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

Percentage Accurate: 100.0% → 100.0%

Time: 8.9s

Alternatives: 12

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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 84.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{2 - \left(x + y\right)}\\ \mathbf{if}\;t\_0 \leq -0.5:\\ \;\;\;\;-1\\ \mathbf{elif}\;t\_0 \leq -1 \cdot 10^{-62}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(y, -0.25, -0.5\right)\\ \mathbf{elif}\;t\_0 \leq 0.01:\\ \;\;\;\;x \cdot \mathsf{fma}\left(x, 0.25, 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- x y) (- 2.0 (+ x y)))))
   (if (<= t_0 -0.5)
     -1.0
     (if (<= t_0 -1e-62)
       (* y (fma y -0.25 -0.5))
       (if (<= t_0 0.01) (* x (fma x 0.25 0.5)) 1.0)))))

C

double code(double x, double y) {
	double t_0 = (x - y) / (2.0 - (x + y));
	double tmp;
	if (t_0 <= -0.5) {
		tmp = -1.0;
	} else if (t_0 <= -1e-62) {
		tmp = y * fma(y, -0.25, -0.5);
	} else if (t_0 <= 0.01) {
		tmp = x * fma(x, 0.25, 0.5);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
	tmp = 0.0
	if (t_0 <= -0.5)
		tmp = -1.0;
	elseif (t_0 <= -1e-62)
		tmp = Float64(y * fma(y, -0.25, -0.5));
	elseif (t_0 <= 0.01)
		tmp = Float64(x * fma(x, 0.25, 0.5));
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.5], -1.0, If[LessEqual[t$95$0, -1e-62], N[(y * N[(y * -0.25 + -0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.01], N[(x * N[(x * 0.25 + 0.5), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < -0.5

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1} \]
   4. Step-by-step derivation

   5. Simplified 96.9%

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

   if -0.5 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < -1e-62

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. mul-1-neg N/A

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

      11. associate-*r* N/A

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

      12. metadata-eval N/A

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

      13. *-lft-identity N/A

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

      14. +-lowering-+.f64 N/A

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

      15. metadata-eval 71.1

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

   5. Simplified 71.1%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{2}\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

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

      2. sub-neg N/A

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

      3. *-commutative N/A

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

      4. metadata-eval N/A

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

      5. accelerator-lowering-fma.f64 70.8

         \[\leadsto y \cdot \color{blue}{\mathsf{fma}\left(y, -0.25, -0.5\right)} \]

   8. Simplified 70.8%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(y, -0.25, -0.5\right)} \]

   if -1e-62 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < 0.0100000000000000002

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 54.5

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

   5. Simplified 54.5%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x \cdot \left(\frac{1}{2} + \frac{1}{4} \cdot x\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 53.3

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(x, 0.25, 0.5\right)} \]

   8. Simplified 53.3%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(x, 0.25, 0.5\right)} \]

   if 0.0100000000000000002 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y)))

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 96.5%

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

Alternative 3: 84.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{2 - \left(x + y\right)}\\ \mathbf{if}\;t\_0 \leq -0.5:\\ \;\;\;\;-1\\ \mathbf{elif}\;t\_0 \leq -1 \cdot 10^{-62}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;t\_0 \leq 0.01:\\ \;\;\;\;x \cdot \mathsf{fma}\left(x, 0.25, 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- x y) (- 2.0 (+ x y)))))
   (if (<= t_0 -0.5)
     -1.0
     (if (<= t_0 -1e-62)
       (* y -0.5)
       (if (<= t_0 0.01) (* x (fma x 0.25 0.5)) 1.0)))))

