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

Percentage Accurate: 100.0% → 100.0%

Time: 11.0s

Alternatives: 7

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: 60.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-34}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-87}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-281}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-257}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 4.65 \cdot 10^{-66}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-9}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 10^{+45}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.3e-6)
   1.0
   (if (<= y -7.5e-34)
     -1.0
     (if (<= y -8e-87)
       (* y -0.5)
       (if (<= y 2.3e-281)
         -1.0
         (if (<= y 2.7e-257)
           (* x 0.5)
           (if (<= y 4.65e-66)
             -1.0
             (if (<= y 3.7e-9) (* y -0.5) (if (<= y 1e+45) -1.0 1.0)))))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.3e-6) {
		tmp = 1.0;
	} else if (y <= -7.5e-34) {
		tmp = -1.0;
	} else if (y <= -8e-87) {
		tmp = y * -0.5;
	} else if (y <= 2.3e-281) {
		tmp = -1.0;
	} else if (y <= 2.7e-257) {
		tmp = x * 0.5;
	} else if (y <= 4.65e-66) {
		tmp = -1.0;
	} else if (y <= 3.7e-9) {
		tmp = y * -0.5;
	} else if (y <= 1e+45) {
		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 (y <= (-5.3d-6)) then
        tmp = 1.0d0
    else if (y <= (-7.5d-34)) then
        tmp = -1.0d0
    else if (y <= (-8d-87)) then
        tmp = y * (-0.5d0)
    else if (y <= 2.3d-281) then
        tmp = -1.0d0
    else if (y <= 2.7d-257) then
        tmp = x * 0.5d0
    else if (y <= 4.65d-66) then
        tmp = -1.0d0
    else if (y <= 3.7d-9) then
        tmp = y * (-0.5d0)
    else if (y <= 1d+45) 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 (y <= -5.3e-6) {
		tmp = 1.0;
	} else if (y <= -7.5e-34) {
		tmp = -1.0;
	} else if (y <= -8e-87) {
		tmp = y * -0.5;
	} else if (y <= 2.3e-281) {
		tmp = -1.0;
	} else if (y <= 2.7e-257) {
		tmp = x * 0.5;
	} else if (y <= 4.65e-66) {
		tmp = -1.0;
	} else if (y <= 3.7e-9) {
		tmp = y * -0.5;
	} else if (y <= 1e+45) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.3e-6:
		tmp = 1.0
	elif y <= -7.5e-34:
		tmp = -1.0
	elif y <= -8e-87:
		tmp = y * -0.5
	elif y <= 2.3e-281:
		tmp = -1.0
	elif y <= 2.7e-257:
		tmp = x * 0.5
	elif y <= 4.65e-66:
		tmp = -1.0
	elif y <= 3.7e-9:
		tmp = y * -0.5
	elif y <= 1e+45:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.3e-6)
		tmp = 1.0;
	elseif (y <= -7.5e-34)
		tmp = -1.0;
	elseif (y <= -8e-87)
		tmp = Float64(y * -0.5);
	elseif (y <= 2.3e-281)
		tmp = -1.0;
	elseif (y <= 2.7e-257)
		tmp = Float64(x * 0.5);
	elseif (y <= 4.65e-66)
		tmp = -1.0;
	elseif (y <= 3.7e-9)
		tmp = Float64(y * -0.5);
	elseif (y <= 1e+45)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5.3e-6)
		tmp = 1.0;
	elseif (y <= -7.5e-34)
		tmp = -1.0;
	elseif (y <= -8e-87)
		tmp = y * -0.5;
	elseif (y <= 2.3e-281)
		tmp = -1.0;
	elseif (y <= 2.7e-257)
		tmp = x * 0.5;
	elseif (y <= 4.65e-66)
		tmp = -1.0;
	elseif (y <= 3.7e-9)
		tmp = y * -0.5;
	elseif (y <= 1e+45)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.3e-6], 1.0, If[LessEqual[y, -7.5e-34], -1.0, If[LessEqual[y, -8e-87], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 2.3e-281], -1.0, If[LessEqual[y, 2.7e-257], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 4.65e-66], -1.0, If[LessEqual[y, 3.7e-9], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 1e+45], -1.0, 1.0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.3000000000000001e-6 or 9.9999999999999993e44 < 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 82.6%

