Data.Colour.RGB:hslsv from colour-2.3.3, C

Percentage Accurate: 100.0% → 100.0%

Time: 5.2s

Alternatives: 8

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{2 - \left(x + y\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{2 - \left(x + y\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{2 - \left(x + y\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{2 - \left(x + y\right)} \]

2. Final simplification 100.0%

   \[\leadsto \frac{x - y}{2 - \left(x + y\right)} \]

Alternative 2: 59.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{+103}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-197}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-273}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-78}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.9e+103)
   -1.0
   (if (<= x -1.7e-197)
     1.0
     (if (<= x 1.4e-273)
       (* y -0.5)
       (if (<= x 4e-78) 1.0 (if (<= x 3.0) (* x 0.5) -1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.9e+103) {
		tmp = -1.0;
	} else if (x <= -1.7e-197) {
		tmp = 1.0;
	} else if (x <= 1.4e-273) {
		tmp = y * -0.5;
	} else if (x <= 4e-78) {
		tmp = 1.0;
	} else if (x <= 3.0) {
		tmp = x * 0.5;
	} else {
		tmp = -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 (x <= (-4.9d+103)) then
        tmp = -1.0d0
    else if (x <= (-1.7d-197)) then
        tmp = 1.0d0
    else if (x <= 1.4d-273) then
        tmp = y * (-0.5d0)
    else if (x <= 4d-78) then
        tmp = 1.0d0
    else if (x <= 3.0d0) then
        tmp = x * 0.5d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.9e+103) {
		tmp = -1.0;
	} else if (x <= -1.7e-197) {
		tmp = 1.0;
	} else if (x <= 1.4e-273) {
		tmp = y * -0.5;
	} else if (x <= 4e-78) {
		tmp = 1.0;
	} else if (x <= 3.0) {
		tmp = x * 0.5;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.9e+103:
		tmp = -1.0
	elif x <= -1.7e-197:
		tmp = 1.0
	elif x <= 1.4e-273:
		tmp = y * -0.5
	elif x <= 4e-78:
		tmp = 1.0
	elif x <= 3.0:
		tmp = x * 0.5
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.9e+103)
		tmp = -1.0;
	elseif (x <= -1.7e-197)
		tmp = 1.0;
	elseif (x <= 1.4e-273)
		tmp = Float64(y * -0.5);
	elseif (x <= 4e-78)
		tmp = 1.0;
	elseif (x <= 3.0)
		tmp = Float64(x * 0.5);
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.9e+103)
		tmp = -1.0;
	elseif (x <= -1.7e-197)
		tmp = 1.0;
	elseif (x <= 1.4e-273)
		tmp = y * -0.5;
	elseif (x <= 4e-78)
		tmp = 1.0;
	elseif (x <= 3.0)
		tmp = x * 0.5;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.9e+103], -1.0, If[LessEqual[x, -1.7e-197], 1.0, If[LessEqual[x, 1.4e-273], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 4e-78], 1.0, If[LessEqual[x, 3.0], N[(x * 0.5), $MachinePrecision], -1.0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.8999999999999999e103 or 3 < x

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Step-by-step derivation

      1. associate--r+ 100.0%

         \[\leadsto \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]

   4. Taylor expanded in x around inf 74.6%

      \[\leadsto \color{blue}{-1} \]

   if -4.8999999999999999e103 < x < -1.6999999999999999e-197 or 1.39999999999999993e-273 < x < 4e-78

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Step-by-step derivation

      1. associate--r+ 99.9%

         \[\leadsto \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]

   4. Taylor expanded in y around inf 59.5%

      \[\leadsto \color{blue}{1} \]

   if -1.6999999999999999e-197 < x < 1.39999999999999993e-273

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Step-by-step derivation

      1. associate--r+ 100.0%

         \[\leadsto \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]

   4. Taylor expanded in x around 0 90.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{2 - y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 90.9%

         \[\leadsto \color{blue}{-\frac{y}{2 - y}} \]

      2. distribute-neg-frac 90.9%

         \[\leadsto \color{blue}{\frac{-y}{2 - y}} \]

   6. Simplified 90.9%

      \[\leadsto \color{blue}{\frac{-y}{2 - y}} \]

   7. Taylor expanded in y around 0 58.9%

      \[\leadsto \color{blue}{-0.5 \cdot y} \]
   8. Step-by-step derivation

      1. *-commutative 58.9%

         \[\leadsto \color{blue}{y \cdot -0.5} \]

   9. Simplified 58.9%

      \[\leadsto \color{blue}{y \cdot -0.5} \]

   if 4e-78 < x < 3

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Step-by-step derivation

      1. associate--r+ 100.0%

         \[\leadsto \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]