C

double code(double x, double y) {
	double t_0 = (x - y) / (2.0 - (x + y));
	double tmp;
	if (t_0 <= -0.5) {
		tmp = -1.0;
	} else if (t_0 <= -1e-62) {
		tmp = y * -0.5;
	} else if (t_0 <= 0.01) {
		tmp = x * fma(x, 0.25, 0.5);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
	tmp = 0.0
	if (t_0 <= -0.5)
		tmp = -1.0;
	elseif (t_0 <= -1e-62)
		tmp = Float64(y * -0.5);
	elseif (t_0 <= 0.01)
		tmp = Float64(x * fma(x, 0.25, 0.5));
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.5], -1.0, If[LessEqual[t$95$0, -1e-62], N[(y * -0.5), $MachinePrecision], If[LessEqual[t$95$0, 0.01], N[(x * N[(x * 0.25 + 0.5), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < -0.5

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1} \]
   4. Step-by-step derivation

   5. Simplified 96.9%

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

   if -0.5 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < -1e-62

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. mul-1-neg N/A

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

      11. associate-*r* N/A

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

      12. metadata-eval N/A

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

      13. *-lft-identity N/A

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

      14. +-lowering-+.f64 N/A

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

      15. metadata-eval 71.1

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

   5. Simplified 71.1%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 68.4

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

   8. Simplified 68.4%

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

   if -1e-62 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < 0.0100000000000000002

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 54.5

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

   5. Simplified 54.5%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x \cdot \left(\frac{1}{2} + \frac{1}{4} \cdot x\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 53.3

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(x, 0.25, 0.5\right)} \]

   8. Simplified 53.3%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(x, 0.25, 0.5\right)} \]

   if 0.0100000000000000002 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y)))

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 96.5%

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

Alternative 4: 84.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{2 - \left(x + y\right)}\\ \mathbf{if}\;t\_0 \leq -0.5:\\ \;\;\;\;-1\\ \mathbf{elif}\;t\_0 \leq -1 \cdot 10^{-62}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;t\_0 \leq 0.01:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- x y) (- 2.0 (+ x y)))))
   (if (<= t_0 -0.5)
     -1.0
     (if (<= t_0 -1e-62) (* y -0.5) (if (<= t_0 0.01) (* x 0.5) 1.0)))))

C

double code(double x, double y) {
	double t_0 = (x - y) / (2.0 - (x + y));
	double tmp;
	if (t_0 <= -0.5) {
		tmp = -1.0;
	} else if (t_0 <= -1e-62) {
		tmp = y * -0.5;
	} else if (t_0 <= 0.01) {
		tmp = x * 0.5;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x - y) / (2.0d0 - (x + y))
    if (t_0 <= (-0.5d0)) then
        tmp = -1.0d0
    else if (t_0 <= (-1d-62)) then
        tmp = y * (-0.5d0)
    else if (t_0 <= 0.01d0) then
        tmp = x * 0.5d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x - y) / (2.0 - (x + y));
	double tmp;
	if (t_0 <= -0.5) {
		tmp = -1.0;
	} else if (t_0 <= -1e-62) {
		tmp = y * -0.5;
	} else if (t_0 <= 0.01) {
		tmp = x * 0.5;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x - y) / (2.0 - (x + y))
	tmp = 0
	if t_0 <= -0.5:
		tmp = -1.0
	elif t_0 <= -1e-62:
		tmp = y * -0.5
	elif t_0 <= 0.01:
		tmp = x * 0.5
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
	tmp = 0.0
	if (t_0 <= -0.5)
		tmp = -1.0;
	elseif (t_0 <= -1e-62)
		tmp = Float64(y * -0.5);
	elseif (t_0 <= 0.01)
		tmp = Float64(x * 0.5);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x - y) / (2.0 - (x + y));
	tmp = 0.0;
	if (t_0 <= -0.5)
		tmp = -1.0;
	elseif (t_0 <= -1e-62)
		tmp = y * -0.5;
	elseif (t_0 <= 0.01)
		tmp = x * 0.5;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.5], -1.0, If[LessEqual[t$95$0, -1e-62], N[(y * -0.5), $MachinePrecision], If[LessEqual[t$95$0, 0.01], N[(x * 0.5), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < -0.5

