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

Percentage Accurate: 100.0% → 100.0%

Time: 5.5s

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, 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]]

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. Step-by-step derivation

   1. div-sub 100.0%

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

   2. associate--l- 100.0%

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

   3. associate--l- 100.0%

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

5. Applied egg-rr 100.0%

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

6. Final simplification 100.0%

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

Alternative 2: 60.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+51}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-233}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-229}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 350000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+81}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+123}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -9.2e+51)
   1.0
   (if (<= y -5.4e-233)
     -1.0
     (if (<= y 1.3e-229)
       (* x 0.5)
       (if (<= y 350000000.0)
         -1.0
         (if (<= y 1.8e+81)
           (+ 1.0 (/ 2.0 y))
           (if (<= y 6.2e+123) -1.0 1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -9.2e+51) {
		tmp = 1.0;
	} else if (y <= -5.4e-233) {
		tmp = -1.0;
	} else if (y <= 1.3e-229) {
		tmp = x * 0.5;
	} else if (y <= 350000000.0) {
		tmp = -1.0;
	} else if (y <= 1.8e+81) {
		tmp = 1.0 + (2.0 / y);
	} else if (y <= 6.2e+123) {
		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 <= (-9.2d+51)) then
        tmp = 1.0d0
    else if (y <= (-5.4d-233)) then
        tmp = -1.0d0
    else if (y <= 1.3d-229) then
        tmp = x * 0.5d0
    else if (y <= 350000000.0d0) then
        tmp = -1.0d0
    else if (y <= 1.8d+81) then
        tmp = 1.0d0 + (2.0d0 / y)
    else if (y <= 6.2d+123) 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 <= -9.2e+51) {
		tmp = 1.0;
	} else if (y <= -5.4e-233) {
		tmp = -1.0;
	} else if (y <= 1.3e-229) {
		tmp = x * 0.5;
	} else if (y <= 350000000.0) {
		tmp = -1.0;
	} else if (y <= 1.8e+81) {
		tmp = 1.0 + (2.0 / y);
	} else if (y <= 6.2e+123) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -9.2e+51:
		tmp = 1.0
	elif y <= -5.4e-233:
		tmp = -1.0
	elif y <= 1.3e-229:
		tmp = x * 0.5
	elif y <= 350000000.0:
		tmp = -1.0
	elif y <= 1.8e+81:
		tmp = 1.0 + (2.0 / y)
	elif y <= 6.2e+123:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -9.2e+51)
		tmp = 1.0;
	elseif (y <= -5.4e-233)
		tmp = -1.0;
	elseif (y <= 1.3e-229)
		tmp = Float64(x * 0.5);
	elseif (y <= 350000000.0)
		tmp = -1.0;
	elseif (y <= 1.8e+81)
		tmp = Float64(1.0 + Float64(2.0 / y));
	elseif (y <= 6.2e+123)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -9.2e+51)
		tmp = 1.0;
	elseif (y <= -5.4e-233)
		tmp = -1.0;
	elseif (y <= 1.3e-229)
		tmp = x * 0.5;
	elseif (y <= 350000000.0)
		tmp = -1.0;
	elseif (y <= 1.8e+81)
		tmp = 1.0 + (2.0 / y);
	elseif (y <= 6.2e+123)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -9.2e+51], 1.0, If[LessEqual[y, -5.4e-233], -1.0, If[LessEqual[y, 1.3e-229], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 350000000.0], -1.0, If[LessEqual[y, 1.8e+81], N[(1.0 + N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+123], -1.0, 1.0]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.2000000000000002e51 or 6.20000000000000013e123 < 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 88.6%

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

   if -9.2000000000000002e51 < y < -5.3999999999999999e-233 or 1.3000000000000001e-229 < y < 3.5e8 or 1.80000000000000003e81 < y < 6.20000000000000013e123

