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

Percentage Accurate: 100.0% → 100.0%

Time: 8.9s

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 99.9%

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

2. Final simplification 99.9%

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

Alternative 2: 74.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{-83} \lor \neg \left(y \leq 6.6 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{y + 2}{y - \frac{4}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{x + -2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.85e-83) (not (<= y 6.6e-18)))
   (/ (+ y 2.0) (- y (/ 4.0 y)))
   (/ (- x) (+ x -2.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.85e-83) || !(y <= 6.6e-18)) {
		tmp = (y + 2.0) / (y - (4.0 / y));
	} else {
		tmp = -x / (x + -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 <= (-2.85d-83)) .or. (.not. (y <= 6.6d-18))) then
        tmp = (y + 2.0d0) / (y - (4.0d0 / y))
    else
        tmp = -x / (x + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.85e-83) || !(y <= 6.6e-18)) {
		tmp = (y + 2.0) / (y - (4.0 / y));
	} else {
		tmp = -x / (x + -2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.85e-83) or not (y <= 6.6e-18):
		tmp = (y + 2.0) / (y - (4.0 / y))
	else:
		tmp = -x / (x + -2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.85e-83) || !(y <= 6.6e-18))
		tmp = Float64(Float64(y + 2.0) / Float64(y - Float64(4.0 / y)));
	else
		tmp = Float64(Float64(-x) / Float64(x + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.85e-83) || ~((y <= 6.6e-18)))
		tmp = (y + 2.0) / (y - (4.0 / y));
	else
		tmp = -x / (x + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.85e-83], N[Not[LessEqual[y, 6.6e-18]], $MachinePrecision]], N[(N[(y + 2.0), $MachinePrecision] / N[(y - N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-x) / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.85e-83 or 6.6000000000000003e-18 < y

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

      1. add-cbrt-cube 99.9%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\frac{y - x}{x + \left(y + -2\right)} \cdot \frac{y - x}{x + \left(y + -2\right)}\right) \cdot \frac{y - x}{x + \left(y + -2\right)}}} \]

      2. pow3 99.9%

         \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{y - x}{x + \left(y + -2\right)}\right)}^{3}}} \]

      3. +-commutative 99.9%

         \[\leadsto \sqrt[3]{{\left(\frac{y - x}{\color{blue}{\left(y + -2\right) + x}}\right)}^{3}} \]

      4. associate-+l+ 99.9%

         \[\leadsto \sqrt[3]{{\left(\frac{y - x}{\color{blue}{y + \left(-2 + x\right)}}\right)}^{3}} \]

      5. +-commutative 99.9%

         \[\leadsto \sqrt[3]{{\left(\frac{y - x}{y + \color{blue}{\left(x + -2\right)}}\right)}^{3}} \]

   5. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\sqrt[3]{{\left(\frac{y - x}{y + \left(x + -2\right)}\right)}^{3}}} \]
   6. Step-by-step derivation

      1. rem-cbrt-cube 99.9%

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

      2. associate-+r+ 99.9%

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

      3. flip-+ 45.1%

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

      4. metadata-eval 45.1%

         \[\leadsto \frac{y - x}{\frac{\left(y + x\right) \cdot \left(y + x\right) - \color{blue}{4}}{\left(y + x\right) - -2}} \]

      5. associate-+r- 45.1%

         \[\leadsto \frac{y - x}{\frac{\left(y + x\right) \cdot \left(y + x\right) - 4}{\color{blue}{y + \left(x - -2\right)}}} \]

      6. associate-/l* 43.3%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(y + \left(x - -2\right)\right)}{\left(y + x\right) \cdot \left(y + x\right) - 4}} \]

      7. associate-*l/ 45.0%

         \[\leadsto \color{blue}{\frac{y - x}{\left(y + x\right) \cdot \left(y + x\right) - 4} \cdot \left(y + \left(x - -2\right)\right)} \]

      8. clear-num 45.0%

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(y + x\right) \cdot \left(y + x\right) - 4}{y - x}}} \cdot \left(y + \left(x - -2\right)\right) \]

      9. associate-*l/ 45.1%

         \[\leadsto \color{blue}{\frac{1 \cdot \left(y + \left(x - -2\right)\right)}{\frac{\left(y + x\right) \cdot \left(y + x\right) - 4}{y - x}}} \]

      10. *-un-lft-identity 45.1%

          \[\leadsto \frac{\color{blue}{y + \left(x - -2\right)}}{\frac{\left(y + x\right) \cdot \left(y + x\right) - 4}{y - x}} \]