   4. Taylor expanded in y around 0 74.5%

      \[\leadsto \color{blue}{\frac{x}{2 - x}} \]

   5. Taylor expanded in x around 0 73.5%

      \[\leadsto \color{blue}{0.5 \cdot x} \]
   6. Step-by-step derivation

      1. *-commutative 73.5%

         \[\leadsto \color{blue}{x \cdot 0.5} \]

   7. Simplified 73.5%

      \[\leadsto \color{blue}{x \cdot 0.5} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{+103}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-197}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-273}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-78}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 3: 59.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+103}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-197}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-273}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-79}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.1:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9.5e+103)
   -1.0
   (if (<= x -2.2e-197)
     (+ 1.0 (/ 2.0 y))
     (if (<= x 7e-273)
       (* y -0.5)
       (if (<= x 2e-79) 1.0 (if (<= x 3.1) (* x 0.5) -1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9.5e+103) {
		tmp = -1.0;
	} else if (x <= -2.2e-197) {
		tmp = 1.0 + (2.0 / y);
	} else if (x <= 7e-273) {
		tmp = y * -0.5;
	} else if (x <= 2e-79) {
		tmp = 1.0;
	} else if (x <= 3.1) {
		tmp = x * 0.5;
	} else {
		tmp = -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 (x <= (-9.5d+103)) then
        tmp = -1.0d0
    else if (x <= (-2.2d-197)) then
        tmp = 1.0d0 + (2.0d0 / y)
    else if (x <= 7d-273) then
        tmp = y * (-0.5d0)
    else if (x <= 2d-79) then
        tmp = 1.0d0
    else if (x <= 3.1d0) then
        tmp = x * 0.5d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -9.5e+103) {
		tmp = -1.0;
	} else if (x <= -2.2e-197) {
		tmp = 1.0 + (2.0 / y);
	} else if (x <= 7e-273) {
		tmp = y * -0.5;
	} else if (x <= 2e-79) {
		tmp = 1.0;
	} else if (x <= 3.1) {
		tmp = x * 0.5;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9.5e+103:
		tmp = -1.0
	elif x <= -2.2e-197:
		tmp = 1.0 + (2.0 / y)
	elif x <= 7e-273:
		tmp = y * -0.5
	elif x <= 2e-79:
		tmp = 1.0
	elif x <= 3.1:
		tmp = x * 0.5
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9.5e+103)
		tmp = -1.0;
	elseif (x <= -2.2e-197)
		tmp = Float64(1.0 + Float64(2.0 / y));
	elseif (x <= 7e-273)
		tmp = Float64(y * -0.5);
	elseif (x <= 2e-79)
		tmp = 1.0;
	elseif (x <= 3.1)
		tmp = Float64(x * 0.5);
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -9.5e+103)
		tmp = -1.0;
	elseif (x <= -2.2e-197)
		tmp = 1.0 + (2.0 / y);
	elseif (x <= 7e-273)
		tmp = y * -0.5;
	elseif (x <= 2e-79)
		tmp = 1.0;
	elseif (x <= 3.1)
		tmp = x * 0.5;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9.5e+103], -1.0, If[LessEqual[x, -2.2e-197], N[(1.0 + N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e-273], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 2e-79], 1.0, If[LessEqual[x, 3.1], N[(x * 0.5), $MachinePrecision], -1.0]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -9.49999999999999922e103 or 3.10000000000000009 < x

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Step-by-step derivation

      1. associate--r+ 100.0%

         \[\leadsto \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]

   4. Taylor expanded in x around inf 74.6%

      \[\leadsto \color{blue}{-1} \]

   if -9.49999999999999922e103 < x < -2.2e-197

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Step-by-step derivation

      1. associate--r+ 100.0%

         \[\leadsto \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]

   4. Taylor expanded in x around 0 64.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{2 - y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 64.2%

         \[\leadsto \color{blue}{-\frac{y}{2 - y}} \]

      2. distribute-neg-frac 64.2%

         \[\leadsto \color{blue}{\frac{-y}{2 - y}} \]

   6. Simplified 64.2%

      \[\leadsto \color{blue}{\frac{-y}{2 - y}} \]

   7. Taylor expanded in y around inf 56.3%

      \[\leadsto \color{blue}{2 \cdot \frac{1}{y} + 1} \]
   8. Step-by-step derivation

      1. +-commutative 56.3%

         \[\leadsto \color{blue}{1 + 2 \cdot \frac{1}{y}} \]

      2. associate-*r/ 56.3%

         \[\leadsto 1 + \color{blue}{\frac{2 \cdot 1}{y}} \]

