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

Percentage Accurate: 100.0% → 100.0%

Time: 5.8s

Alternatives: 9

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: 73.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+30}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-55} \lor \neg \left(y \leq -7.2 \cdot 10^{-89}\right) \land y \leq 8.2 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.95e+30)
   (- 1.0 (/ x y))
   (if (or (<= y -2.55e-55) (and (not (<= y -7.2e-89)) (<= y 8.2e-45)))
     (/ x (- 2.0 x))
     (/ y (+ y -2.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.95e+30) {
		tmp = 1.0 - (x / y);
	} else if ((y <= -2.55e-55) || (!(y <= -7.2e-89) && (y <= 8.2e-45))) {
		tmp = x / (2.0 - x);
	} else {
		tmp = y / (y + -2.0);
	}
	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+30)) then
        tmp = 1.0d0 - (x / y)
    else if ((y <= (-2.55d-55)) .or. (.not. (y <= (-7.2d-89))) .and. (y <= 8.2d-45)) then
        tmp = x / (2.0d0 - x)
    else
        tmp = y / (y + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.95e+30) {
		tmp = 1.0 - (x / y);
	} else if ((y <= -2.55e-55) || (!(y <= -7.2e-89) && (y <= 8.2e-45))) {
		tmp = x / (2.0 - x);
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.95e+30:
		tmp = 1.0 - (x / y)
	elif (y <= -2.55e-55) or (not (y <= -7.2e-89) and (y <= 8.2e-45)):
		tmp = x / (2.0 - x)
	else:
		tmp = y / (y + -2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.95e+30)
		tmp = Float64(1.0 - Float64(x / y));
	elseif ((y <= -2.55e-55) || (!(y <= -7.2e-89) && (y <= 8.2e-45)))
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = Float64(y / Float64(y + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.95e+30)
		tmp = 1.0 - (x / y);
	elseif ((y <= -2.55e-55) || (~((y <= -7.2e-89)) && (y <= 8.2e-45)))
		tmp = x / (2.0 - x);
	else
		tmp = y / (y + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.95e+30], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -2.55e-55], And[N[Not[LessEqual[y, -7.2e-89]], $MachinePrecision], LessEqual[y, 8.2e-45]]], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.95000000000000005e30

   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 75.5%

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

      1. neg-mul-1 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in x around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. unsub-neg 75.5%

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

   9. Simplified 75.5%

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

   if -1.95000000000000005e30 < y < -2.54999999999999998e-55 or -7.20000000000000014e-89 < y < 8.1999999999999998e-45

   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 87.6%

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

   if -2.54999999999999998e-55 < y < -7.20000000000000014e-89 or 8.1999999999999998e-45 < 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 81.9%

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

   5. Taylor expanded in x around 0 81.3%

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

      1. metadata-eval 81.3%

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

      2. times-frac 81.3%

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

      3. *-lft-identity 81.3%

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

      4. neg-mul-1 81.3%

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

      5. neg-sub0 81.3%

         \[\leadsto \frac{y}{\color{blue}{0 - \left(2 - y\right)}} \]

      6. associate--r- 81.3%

         \[\leadsto \frac{y}{\color{blue}{\left(0 - 2\right) + y}} \]

      7. metadata-eval 81.3%

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

   7. Simplified 81.3%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+30}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-55} \lor \neg \left(y \leq -7.2 \cdot 10^{-89}\right) \land y \leq 8.2 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \]

Alternative 3: 61.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x} + -1\\ \mathbf{if}\;x \leq -245000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-162}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-73}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 18500:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (/ y x) -1.0)))
   (if (<= x -245000.0)
     t_0
     (if (<= x 3.1e-162)
       (- 1.0 (/ x y))
       (if (<= x 5e-73) (* x 0.5) (if (<= x 18500.0) 1.0 t_0))))))

C

double code(double x, double y) {
	double t_0 = (y / x) + -1.0;
	double tmp;
	if (x <= -245000.0) {
		tmp = t_0;
	} else if (x <= 3.1e-162) {
		tmp = 1.0 - (x / y);
	} else if (x <= 5e-73) {
		tmp = x * 0.5;
	} else if (x <= 18500.0) {
		tmp = 1.0;
	} else {
		tmp = t_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 = (y / x) + (-1.0d0)
    if (x <= (-245000.0d0)) then
        tmp = t_0
    else if (x <= 3.1d-162) then
        tmp = 1.0d0 - (x / y)
    else if (x <= 5d-73) then
        tmp = x * 0.5d0
    else if (x <= 18500.0d0) then
        tmp = 1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y / x) + -1.0;
	double tmp;
	if (x <= -245000.0) {
		tmp = t_0;
	} else if (x <= 3.1e-162) {
		tmp = 1.0 - (x / y);
	} else if (x <= 5e-73) {
		tmp = x * 0.5;
	} else if (x <= 18500.0) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y / x) + -1.0
	tmp = 0
	if x <= -245000.0:
		tmp = t_0
	elif x <= 3.1e-162:
		tmp = 1.0 - (x / y)
	elif x <= 5e-73:
		tmp = x * 0.5
	elif x <= 18500.0:
		tmp = 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y / x) + -1.0)
	tmp = 0.0
	if (x <= -245000.0)
		tmp = t_0;
	elseif (x <= 3.1e-162)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (x <= 5e-73)
		tmp = Float64(x * 0.5);
	elseif (x <= 18500.0)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y / x) + -1.0;
	tmp = 0.0;
	if (x <= -245000.0)
		tmp = t_0;
	elseif (x <= 3.1e-162)
		tmp = 1.0 - (x / y);
	elseif (x <= 5e-73)
		tmp = x * 0.5;
	elseif (x <= 18500.0)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision]}, If[LessEqual[x, -245000.0], t$95$0, If[LessEqual[x, 3.1e-162], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e-73], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 18500.0], 1.0, t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -245000 or 18500 < 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 85.4%