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

   if -5.3000000000000001e-6 < y < -7.5000000000000004e-34 or -8.00000000000000014e-87 < y < 2.29999999999999989e-281 or 2.6999999999999999e-257 < y < 4.65000000000000014e-66 or 3.7e-9 < y < 9.9999999999999993e44

   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 x around inf 67.1%

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

   if -7.5000000000000004e-34 < y < -8.00000000000000014e-87 or 4.65000000000000014e-66 < y < 3.7e-9

   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 81.3%

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

      1. mul-1-neg 81.3%

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

      2. distribute-neg-frac 81.3%

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

   6. Simplified 81.3%

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

   7. Taylor expanded in y around 0 79.5%

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

      1. *-commutative 79.5%

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

   9. Simplified 79.5%

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

   if 2.29999999999999989e-281 < y < 2.6999999999999999e-257

   1. Initial program 99.8%

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

      1. associate--r+ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 91.2%

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

   5. Taylor expanded in x around 0 70.2%

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

      1. *-commutative 70.2%

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

   7. Simplified 70.2%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-34}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-87}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-281}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-257}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 4.65 \cdot 10^{-66}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-9}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 10^{+45}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3: 72.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+20}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-31}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-59}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-64}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-9}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+61}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 2.0 x))))
   (if (<= y -4.5e+20)
     1.0
     (if (<= y -1.55e-31)
       t_0
       (if (<= y -3.9e-59)
         (* y -0.5)
         (if (<= y 1.35e-64)
           t_0
           (if (<= y 3.7e-9) (* y -0.5) (if (<= y 3.5e+61) t_0 1.0))))))))

C

double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (y <= -4.5e+20) {
		tmp = 1.0;
	} else if (y <= -1.55e-31) {
		tmp = t_0;
	} else if (y <= -3.9e-59) {
		tmp = y * -0.5;
	} else if (y <= 1.35e-64) {
		tmp = t_0;
	} else if (y <= 3.7e-9) {
		tmp = y * -0.5;
	} else if (y <= 3.5e+61) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = x / (2.0d0 - x)
    if (y <= (-4.5d+20)) then
        tmp = 1.0d0
    else if (y <= (-1.55d-31)) then
        tmp = t_0
    else if (y <= (-3.9d-59)) then
        tmp = y * (-0.5d0)
    else if (y <= 1.35d-64) then
        tmp = t_0
    else if (y <= 3.7d-9) then
        tmp = y * (-0.5d0)
    else if (y <= 3.5d+61) then
        tmp = t_0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (y <= -4.5e+20) {
		tmp = 1.0;
	} else if (y <= -1.55e-31) {
		tmp = t_0;
	} else if (y <= -3.9e-59) {
		tmp = y * -0.5;
	} else if (y <= 1.35e-64) {
		tmp = t_0;
	} else if (y <= 3.7e-9) {
		tmp = y * -0.5;
	} else if (y <= 3.5e+61) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (2.0 - x)
	tmp = 0
	if y <= -4.5e+20:
		tmp = 1.0
	elif y <= -1.55e-31:
		tmp = t_0
	elif y <= -3.9e-59:
		tmp = y * -0.5
	elif y <= 1.35e-64:
		tmp = t_0
	elif y <= 3.7e-9:
		tmp = y * -0.5
	elif y <= 3.5e+61:
		tmp = t_0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(2.0 - x))
	tmp = 0.0
	if (y <= -4.5e+20)
		tmp = 1.0;
	elseif (y <= -1.55e-31)
		tmp = t_0;
	elseif (y <= -3.9e-59)
		tmp = Float64(y * -0.5);
	elseif (y <= 1.35e-64)
		tmp = t_0;
	elseif (y <= 3.7e-9)
		tmp = Float64(y * -0.5);
	elseif (y <= 3.5e+61)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (2.0 - x);
	tmp = 0.0;
	if (y <= -4.5e+20)
		tmp = 1.0;
	elseif (y <= -1.55e-31)
		tmp = t_0;
	elseif (y <= -3.9e-59)
		tmp = y * -0.5;
	elseif (y <= 1.35e-64)
		tmp = t_0;
	elseif (y <= 3.7e-9)
		tmp = y * -0.5;
	elseif (y <= 3.5e+61)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+20], 1.0, If[LessEqual[y, -1.55e-31], t$95$0, If[LessEqual[y, -3.9e-59], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 1.35e-64], t$95$0, If[LessEqual[y, 3.7e-9], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 3.5e+61], t$95$0, 1.0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5e20 or 3.50000000000000018e61 < 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 85.4%