      3. metadata-eval 56.3%

         \[\leadsto 1 + \frac{\color{blue}{2}}{y} \]

   9. Simplified 56.3%

      \[\leadsto \color{blue}{1 + \frac{2}{y}} \]

   if -2.2e-197 < x < 6.99999999999999984e-273

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Step-by-step derivation

      1. associate--r+ 100.0%

         \[\leadsto \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]

   4. Taylor expanded in x around 0 90.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{2 - y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 90.9%

         \[\leadsto \color{blue}{-\frac{y}{2 - y}} \]

      2. distribute-neg-frac 90.9%

         \[\leadsto \color{blue}{\frac{-y}{2 - y}} \]

   6. Simplified 90.9%

      \[\leadsto \color{blue}{\frac{-y}{2 - y}} \]

   7. Taylor expanded in y around 0 58.9%

      \[\leadsto \color{blue}{-0.5 \cdot y} \]
   8. Step-by-step derivation

      1. *-commutative 58.9%

         \[\leadsto \color{blue}{y \cdot -0.5} \]

   9. Simplified 58.9%

      \[\leadsto \color{blue}{y \cdot -0.5} \]

   if 6.99999999999999984e-273 < x < 2e-79

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Step-by-step derivation

      1. associate--r+ 99.9%

         \[\leadsto \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]

   4. Taylor expanded in y around inf 64.0%

      \[\leadsto \color{blue}{1} \]

   if 2e-79 < x < 3.10000000000000009

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Step-by-step derivation

      1. associate--r+ 100.0%

         \[\leadsto \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]

   4. Taylor expanded in y around 0 74.5%

      \[\leadsto \color{blue}{\frac{x}{2 - x}} \]

   5. Taylor expanded in x around 0 73.5%

      \[\leadsto \color{blue}{0.5 \cdot x} \]
   6. Step-by-step derivation

      1. *-commutative 73.5%

         \[\leadsto \color{blue}{x \cdot 0.5} \]

   7. Simplified 73.5%

      \[\leadsto \color{blue}{x \cdot 0.5} \]
3. Recombined 5 regimes into one program.

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+103}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-197}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-273}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-79}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.1:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4: 74.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+88} \lor \neg \left(y \leq 1.1 \cdot 10^{+54}\right):\\ \;\;\;\;1 + \frac{x \cdot -2}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4.8e+88) (not (<= y 1.1e+54)))
   (+ 1.0 (/ (* x -2.0) y))
   (/ x (- 2.0 x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4.8e+88) || !(y <= 1.1e+54)) {
		tmp = 1.0 + ((x * -2.0) / y);
	} else {
		tmp = x / (2.0 - 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 <= (-4.8d+88)) .or. (.not. (y <= 1.1d+54))) then
        tmp = 1.0d0 + ((x * (-2.0d0)) / y)
    else
        tmp = x / (2.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -4.8e+88) || !(y <= 1.1e+54)) {
		tmp = 1.0 + ((x * -2.0) / y);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4.8e+88) or not (y <= 1.1e+54):
		tmp = 1.0 + ((x * -2.0) / y)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4.8e+88) || !(y <= 1.1e+54))
		tmp = Float64(1.0 + Float64(Float64(x * -2.0) / y));
	else
		tmp = Float64(x / Float64(2.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -4.8e+88) || ~((y <= 1.1e+54)))
		tmp = 1.0 + ((x * -2.0) / y);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4.8e+88], N[Not[LessEqual[y, 1.1e+54]], $MachinePrecision]], N[(1.0 + N[(N[(x * -2.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.7999999999999998e88 or 1.09999999999999995e54 < y

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Step-by-step derivation

      1. associate--r+ 99.9%

         \[\leadsto \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]

   4. Taylor expanded in y around inf 84.0%

      \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{x}{y}\right) - -1 \cdot \frac{2 - x}{y}} \]
   5. Step-by-step derivation

      1. associate--l+ 84.1%

         \[\leadsto \color{blue}{1 + \left(-1 \cdot \frac{x}{y} - -1 \cdot \frac{2 - x}{y}\right)} \]

      2. associate-*r/ 84.1%

         \[\leadsto 1 + \left(\color{blue}{\frac{-1 \cdot x}{y}} - -1 \cdot \frac{2 - x}{y}\right) \]

      3. associate-*r/ 84.1%

         \[\leadsto 1 + \left(\frac{-1 \cdot x}{y} - \color{blue}{\frac{-1 \cdot \left(2 - x\right)}{y}}\right) \]