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

      1. neg-mul-1 85.4%

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

   6. Simplified 85.4%

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

   7. Taylor expanded in x around 0 85.4%

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

   if -245000 < x < 3.0999999999999999e-162

   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 56.6%

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

      1. neg-mul-1 56.6%

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

   6. Simplified 56.6%

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

   7. Taylor expanded in x around 0 56.6%

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

      1. mul-1-neg 56.6%

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

      2. unsub-neg 56.6%

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

   9. Simplified 56.6%

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

   if 3.0999999999999999e-162 < x < 4.9999999999999998e-73

   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 0 100.0%

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

   5. Taylor expanded in y around 0 73.0%

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

      1. *-commutative 73.0%

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

   7. Simplified 73.0%

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

   if 4.9999999999999998e-73 < x < 18500

   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 62.2%

      \[\leadsto \color{blue}{1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -245000:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-162}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-73}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 18500:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \]

Alternative 4: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1200000 \lor \neg \left(x \leq 1.35 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1200000.0) (not (<= x 1.35e-10)))
   (/ x (- 2.0 x))
   (/ (- x y) (- 2.0 y))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1200000.0) || !(x <= 1.35e-10)) {
		tmp = x / (2.0 - x);
	} else {
		tmp = (x - y) / (2.0 - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1200000.0d0)) .or. (.not. (x <= 1.35d-10))) then
        tmp = x / (2.0d0 - x)
    else
        tmp = (x - y) / (2.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1200000.0) || !(x <= 1.35e-10)) {
		tmp = x / (2.0 - x);
	} else {
		tmp = (x - y) / (2.0 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1200000.0) or not (x <= 1.35e-10):
		tmp = x / (2.0 - x)
	else:
		tmp = (x - y) / (2.0 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1200000.0) || !(x <= 1.35e-10))
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = Float64(Float64(x - y) / Float64(2.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1200000.0) || ~((x <= 1.35e-10)))
		tmp = x / (2.0 - x);
	else
		tmp = (x - y) / (2.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1200000.0], N[Not[LessEqual[x, 1.35e-10]], $MachinePrecision]], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / N[(2.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2e6 or 1.35e-10 < 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 y around 0 86.2%

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

   if -1.2e6 < x < 1.35e-10

   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 99.0%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1200000 \lor \neg \left(x \leq 1.35 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \end{array} \]

Alternative 5: 61.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2600000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-141}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 10^{-71}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 10000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2600000.0)
   -1.0
   (if (<= x 4.8e-141)
     1.0
     (if (<= x 1e-71) (* x 0.5) (if (<= x 10000.0) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2600000.0) {
		tmp = -1.0;
	} else if (x <= 4.8e-141) {
		tmp = 1.0;
	} else if (x <= 1e-71) {
		tmp = x * 0.5;
	} else if (x <= 10000.0) {
		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 <= (-2600000.0d0)) then
        tmp = -1.0d0
    else if (x <= 4.8d-141) then
        tmp = 1.0d0
    else if (x <= 1d-71) then
        tmp = x * 0.5d0
    else if (x <= 10000.0d0) 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 <= -2600000.0) {
		tmp = -1.0;
	} else if (x <= 4.8e-141) {
		tmp = 1.0;
	} else if (x <= 1e-71) {
		tmp = x * 0.5;
	} else if (x <= 10000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2600000.0:
		tmp = -1.0
	elif x <= 4.8e-141:
		tmp = 1.0
	elif x <= 1e-71:
		tmp = x * 0.5
	elif x <= 10000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2600000.0)
		tmp = -1.0;
	elseif (x <= 4.8e-141)
		tmp = 1.0;
	elseif (x <= 1e-71)
		tmp = Float64(x * 0.5);
	elseif (x <= 10000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2600000.0)
		tmp = -1.0;
	elseif (x <= 4.8e-141)
		tmp = 1.0;
	elseif (x <= 1e-71)
		tmp = x * 0.5;
	elseif (x <= 10000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2600000.0], -1.0, If[LessEqual[x, 4.8e-141], 1.0, If[LessEqual[x, 1e-71], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 10000.0], 1.0, -1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.6e6 or 1e4 < 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 85.0%