      11. sub-neg 45.1%

          \[\leadsto \frac{y + \color{blue}{\left(x + \left(--2\right)\right)}}{\frac{\left(y + x\right) \cdot \left(y + x\right) - 4}{y - x}} \]

      12. metadata-eval 45.1%

          \[\leadsto \frac{y + \left(x + \color{blue}{2}\right)}{\frac{\left(y + x\right) \cdot \left(y + x\right) - 4}{y - x}} \]

      13. div-sub 45.1%

          \[\leadsto \frac{y + \left(x + 2\right)}{\color{blue}{\frac{\left(y + x\right) \cdot \left(y + x\right)}{y - x} - \frac{4}{y - x}}} \]

   7. Applied egg-rr 75.9%

      \[\leadsto \color{blue}{\frac{y + \left(x + 2\right)}{\left(y + x\right) - \frac{4}{y + x}}} \]

   8. Taylor expanded in x around 0 75.9%

      \[\leadsto \color{blue}{\frac{2 + y}{y - 4 \cdot \frac{1}{y}}} \]
   9. Step-by-step derivation

      1. +-commutative 75.9%

         \[\leadsto \frac{\color{blue}{y + 2}}{y - 4 \cdot \frac{1}{y}} \]

      2. associate-*r/ 75.9%

         \[\leadsto \frac{y + 2}{y - \color{blue}{\frac{4 \cdot 1}{y}}} \]

      3. metadata-eval 75.9%

         \[\leadsto \frac{y + 2}{y - \frac{\color{blue}{4}}{y}} \]

   10. Simplified 75.9%

       \[\leadsto \color{blue}{\frac{y + 2}{y - \frac{4}{y}}} \]

   if -2.85e-83 < y < 6.6000000000000003e-18

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 82.5%

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

      1. associate-*r/ 82.5%

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

      2. mul-1-neg 82.5%

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

      3. sub-neg 82.5%

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

      4. metadata-eval 82.5%

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

   6. Simplified 82.5%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{-83} \lor \neg \left(y \leq 6.6 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{y + 2}{y - \frac{4}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{x + -2}\\ \end{array} \]

Alternative 3: 74.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-82} \lor \neg \left(y \leq 6.4 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{x + -2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.05e-82) (not (<= y 6.4e-25)))
   (/ y (- y 2.0))
   (/ (- x) (+ x -2.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.05e-82) || !(y <= 6.4e-25)) {
		tmp = y / (y - 2.0);
	} else {
		tmp = -x / (x + -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 <= (-1.05d-82)) .or. (.not. (y <= 6.4d-25))) then
        tmp = y / (y - 2.0d0)
    else
        tmp = -x / (x + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.05e-82) || !(y <= 6.4e-25)) {
		tmp = y / (y - 2.0);
	} else {
		tmp = -x / (x + -2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.05e-82) or not (y <= 6.4e-25):
		tmp = y / (y - 2.0)
	else:
		tmp = -x / (x + -2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.05e-82) || !(y <= 6.4e-25))
		tmp = Float64(y / Float64(y - 2.0));
	else
		tmp = Float64(Float64(-x) / Float64(x + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.05e-82) || ~((y <= 6.4e-25)))
		tmp = y / (y - 2.0);
	else
		tmp = -x / (x + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.05e-82], N[Not[LessEqual[y, 6.4e-25]], $MachinePrecision]], N[(y / N[(y - 2.0), $MachinePrecision]), $MachinePrecision], N[((-x) / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e-82 or 6.4000000000000002e-25 < y

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 75.9%

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

   if -1.05e-82 < y < 6.4000000000000002e-25

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 82.5%

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

      1. associate-*r/ 82.5%

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

      2. mul-1-neg 82.5%

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

      3. sub-neg 82.5%

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

      4. metadata-eval 82.5%

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

   6. Simplified 82.5%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-82} \lor \neg \left(y \leq 6.4 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{x + -2}\\ \end{array} \]