   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 55.2%

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

   if -5.3999999999999999e-233 < y < 1.3000000000000001e-229

   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 91.0%

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

   5. Taylor expanded in x around 0 61.5%

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

      1. *-commutative 61.5%

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

   7. Simplified 61.5%

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

   if 3.5e8 < y < 1.80000000000000003e81

   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 68.6%

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

      1. associate--l+ 68.6%

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

      2. associate-*r/ 68.6%

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

      3. associate-*r/ 68.6%

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

      4. div-sub 68.6%

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

      5. cancel-sign-sub-inv 68.6%

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

      6. metadata-eval 68.6%

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

      7. *-lft-identity 68.6%

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

      8. +-commutative 68.6%

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

      9. mul-1-neg 68.6%

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

      10. unsub-neg 68.6%

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

   6. Simplified 68.6%

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

   7. Taylor expanded in x around 0 66.6%

      \[\leadsto 1 + \frac{\color{blue}{2}}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+51}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-233}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-229}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 350000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+81}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+123}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-y}{2 - y}\\ t_1 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -2.75 \cdot 10^{-33}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+81}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x \cdot -2}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- y) (- 2.0 y))) (t_1 (/ x (- 2.0 x))))
   (if (<= y -2.75e-33)
     t_0
     (if (<= y 1.1e-73)
       t_1
       (if (<= y 1.8e+81)
         t_0
         (if (<= y 6.2e+123) t_1 (+ 1.0 (/ (* x -2.0) y))))))))

C

double code(double x, double y) {
	double t_0 = -y / (2.0 - y);
	double t_1 = x / (2.0 - x);
	double tmp;
	if (y <= -2.75e-33) {
		tmp = t_0;
	} else if (y <= 1.1e-73) {
		tmp = t_1;
	} else if (y <= 1.8e+81) {
		tmp = t_0;
	} else if (y <= 6.2e+123) {
		tmp = t_1;
	} else {
		tmp = 1.0 + ((x * -2.0) / y);
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = -y / (2.0d0 - y)
    t_1 = x / (2.0d0 - x)
    if (y <= (-2.75d-33)) then
        tmp = t_0
    else if (y <= 1.1d-73) then
        tmp = t_1
    else if (y <= 1.8d+81) then
        tmp = t_0
    else if (y <= 6.2d+123) then
        tmp = t_1
    else
        tmp = 1.0d0 + ((x * (-2.0d0)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = -y / (2.0 - y);
	double t_1 = x / (2.0 - x);
	double tmp;
	if (y <= -2.75e-33) {
		tmp = t_0;
	} else if (y <= 1.1e-73) {
		tmp = t_1;
	} else if (y <= 1.8e+81) {
		tmp = t_0;
	} else if (y <= 6.2e+123) {
		tmp = t_1;
	} else {
		tmp = 1.0 + ((x * -2.0) / y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = -y / (2.0 - y)
	t_1 = x / (2.0 - x)
	tmp = 0
	if y <= -2.75e-33:
		tmp = t_0
	elif y <= 1.1e-73:
		tmp = t_1
	elif y <= 1.8e+81:
		tmp = t_0
	elif y <= 6.2e+123:
		tmp = t_1
	else:
		tmp = 1.0 + ((x * -2.0) / y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(-y) / Float64(2.0 - y))
	t_1 = Float64(x / Float64(2.0 - x))
	tmp = 0.0
	if (y <= -2.75e-33)
		tmp = t_0;
	elseif (y <= 1.1e-73)
		tmp = t_1;
	elseif (y <= 1.8e+81)
		tmp = t_0;
	elseif (y <= 6.2e+123)
		tmp = t_1;
	else
		tmp = Float64(1.0 + Float64(Float64(x * -2.0) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = -y / (2.0 - y);
	t_1 = x / (2.0 - x);
	tmp = 0.0;
	if (y <= -2.75e-33)
		tmp = t_0;
	elseif (y <= 1.1e-73)
		tmp = t_1;
	elseif (y <= 1.8e+81)
		tmp = t_0;
	elseif (y <= 6.2e+123)
		tmp = t_1;
	else
		tmp = 1.0 + ((x * -2.0) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[((-y) / N[(2.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.75e-33], t$95$0, If[LessEqual[y, 1.1e-73], t$95$1, If[LessEqual[y, 1.8e+81], t$95$0, If[LessEqual[y, 6.2e+123], t$95$1, N[(1.0 + N[(N[(x * -2.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.75e-33 or 1.1e-73 < y < 1.80000000000000003e81