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

   if -2.6e6 < x < 4.8000000000000002e-141 or 9.9999999999999992e-72 < x < 1e4

   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 57.5%

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

   if 4.8000000000000002e-141 < x < 9.9999999999999992e-72

   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 0 100.0%

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

   5. Taylor expanded in y around 0 81.4%

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

      1. *-commutative 81.4%

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

   7. Simplified 81.4%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2600000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-141}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 10^{-71}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 10000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 6: 61.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -27000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-161}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-71}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 13600:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -27000.0)
   -1.0
   (if (<= x 5.3e-161)
     (- 1.0 (/ x y))
     (if (<= x 2e-71) (* x 0.5) (if (<= x 13600.0) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -27000.0) {
		tmp = -1.0;
	} else if (x <= 5.3e-161) {
		tmp = 1.0 - (x / y);
	} else if (x <= 2e-71) {
		tmp = x * 0.5;
	} else if (x <= 13600.0) {
		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 <= (-27000.0d0)) then
        tmp = -1.0d0
    else if (x <= 5.3d-161) then
        tmp = 1.0d0 - (x / y)
    else if (x <= 2d-71) then
        tmp = x * 0.5d0
    else if (x <= 13600.0d0) 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 <= -27000.0) {
		tmp = -1.0;
	} else if (x <= 5.3e-161) {
		tmp = 1.0 - (x / y);
	} else if (x <= 2e-71) {
		tmp = x * 0.5;
	} else if (x <= 13600.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -27000.0:
		tmp = -1.0
	elif x <= 5.3e-161:
		tmp = 1.0 - (x / y)
	elif x <= 2e-71:
		tmp = x * 0.5
	elif x <= 13600.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -27000.0)
		tmp = -1.0;
	elseif (x <= 5.3e-161)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (x <= 2e-71)
		tmp = Float64(x * 0.5);
	elseif (x <= 13600.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -27000.0)
		tmp = -1.0;
	elseif (x <= 5.3e-161)
		tmp = 1.0 - (x / y);
	elseif (x <= 2e-71)
		tmp = x * 0.5;
	elseif (x <= 13600.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -27000.0], -1.0, If[LessEqual[x, 5.3e-161], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e-71], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 13600.0], 1.0, -1.0]]]]

Derivation

1. Split input into 4 regimes

2. if x < -27000 or 13600 < 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 85.0%

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

   if -27000 < x < 5.30000000000000029e-161

   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 56.6%

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

      1. neg-mul-1 56.6%

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

   6. Simplified 56.6%

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

   7. Taylor expanded in x around 0 56.6%

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

      1. mul-1-neg 56.6%

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

      2. unsub-neg 56.6%

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

   9. Simplified 56.6%

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

   if 5.30000000000000029e-161 < x < 1.9999999999999998e-71

   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 0 100.0%

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

   5. Taylor expanded in y around 0 73.0%

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

      1. *-commutative 73.0%

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

   7. Simplified 73.0%

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

   if 1.9999999999999998e-71 < x < 13600

   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 62.2%

      \[\leadsto \color{blue}{1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -27000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-161}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-71}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 13600:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 7: 74.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+32} \lor \neg \left(y \leq 1.65 \cdot 10^{+18}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.7e+32) (not (<= y 1.65e+18)))
   (- 1.0 (/ x y))
   (/ x (- 2.0 x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.7e+32) || !(y <= 1.65e+18)) {
		tmp = 1.0 - (x / 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 <= (-1.7d+32)) .or. (.not. (y <= 1.65d+18))) then
        tmp = 1.0d0 - (x / 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 <= -1.7e+32) || !(y <= 1.65e+18)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.7e+32) or not (y <= 1.65e+18):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.7e+32) || !(y <= 1.65e+18))
		tmp = Float64(1.0 - Float64(x / 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 <= -1.7e+32) || ~((y <= 1.65e+18)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.7e+32], N[Not[LessEqual[y, 1.65e+18]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.69999999999999989e32 or 1.65e18 < 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 78.3%

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

      1. neg-mul-1 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in x around 0 78.3%

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

      1. mul-1-neg 78.3%

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

      2. unsub-neg 78.3%

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

   9. Simplified 78.3%

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

   if -1.69999999999999989e32 < y < 1.65e18

   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 79.9%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+32} \lor \neg \left(y \leq 1.65 \cdot 10^{+18}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 8: 62.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2600000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 18500:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2600000.0) -1.0 (if (<= x 18500.0) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2600000.0) {
		tmp = -1.0;
	} else if (x <= 18500.0) {
		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 <= (-2600000.0d0)) then
        tmp = -1.0d0
    else if (x <= 18500.0d0) 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 <= -2600000.0) {
		tmp = -1.0;
	} else if (x <= 18500.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2600000.0:
		tmp = -1.0
	elif x <= 18500.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2600000.0)
		tmp = -1.0;
	elseif (x <= 18500.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2600000.0)
		tmp = -1.0;
	elseif (x <= 18500.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2600000.0], -1.0, If[LessEqual[x, 18500.0], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6e6 or 18500 < 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 85.0%

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

   if -2.6e6 < x < 18500

   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 54.4%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2600000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 18500:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 9: 38.0% 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 40.8%

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

5. Final simplification 40.8%

   \[\leadsto -1 \]

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 2023193 
(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))))