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

   if -4.5e20 < y < -1.55e-31 or -3.90000000000000019e-59 < y < 1.34999999999999993e-64 or 3.7e-9 < y < 3.50000000000000018e61

   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 0 83.6%

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

   if -1.55e-31 < y < -3.90000000000000019e-59 or 1.34999999999999993e-64 < y < 3.7e-9

   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 93.9%

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

      1. mul-1-neg 93.9%

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

      2. distribute-neg-frac 93.9%

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

   6. Simplified 93.9%

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

   7. Taylor expanded in y around 0 91.5%

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

      1. *-commutative 91.5%

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

   9. Simplified 91.5%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+20}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-31}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-59}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-9}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+61}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{y + -2}\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{-8}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-35}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-59} \lor \neg \left(y \leq 2.65 \cdot 10^{-65}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ y (+ y -2.0))))
   (if (<= y -4.5e-8)
     t_0
     (if (<= y -6.5e-35)
       -1.0
       (if (or (<= y -7e-59) (not (<= y 2.65e-65))) t_0 (/ x (- 2.0 x)))))))

C

double code(double x, double y) {
	double t_0 = y / (y + -2.0);
	double tmp;
	if (y <= -4.5e-8) {
		tmp = t_0;
	} else if (y <= -6.5e-35) {
		tmp = -1.0;
	} else if ((y <= -7e-59) || !(y <= 2.65e-65)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = y / (y + (-2.0d0))
    if (y <= (-4.5d-8)) then
        tmp = t_0
    else if (y <= (-6.5d-35)) then
        tmp = -1.0d0
    else if ((y <= (-7d-59)) .or. (.not. (y <= 2.65d-65))) then
        tmp = t_0
    else
        tmp = x / (2.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y / (y + -2.0);
	double tmp;
	if (y <= -4.5e-8) {
		tmp = t_0;
	} else if (y <= -6.5e-35) {
		tmp = -1.0;
	} else if ((y <= -7e-59) || !(y <= 2.65e-65)) {
		tmp = t_0;
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y / (y + -2.0)
	tmp = 0
	if y <= -4.5e-8:
		tmp = t_0
	elif y <= -6.5e-35:
		tmp = -1.0
	elif (y <= -7e-59) or not (y <= 2.65e-65):
		tmp = t_0
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y / Float64(y + -2.0))
	tmp = 0.0
	if (y <= -4.5e-8)
		tmp = t_0;
	elseif (y <= -6.5e-35)
		tmp = -1.0;
	elseif ((y <= -7e-59) || !(y <= 2.65e-65))
		tmp = t_0;
	else
		tmp = Float64(x / Float64(2.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y / (y + -2.0);
	tmp = 0.0;
	if (y <= -4.5e-8)
		tmp = t_0;
	elseif (y <= -6.5e-35)
		tmp = -1.0;
	elseif ((y <= -7e-59) || ~((y <= 2.65e-65)))
		tmp = t_0;
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e-8], t$95$0, If[LessEqual[y, -6.5e-35], -1.0, If[Or[LessEqual[y, -7e-59], N[Not[LessEqual[y, 2.65e-65]], $MachinePrecision]], t$95$0, N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.49999999999999993e-8 or -6.4999999999999999e-35 < y < -7.0000000000000002e-59 or 2.65000000000000019e-65 < 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 x around 0 82.3%