      4. div-sub 84.1%

         \[\leadsto 1 + \color{blue}{\frac{-1 \cdot x - -1 \cdot \left(2 - x\right)}{y}} \]

      5. cancel-sign-sub-inv 84.1%

         \[\leadsto 1 + \frac{\color{blue}{-1 \cdot x + \left(--1\right) \cdot \left(2 - x\right)}}{y} \]

      6. metadata-eval 84.1%

         \[\leadsto 1 + \frac{-1 \cdot x + \color{blue}{1} \cdot \left(2 - x\right)}{y} \]

      7. *-lft-identity 84.1%

         \[\leadsto 1 + \frac{-1 \cdot x + \color{blue}{\left(2 - x\right)}}{y} \]

      8. +-commutative 84.1%

         \[\leadsto 1 + \frac{\color{blue}{\left(2 - x\right) + -1 \cdot x}}{y} \]

      9. mul-1-neg 84.1%

         \[\leadsto 1 + \frac{\left(2 - x\right) + \color{blue}{\left(-x\right)}}{y} \]

      10. unsub-neg 84.1%

          \[\leadsto 1 + \frac{\color{blue}{\left(2 - x\right) - x}}{y} \]

   6. Simplified 84.1%

      \[\leadsto \color{blue}{1 + \frac{\left(2 - x\right) - x}{y}} \]

   7. Taylor expanded in x around inf 84.1%

      \[\leadsto 1 + \frac{\color{blue}{-2 \cdot x}}{y} \]
   8. Step-by-step derivation

      1. *-commutative 84.1%

         \[\leadsto 1 + \frac{\color{blue}{x \cdot -2}}{y} \]

   9. Simplified 84.1%

      \[\leadsto 1 + \frac{\color{blue}{x \cdot -2}}{y} \]

   if -4.7999999999999998e88 < y < 1.09999999999999995e54

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Step-by-step derivation

      1. associate--r+ 100.0%

         \[\leadsto \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]

   4. Taylor expanded in y around 0 74.5%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+88} \lor \neg \left(y \leq 1.1 \cdot 10^{+54}\right):\\ \;\;\;\;1 + \frac{x \cdot -2}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 5: 60.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+110}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-78}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 15:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.8e+110)
   -1.0
   (if (<= x 1.6e-78) 1.0 (if (<= x 15.0) (* x 0.5) -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.8e+110) {
		tmp = -1.0;
	} else if (x <= 1.6e-78) {
		tmp = 1.0;
	} else if (x <= 15.0) {
		tmp = x * 0.5;
	} else {
		tmp = -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 (x <= (-2.8d+110)) then
        tmp = -1.0d0
    else if (x <= 1.6d-78) then
        tmp = 1.0d0
    else if (x <= 15.0d0) then
        tmp = x * 0.5d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.8e+110) {
		tmp = -1.0;
	} else if (x <= 1.6e-78) {
		tmp = 1.0;
	} else if (x <= 15.0) {
		tmp = x * 0.5;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.8e+110:
		tmp = -1.0
	elif x <= 1.6e-78:
		tmp = 1.0
	elif x <= 15.0:
		tmp = x * 0.5
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.8e+110)
		tmp = -1.0;
	elseif (x <= 1.6e-78)
		tmp = 1.0;
	elseif (x <= 15.0)
		tmp = Float64(x * 0.5);
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.8e+110)
		tmp = -1.0;
	elseif (x <= 1.6e-78)
		tmp = 1.0;
	elseif (x <= 15.0)
		tmp = x * 0.5;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.8e+110], -1.0, If[LessEqual[x, 1.6e-78], 1.0, If[LessEqual[x, 15.0], N[(x * 0.5), $MachinePrecision], -1.0]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.79999999999999987e110 or 15 < x

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Step-by-step derivation

      1. associate--r+ 100.0%

         \[\leadsto \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]

   4. Taylor expanded in x around inf 74.6%

      \[\leadsto \color{blue}{-1} \]

   if -2.79999999999999987e110 < x < 1.6e-78

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Step-by-step derivation

      1. associate--r+ 100.0%

         \[\leadsto \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]

   4. Taylor expanded in y around inf 54.1%

      \[\leadsto \color{blue}{1} \]

   if 1.6e-78 < x < 15

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Step-by-step derivation

      1. associate--r+ 100.0%

         \[\leadsto \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]

   4. Taylor expanded in y around 0 74.5%

      \[\leadsto \color{blue}{\frac{x}{2 - x}} \]

   5. Taylor expanded in x around 0 73.5%

      \[\leadsto \color{blue}{0.5 \cdot x} \]
   6. Step-by-step derivation

      1. *-commutative 73.5%

         \[\leadsto \color{blue}{x \cdot 0.5} \]