   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 77.8%

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

      1. mul-1-neg 77.8%

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

      2. distribute-neg-frac 77.8%

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

   6. Simplified 77.8%

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

   if -2.75e-33 < y < 1.1e-73 or 1.80000000000000003e81 < y < 6.20000000000000013e123

   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 84.7%

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

   if 6.20000000000000013e123 < y

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 86.5%

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

      1. associate--l+ 86.5%

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

      2. associate-*r/ 86.5%

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

      3. associate-*r/ 86.5%

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

      4. div-sub 86.5%

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

      5. cancel-sign-sub-inv 86.5%

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

      6. metadata-eval 86.5%

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

      7. *-lft-identity 86.5%

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

      8. +-commutative 86.5%

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

      9. mul-1-neg 86.5%

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

      10. unsub-neg 86.5%

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

   6. Simplified 86.5%

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

   7. Taylor expanded in x around inf 86.5%

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

      1. *-commutative 86.5%

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

   9. Simplified 86.5%

      \[\leadsto 1 + \frac{\color{blue}{x \cdot -2}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-33}:\\ \;\;\;\;\frac{-y}{2 - y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-73}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+81}:\\ \;\;\;\;\frac{-y}{2 - y}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x \cdot -2}{y}\\ \end{array} \]

Alternative 4: 60.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+51}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-230}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-225}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 225000000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+81}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+123}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -9.2e+51)
   1.0
   (if (<= y -3.1e-230)
     -1.0
     (if (<= y 5.1e-225)
       (* x 0.5)
       (if (<= y 225000000000.0)
         -1.0
         (if (<= y 1.32e+81) 1.0 (if (<= y 6.2e+123) -1.0 1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -9.2e+51) {
		tmp = 1.0;
	} else if (y <= -3.1e-230) {
		tmp = -1.0;
	} else if (y <= 5.1e-225) {
		tmp = x * 0.5;
	} else if (y <= 225000000000.0) {
		tmp = -1.0;
	} else if (y <= 1.32e+81) {
		tmp = 1.0;
	} else if (y <= 6.2e+123) {
		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 <= (-9.2d+51)) then
        tmp = 1.0d0
    else if (y <= (-3.1d-230)) then
        tmp = -1.0d0
    else if (y <= 5.1d-225) then
        tmp = x * 0.5d0
    else if (y <= 225000000000.0d0) then
        tmp = -1.0d0
    else if (y <= 1.32d+81) then
        tmp = 1.0d0
    else if (y <= 6.2d+123) 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 <= -9.2e+51) {
		tmp = 1.0;
	} else if (y <= -3.1e-230) {
		tmp = -1.0;
	} else if (y <= 5.1e-225) {
		tmp = x * 0.5;
	} else if (y <= 225000000000.0) {
		tmp = -1.0;
	} else if (y <= 1.32e+81) {
		tmp = 1.0;
	} else if (y <= 6.2e+123) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -9.2e+51:
		tmp = 1.0
	elif y <= -3.1e-230:
		tmp = -1.0
	elif y <= 5.1e-225:
		tmp = x * 0.5
	elif y <= 225000000000.0:
		tmp = -1.0
	elif y <= 1.32e+81:
		tmp = 1.0
	elif y <= 6.2e+123:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -9.2e+51)
		tmp = 1.0;
	elseif (y <= -3.1e-230)
		tmp = -1.0;
	elseif (y <= 5.1e-225)
		tmp = Float64(x * 0.5);
	elseif (y <= 225000000000.0)
		tmp = -1.0;
	elseif (y <= 1.32e+81)
		tmp = 1.0;
	elseif (y <= 6.2e+123)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -9.2e+51)
		tmp = 1.0;
	elseif (y <= -3.1e-230)
		tmp = -1.0;
	elseif (y <= 5.1e-225)
		tmp = x * 0.5;
	elseif (y <= 225000000000.0)
		tmp = -1.0;
	elseif (y <= 1.32e+81)
		tmp = 1.0;
	elseif (y <= 6.2e+123)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -9.2e+51], 1.0, If[LessEqual[y, -3.1e-230], -1.0, If[LessEqual[y, 5.1e-225], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 225000000000.0], -1.0, If[LessEqual[y, 1.32e+81], 1.0, If[LessEqual[y, 6.2e+123], -1.0, 1.0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.2000000000000002e51 or 2.25e11 < y < 1.31999999999999996e81 or 6.20000000000000013e123 < 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 85.5%

