999999983e23 < y < 9.80000000000000052e197 or 5.2000000000000001e224 < 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 98.7%

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

   4. Taylor expanded in x around inf 75.7%

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

   if -1 < y < 1.69999999999999996e-116 or 2.4e-97 < y < 3.40000000000000021e-84

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 82.3%

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

      1. neg-mul-1 82.3%

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

   4. Simplified 82.3%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+126}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-116}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-97}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-84}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+23}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+197}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+224}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 3: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+125}:\\ \;\;\;\;y - x\\ \mathbf{elif}\;y \leq -1.8:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+23}:\\ \;\;\;\;y - x\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+196}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+224}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.05e+125)
   (- y x)
   (if (<= y -1.8)
     (* y x)
     (if (<= y 6.2e+23)
       (- y x)
       (if (<= y 3.3e+196) (* y x) (if (<= y 3.5e+224) y (* y x)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.05e+125) {
		tmp = y - x;
	} else if (y <= -1.8) {
		tmp = y * x;
	} else if (y <= 6.2e+23) {
		tmp = y - x;
	} else if (y <= 3.3e+196) {
		tmp = y * x;
	} else if (y <= 3.5e+224) {
		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 <= (-1.05d+125)) then
        tmp = y - x
    else if (y <= (-1.8d0)) then
        tmp = y * x
    else if (y <= 6.2d+23) then
        tmp = y - x
    else if (y <= 3.3d+196) then
        tmp = y * x
    else if (y <= 3.5d+224) 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 <= -1.05e+125) {
		tmp = y - x;
	} else if (y <= -1.8) {
		tmp = y * x;
	} else if (y <= 6.2e+23) {
		tmp = y - x;
	} else if (y <= 3.3e+196) {
		tmp = y * x;
	} else if (y <= 3.5e+224) {
		tmp = y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.05e+125:
		tmp = y - x
	elif y <= -1.8:
		tmp = y * x
	elif y <= 6.2e+23:
		tmp = y - x
	elif y <= 3.3e+196:
		tmp = y * x
	elif y <= 3.5e+224:
		tmp = y
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.05e+125)
		tmp = Float64(y - x);
	elseif (y <= -1.8)
		tmp = Float64(y * x);
	elseif (y <= 6.2e+23)
		tmp = Float64(y - x);
	elseif (y <= 3.3e+196)
		tmp = Float64(y * x);
	elseif (y <= 3.5e+224)
		tmp = y;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.05e+125)
		tmp = y - x;
	elseif (y <= -1.8)
		tmp = y * x;
	elseif (y <= 6.2e+23)
		tmp = y - x;
	elseif (y <= 3.3e+196)
		tmp = y * x;
	elseif (y <= 3.5e+224)
		tmp = y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.05e+125], N[(y - x), $MachinePrecision], If[LessEqual[y, -1.8], N[(y * x), $MachinePrecision], If[LessEqual[y, 6.2e+23], N[(y - x), $MachinePrecision], If[LessEqual[y, 3.3e+196], N[(y * x), $MachinePrecision], If[LessEqual[y, 3.5e+224], y, N[(y * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05e125 or -1.80000000000000004 < y < 6.19999999999999941e23

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 89.8%

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

   if -1.05e125 < y < -1.80000000000000004 or 6.19999999999999941e23 < y < 3.3000000000000002e196 or 3.5e224 < 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 98.7%

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

   4. Taylor expanded in x around inf 75.7%

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

   if 3.3000000000000002e196 < y < 3.5e224

   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 78.4%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+125}:\\ \;\;\;\;y - x\\ \mathbf{elif}\;y \leq -1.8:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+23}:\\ \;\;\;\;y - x\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+196}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+224}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 4: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1.05 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.05e-18))) (* y (+ x 1.0)) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.05e-18)) {
		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 <= (-1.0d0)) .or. (.not. (y <= 1.05d-18))) 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 <= -1.0) || !(y <= 1.05e-18)) {
		tmp = y * (x + 1.0);
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 1.05e-18):
		tmp = y * (x + 1.0)
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.05e-18))
		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 <= -1.0) || ~((y <= 1.05e-18)))
		tmp = y * (x + 1.0);
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 1.05e-18]], $MachinePrecision]], N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1.05e-18 < y

   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 y around inf 97.9%

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

   if -1 < y < 1.05e-18

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 99.2%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1.05 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]

Alternative 5: 99.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -130 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -130.0) (not (<= x 1.0))) (* x (+ y -1.0)) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -130.0) || !(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 <= (-130.0d0)) .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 <= -130.0) || !(x <= 1.0)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -130.0) 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 <= -130.0) || !(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 <= -130.0) || ~((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, -130.0], 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 < -130 or 1 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 99.4%

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

   if -130 < x < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 98.4%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -130 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]

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: 61.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.1 \cdot 10^{-78}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-83}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -8.1e-78) (- x) (if (<= x 1.85e-83) y (- x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -8.1e-78) {
		tmp = -x;
	} else if (x <= 1.85e-83) {
		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 <= (-8.1d-78)) then
        tmp = -x
    else if (x <= 1.85d-83) 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 <= -8.1e-78) {
		tmp = -x;
	} else if (x <= 1.85e-83) {
		tmp = y;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -8.1e-78:
		tmp = -x
	elif x <= 1.85e-83:
		tmp = y
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -8.1e-78)
		tmp = Float64(-x);
	elseif (x <= 1.85e-83)
		tmp = y;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -8.1e-78)
		tmp = -x;
	elseif (x <= 1.85e-83)
		tmp = y;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -8.1e-78], (-x), If[LessEqual[x, 1.85e-83], y, (-x)]]

Derivation

1. Split input into 2 regimes

2. if x < -8.10000000000000029e-78 or 1.84999999999999997e-83 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 52.0%

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

      1. neg-mul-1 52.0%

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

   4. Simplified 52.0%

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

   if -8.10000000000000029e-78 < x < 1.84999999999999997e-83

   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 84.8%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.1 \cdot 10^{-78}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-83}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 8: 38.4% 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 34.7%

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

4. Final simplification 34.7%

   \[\leadsto y \]

Reproduce

herbie shell --seed 2023244 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))