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

      1. mul-1-neg 82.3%

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

      2. distribute-neg-frac 82.3%

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

   6. Simplified 82.3%

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

      1. frac-2neg 82.3%

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

      2. div-inv 82.1%

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

      3. remove-double-neg 82.1%

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

      4. sub-neg 82.1%

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

      5. distribute-neg-in 82.1%

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

      6. metadata-eval 82.1%

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

      7. remove-double-neg 82.1%

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

   8. Applied egg-rr 82.1%

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

      1. associate-*r/ 82.3%

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

      2. *-rgt-identity 82.3%

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

      3. +-commutative 82.3%

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

   10. Simplified 82.3%

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

   if -4.49999999999999993e-8 < y < -6.4999999999999999e-35

   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 100.0%

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

   if -7.0000000000000002e-59 < y < 2.65000000000000019e-65

   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 0 87.1%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-35}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-59} \lor \neg \left(y \leq 2.65 \cdot 10^{-65}\right):\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 5: 61.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-281}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-255}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+45}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.3e-6)
   1.0
   (if (<= y 2.4e-281)
     -1.0
     (if (<= y 6.1e-255) (* x 0.5) (if (<= y 5e+45) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.3e-6) {
		tmp = 1.0;
	} else if (y <= 2.4e-281) {
		tmp = -1.0;
	} else if (y <= 6.1e-255) {
		tmp = x * 0.5;
	} else if (y <= 5e+45) {
		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 (y <= (-5.3d-6)) then
        tmp = 1.0d0
    else if (y <= 2.4d-281) then
        tmp = -1.0d0
    else if (y <= 6.1d-255) then
        tmp = x * 0.5d0
    else if (y <= 5d+45) 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 (y <= -5.3e-6) {
		tmp = 1.0;
	} else if (y <= 2.4e-281) {
		tmp = -1.0;
	} else if (y <= 6.1e-255) {
		tmp = x * 0.5;
	} else if (y <= 5e+45) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.3e-6:
		tmp = 1.0
	elif y <= 2.4e-281:
		tmp = -1.0
	elif y <= 6.1e-255:
		tmp = x * 0.5
	elif y <= 5e+45:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.3e-6)
		tmp = 1.0;
	elseif (y <= 2.4e-281)
		tmp = -1.0;
	elseif (y <= 6.1e-255)
		tmp = Float64(x * 0.5);
	elseif (y <= 5e+45)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5.3e-6)
		tmp = 1.0;
	elseif (y <= 2.4e-281)
		tmp = -1.0;
	elseif (y <= 6.1e-255)
		tmp = x * 0.5;
	elseif (y <= 5e+45)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.3e-6], 1.0, If[LessEqual[y, 2.4e-281], -1.0, If[LessEqual[y, 6.1e-255], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 5e+45], -1.0, 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.3000000000000001e-6 or 5e45 < 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 82.6%

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

   if -5.3000000000000001e-6 < y < 2.4e-281 or 6.1e-255 < y < 5e45

   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 59.2%

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

   if 2.4e-281 < y < 6.1e-255

   1. Initial program 99.8%

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

      1. associate--r+ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 91.2%

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

   5. Taylor expanded in x around 0 70.2%

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

      1. *-commutative 70.2%

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

   7. Simplified 70.2%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-281}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-255}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+45}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 61.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+45}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.3e-6) 1.0 (if (<= y 6.5e+45) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.3e-6) {
		tmp = 1.0;
	} else if (y <= 6.5e+45) {
		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 (y <= (-5.3d-6)) then
        tmp = 1.0d0
    else if (y <= 6.5d+45) 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 (y <= -5.3e-6) {
		tmp = 1.0;
	} else if (y <= 6.5e+45) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.3e-6:
		tmp = 1.0
	elif y <= 6.5e+45:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.3e-6)
		tmp = 1.0;
	elseif (y <= 6.5e+45)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5.3e-6)
		tmp = 1.0;
	elseif (y <= 6.5e+45)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.3e-6], 1.0, If[LessEqual[y, 6.5e+45], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -5.3000000000000001e-6 or 6.50000000000000034e45 < 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 82.6%

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

   if -5.3000000000000001e-6 < y < 6.50000000000000034e45

   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 x around inf 56.8%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+45}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 38.3% 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 39.9%

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

5. Final simplification 39.9%

   \[\leadsto -1 \]

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 2023187 
(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))))