   7. Simplified 73.5%

      \[\leadsto \color{blue}{x \cdot 0.5} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+110}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-78}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 15:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 6: 73.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+92}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+81}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.95e+92) 1.0 (if (<= y 1.2e+81) (/ x (- 2.0 x)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.95e+92) {
		tmp = 1.0;
	} else if (y <= 1.2e+81) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 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 <= (-1.95d+92)) then
        tmp = 1.0d0
    else if (y <= 1.2d+81) then
        tmp = x / (2.0d0 - x)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.95e+92) {
		tmp = 1.0;
	} else if (y <= 1.2e+81) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.95e+92:
		tmp = 1.0
	elif y <= 1.2e+81:
		tmp = x / (2.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.95e+92)
		tmp = 1.0;
	elseif (y <= 1.2e+81)
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.95e+92)
		tmp = 1.0;
	elseif (y <= 1.2e+81)
		tmp = x / (2.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.95e+92], 1.0, If[LessEqual[y, 1.2e+81], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.95000000000000006e92 or 1.19999999999999995e81 < y

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Step-by-step derivation

      1. associate--r+ 100.0%

         \[\leadsto \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]

   4. Taylor expanded in y around inf 86.5%

      \[\leadsto \color{blue}{1} \]

   if -1.95000000000000006e92 < y < 1.19999999999999995e81

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Step-by-step derivation

      1. associate--r+ 100.0%

         \[\leadsto \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]

   4. Taylor expanded in y around 0 73.1%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+92}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+81}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 61.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.3 \cdot 10^{+103}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 11500:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6.3e+103) -1.0 (if (<= x 11500.0) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.3e+103) {
		tmp = -1.0;
	} else if (x <= 11500.0) {
		tmp = 1.0;
	} else {
		tmp = -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 (x <= (-6.3d+103)) then
        tmp = -1.0d0
    else if (x <= 11500.0d0) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -6.3e+103) {
		tmp = -1.0;
	} else if (x <= 11500.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.3e+103:
		tmp = -1.0
	elif x <= 11500.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.3e+103)
		tmp = -1.0;
	elseif (x <= 11500.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6.3e+103)
		tmp = -1.0;
	elseif (x <= 11500.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.3e+103], -1.0, If[LessEqual[x, 11500.0], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -6.29999999999999969e103 or 11500 < x

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Step-by-step derivation

      1. associate--r+ 100.0%

         \[\leadsto \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]

   4. Taylor expanded in x around inf 74.6%

      \[\leadsto \color{blue}{-1} \]

   if -6.29999999999999969e103 < x < 11500

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Step-by-step derivation

      1. associate--r+ 100.0%

         \[\leadsto \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]

   4. Taylor expanded in y around inf 50.3%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.3 \cdot 10^{+103}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 11500:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 8: 38.2% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ -1 \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = -1.0d0
end function

Java

public static double code(double x, double y) {
	return -1.0;
}

Python

def code(x, y):
	return -1.0

Julia

function code(x, y)
	return -1.0
end

MATLAB

function tmp = code(x, y)
	tmp = -1.0;
end

Wolfram

code[x_, y_] := -1.0

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{2 - \left(x + y\right)} \]
2. Step-by-step derivation

   1. associate--r+ 100.0%

      \[\leadsto \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]

4. Taylor expanded in x around inf 38.0%

   \[\leadsto \color{blue}{-1} \]

5. Final simplification 38.0%

   \[\leadsto -1 \]

Developer target: 100.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 - \left(x + y\right)\\ \frac{x}{t_0} - \frac{y}{t_0} \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 2.0 (+ x y)))) (- (/ x t_0) (/ y t_0))))

C

double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	return (x / t_0) - (y / t_0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    t_0 = 2.0d0 - (x + y)
    code = (x / t_0) - (y / t_0)
end function

Java

public static double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	return (x / t_0) - (y / t_0);
}

Python

def code(x, y):
	t_0 = 2.0 - (x + y)
	return (x / t_0) - (y / t_0)

Julia

function code(x, y)
	t_0 = Float64(2.0 - Float64(x + y))
	return Float64(Float64(x / t_0) - Float64(y / t_0))
end

MATLAB

function tmp = code(x, y)
	t_0 = 2.0 - (x + y);
	tmp = (x / t_0) - (y / t_0);
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]}, N[(N[(x / t$95$0), $MachinePrecision] - N[(y / t$95$0), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2023229 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :herbie-target
  (- (/ x (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))

  (/ (- x y) (- 2.0 (+ x y))))