Alternative 4: 61.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-217}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-240}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+64}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.7e-6)
   1.0
   (if (<= y -4.4e-217)
     -1.0
     (if (<= y 3e-240) (* x 0.5) (if (<= y 3e+64) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.7e-6) {
		tmp = 1.0;
	} else if (y <= -4.4e-217) {
		tmp = -1.0;
	} else if (y <= 3e-240) {
		tmp = x * 0.5;
	} else if (y <= 3e+64) {
		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 <= (-2.7d-6)) then
        tmp = 1.0d0
    else if (y <= (-4.4d-217)) then
        tmp = -1.0d0
    else if (y <= 3d-240) then
        tmp = x * 0.5d0
    else if (y <= 3d+64) 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 <= -2.7e-6) {
		tmp = 1.0;
	} else if (y <= -4.4e-217) {
		tmp = -1.0;
	} else if (y <= 3e-240) {
		tmp = x * 0.5;
	} else if (y <= 3e+64) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.7e-6:
		tmp = 1.0
	elif y <= -4.4e-217:
		tmp = -1.0
	elif y <= 3e-240:
		tmp = x * 0.5
	elif y <= 3e+64:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.7e-6)
		tmp = 1.0;
	elseif (y <= -4.4e-217)
		tmp = -1.0;
	elseif (y <= 3e-240)
		tmp = Float64(x * 0.5);
	elseif (y <= 3e+64)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.7e-6)
		tmp = 1.0;
	elseif (y <= -4.4e-217)
		tmp = -1.0;
	elseif (y <= 3e-240)
		tmp = x * 0.5;
	elseif (y <= 3e+64)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.7e-6], 1.0, If[LessEqual[y, -4.4e-217], -1.0, If[LessEqual[y, 3e-240], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 3e+64], -1.0, 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.69999999999999998e-6 or 3.0000000000000002e64 < y

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 81.4%

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

   if -2.69999999999999998e-6 < y < -4.39999999999999964e-217 or 2.99999999999999991e-240 < y < 3.0000000000000002e64

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 56.7%

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

   if -4.39999999999999964e-217 < y < 2.99999999999999991e-240

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 90.7%

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

      1. associate-*r/ 90.7%

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

      2. mul-1-neg 90.7%

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

      3. sub-neg 90.7%

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

      4. metadata-eval 90.7%

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

   6. Simplified 90.7%

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

   7. Taylor expanded in x around 0 63.3%

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

      1. *-commutative 63.3%

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

   9. Simplified 63.3%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-217}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-240}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+64}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 72.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+134}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+60}:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9.5e+134) -1.0 (if (<= x 5.2e+60) (/ y (- y 2.0)) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9.5e+134) {
		tmp = -1.0;
	} else if (x <= 5.2e+60) {
		tmp = y / (y - 2.0);
	} 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 <= (-9.5d+134)) then
        tmp = -1.0d0
    else if (x <= 5.2d+60) then
        tmp = y / (y - 2.0d0)
    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+134) {
		tmp = -1.0;
	} else if (x <= 5.2e+60) {
		tmp = y / (y - 2.0);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9.5e+134:
		tmp = -1.0
	elif x <= 5.2e+60:
		tmp = y / (y - 2.0)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9.5e+134)
		tmp = -1.0;
	elseif (x <= 5.2e+60)
		tmp = Float64(y / Float64(y - 2.0));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -9.5e+134)
		tmp = -1.0;
	elseif (x <= 5.2e+60)
		tmp = y / (y - 2.0);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9.5e+134], -1.0, If[LessEqual[x, 5.2e+60], N[(y / N[(y - 2.0), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5000000000000004e134 or 5.20000000000000016e60 < x

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 86.0%

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

   if -9.5000000000000004e134 < x < 5.20000000000000016e60

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 72.0%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+134}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+60}:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 6: 60.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+134}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+58}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9.5e+134) -1.0 (if (<= x 2.6e+58) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9.5e+134) {
		tmp = -1.0;
	} else if (x <= 2.6e+58) {
		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 <= (-9.5d+134)) then
        tmp = -1.0d0
    else if (x <= 2.6d+58) 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 <= -9.5e+134) {
		tmp = -1.0;
	} else if (x <= 2.6e+58) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9.5e+134:
		tmp = -1.0
	elif x <= 2.6e+58:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9.5e+134)
		tmp = -1.0;
	elseif (x <= 2.6e+58)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -9.5e+134)
		tmp = -1.0;
	elseif (x <= 2.6e+58)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9.5e+134], -1.0, If[LessEqual[x, 2.6e+58], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5000000000000004e134 or 2.59999999999999988e58 < x

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 86.0%

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

   if -9.5000000000000004e134 < x < 2.59999999999999988e58

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 56.1%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+134}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+58}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 7: 38.4% 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 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around inf 35.1%

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

5. Final simplification 35.1%

   \[\leadsto -1 \]

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 2023326 
(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))))