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

   if -9.2000000000000002e51 < y < -3.1e-230 or 5.0999999999999999e-225 < y < 2.25e11 or 1.31999999999999996e81 < y < 6.20000000000000013e123

   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 55.2%

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

   if -3.1e-230 < y < 5.0999999999999999e-225

   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 91.0%

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

   5. Taylor expanded in x around 0 61.5%

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

      1. *-commutative 61.5%

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

   7. Simplified 61.5%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+51}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-230}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-225}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 225000000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+81}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+123}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 72.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+52}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4300000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+81}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+123}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 2.0 x))))
   (if (<= y -1.75e+52)
     1.0
     (if (<= y 4300000000.0)
       t_0
       (if (<= y 1.8e+81) (+ 1.0 (/ 2.0 y)) (if (<= y 6.2e+123) t_0 1.0))))))

C

double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (y <= -1.75e+52) {
		tmp = 1.0;
	} else if (y <= 4300000000.0) {
		tmp = t_0;
	} else if (y <= 1.8e+81) {
		tmp = 1.0 + (2.0 / y);
	} else if (y <= 6.2e+123) {
		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 <= (-1.75d+52)) then
        tmp = 1.0d0
    else if (y <= 4300000000.0d0) then
        tmp = t_0
    else if (y <= 1.8d+81) then
        tmp = 1.0d0 + (2.0d0 / y)
    else if (y <= 6.2d+123) 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 <= -1.75e+52) {
		tmp = 1.0;
	} else if (y <= 4300000000.0) {
		tmp = t_0;
	} else if (y <= 1.8e+81) {
		tmp = 1.0 + (2.0 / y);
	} else if (y <= 6.2e+123) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (2.0 - x)
	tmp = 0
	if y <= -1.75e+52:
		tmp = 1.0
	elif y <= 4300000000.0:
		tmp = t_0
	elif y <= 1.8e+81:
		tmp = 1.0 + (2.0 / y)
	elif y <= 6.2e+123:
		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 <= -1.75e+52)
		tmp = 1.0;
	elseif (y <= 4300000000.0)
		tmp = t_0;
	elseif (y <= 1.8e+81)
		tmp = Float64(1.0 + Float64(2.0 / y));
	elseif (y <= 6.2e+123)
		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 <= -1.75e+52)
		tmp = 1.0;
	elseif (y <= 4300000000.0)
		tmp = t_0;
	elseif (y <= 1.8e+81)
		tmp = 1.0 + (2.0 / y);
	elseif (y <= 6.2e+123)
		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, -1.75e+52], 1.0, If[LessEqual[y, 4300000000.0], t$95$0, If[LessEqual[y, 1.8e+81], N[(1.0 + N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+123], t$95$0, 1.0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.75e52 or 6.20000000000000013e123 < 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 88.6%

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

   if -1.75e52 < y < 4.3e9 or 1.80000000000000003e81 < y < 6.20000000000000013e123

   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 75.0%

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

   if 4.3e9 < y < 1.80000000000000003e81

   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 68.6%

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

      1. associate--l+ 68.6%

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

      2. associate-*r/ 68.6%

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

      3. associate-*r/ 68.6%

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

      4. div-sub 68.6%

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

      5. cancel-sign-sub-inv 68.6%

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

      6. metadata-eval 68.6%

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

      7. *-lft-identity 68.6%

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

      8. +-commutative 68.6%

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

      9. mul-1-neg 68.6%

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

      10. unsub-neg 68.6%

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

   6. Simplified 68.6%

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

   7. Taylor expanded in x around 0 66.6%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+52}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4300000000:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+81}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 72.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-y}{2 - y}\\ t_1 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{-33}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+80}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- y) (- 2.0 y))) (t_1 (/ x (- 2.0 x))))
   (if (<= y -6.5e-33)
     t_0
     (if (<= y 2.5e-74)
       t_1
       (if (<= y 8.8e+80) t_0 (if (<= y 6.2e+123) t_1 1.0))))))

C

double code(double x, double y) {
	double t_0 = -y / (2.0 - y);
	double t_1 = x / (2.0 - x);
	double tmp;
	if (y <= -6.5e-33) {
		tmp = t_0;
	} else if (y <= 2.5e-74) {
		tmp = t_1;
	} else if (y <= 8.8e+80) {
		tmp = t_0;
	} else if (y <= 6.2e+123) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = -y / (2.0d0 - y)
    t_1 = x / (2.0d0 - x)
    if (y <= (-6.5d-33)) then
        tmp = t_0
    else if (y <= 2.5d-74) then
        tmp = t_1
    else if (y <= 8.8d+80) then
        tmp = t_0
    else if (y <= 6.2d+123) then
        tmp = t_1
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = -y / (2.0 - y);
	double t_1 = x / (2.0 - x);
	double tmp;
	if (y <= -6.5e-33) {
		tmp = t_0;
	} else if (y <= 2.5e-74) {
		tmp = t_1;
	} else if (y <= 8.8e+80) {
		tmp = t_0;
	} else if (y <= 6.2e+123) {
		tmp = t_1;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = -y / (2.0 - y)
	t_1 = x / (2.0 - x)
	tmp = 0
	if y <= -6.5e-33:
		tmp = t_0
	elif y <= 2.5e-74:
		tmp = t_1
	elif y <= 8.8e+80:
		tmp = t_0
	elif y <= 6.2e+123:
		tmp = t_1
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(-y) / Float64(2.0 - y))
	t_1 = Float64(x / Float64(2.0 - x))
	tmp = 0.0
	if (y <= -6.5e-33)
		tmp = t_0;
	elseif (y <= 2.5e-74)
		tmp = t_1;
	elseif (y <= 8.8e+80)
		tmp = t_0;
	elseif (y <= 6.2e+123)
		tmp = t_1;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = -y / (2.0 - y);
	t_1 = x / (2.0 - x);
	tmp = 0.0;
	if (y <= -6.5e-33)
		tmp = t_0;
	elseif (y <= 2.5e-74)
		tmp = t_1;
	elseif (y <= 8.8e+80)
		tmp = t_0;
	elseif (y <= 6.2e+123)
		tmp = t_1;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[((-y) / N[(2.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e-33], t$95$0, If[LessEqual[y, 2.5e-74], t$95$1, If[LessEqual[y, 8.8e+80], t$95$0, If[LessEqual[y, 6.2e+123], t$95$1, 1.0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.4999999999999993e-33 or 2.49999999999999999e-74 < y < 8.80000000000000011e80

   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 77.8%

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

      1. mul-1-neg 77.8%

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

      2. distribute-neg-frac 77.8%

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

   6. Simplified 77.8%

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

   if -6.4999999999999993e-33 < y < 2.49999999999999999e-74 or 8.80000000000000011e80 < y < 6.20000000000000013e123

   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 84.7%

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

   if 6.20000000000000013e123 < 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 84.0%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-33}:\\ \;\;\;\;\frac{-y}{2 - y}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+80}:\\ \;\;\;\;\frac{-y}{2 - y}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 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 8: 62.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.004:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+37}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.004) -1.0 (if (<= x 4e+37) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.004) {
		tmp = -1.0;
	} else if (x <= 4e+37) {
		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 <= (-0.004d0)) then
        tmp = -1.0d0
    else if (x <= 4d+37) 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 <= -0.004) {
		tmp = -1.0;
	} else if (x <= 4e+37) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.004:
		tmp = -1.0
	elif x <= 4e+37:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.004)
		tmp = -1.0;
	elseif (x <= 4e+37)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.004)
		tmp = -1.0;
	elseif (x <= 4e+37)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.004], -1.0, If[LessEqual[x, 4e+37], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0040000000000000001 or 3.99999999999999982e37 < x

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 74.0%

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

   if -0.0040000000000000001 < x < 3.99999999999999982e37

   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 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.004:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+37}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 9: 37.6% 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 33.5%

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

5. Final simplification 33.5%

   \[\leadsto -1 \]

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 2023202 
(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))))