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1} \]
   4. Step-by-step derivation

   5. Simplified 96.9%

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

   if -0.5 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < -1e-62

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. mul-1-neg N/A

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

      11. associate-*r* N/A

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

      12. metadata-eval N/A

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

      13. *-lft-identity N/A

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

      14. +-lowering-+.f64 N/A

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

      15. metadata-eval 71.1

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

   5. Simplified 71.1%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 68.4

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

   8. Simplified 68.4%

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

   if -1e-62 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < 0.0100000000000000002

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 54.5

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

   5. Simplified 54.5%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 52.5

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

   8. Simplified 52.5%

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

   if 0.0100000000000000002 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y)))

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 96.5%

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

Alternative 5: 97.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 - \left(x + y\right)\\ t_1 := \frac{x - y}{t\_0}\\ \mathbf{if}\;t\_1 \leq -0.5:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{elif}\;t\_1 \leq 0.01:\\ \;\;\;\;\frac{x - y}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 2.0 (+ x y))) (t_1 (/ (- x y) t_0)))
   (if (<= t_1 -0.5)
     (/ x t_0)
     (if (<= t_1 0.01) (/ (- x y) 2.0) (/ y (+ y -2.0))))))

C

double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	double t_1 = (x - y) / t_0;
	double tmp;
	if (t_1 <= -0.5) {
		tmp = x / t_0;
	} else if (t_1 <= 0.01) {
		tmp = (x - y) / 2.0;
	} 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 2.0d0 - (x + y)
    t_1 = (x - y) / t_0
    if (t_1 <= (-0.5d0)) then
        tmp = x / t_0
    else if (t_1 <= 0.01d0) then
        tmp = (x - y) / 2.0d0
    else
        tmp = y / (y + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	double t_1 = (x - y) / t_0;
	double tmp;
	if (t_1 <= -0.5) {
		tmp = x / t_0;
	} else if (t_1 <= 0.01) {
		tmp = (x - y) / 2.0;
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 2.0 - (x + y)
	t_1 = (x - y) / t_0
	tmp = 0
	if t_1 <= -0.5:
		tmp = x / t_0
	elif t_1 <= 0.01:
		tmp = (x - y) / 2.0
	else:
		tmp = y / (y + -2.0)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(2.0 - Float64(x + y))
	t_1 = Float64(Float64(x - y) / t_0)
	tmp = 0.0
	if (t_1 <= -0.5)
		tmp = Float64(x / t_0);
	elseif (t_1 <= 0.01)
		tmp = Float64(Float64(x - y) / 2.0);
	else
		tmp = Float64(y / Float64(y + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 2.0 - (x + y);
	t_1 = (x - y) / t_0;
	tmp = 0.0;
	if (t_1 <= -0.5)
		tmp = x / t_0;
	elseif (t_1 <= 0.01)
		tmp = (x - y) / 2.0;
	else
		tmp = y / (y + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[LessEqual[t$95$1, -0.5], N[(x / t$95$0), $MachinePrecision], If[LessEqual[t$95$1, 0.01], N[(N[(x - y), $MachinePrecision] / 2.0), $MachinePrecision], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < -0.5

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 98.5%

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

   if -0.5 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < 0.0100000000000000002

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. --lowering--.f64 98.4

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

   5. Simplified 98.4%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 97.5%

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

   if 0.0100000000000000002 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y)))

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. mul-1-neg N/A

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

      11. associate-*r* N/A

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

      12. metadata-eval N/A

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

      13. *-lft-identity N/A

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

      14. +-lowering-+.f64 N/A

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

      15. metadata-eval 98.4

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

   5. Simplified 98.4%

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

Alternative 6: 97.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{2 - \left(x + y\right)}\\ \mathbf{if}\;t\_0 \leq -0.5:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;t\_0 \leq 0.01:\\ \;\;\;\;\frac{x - y}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- x y) (- 2.0 (+ x y)))))
   (if (<= t_0 -0.5)
     (/ x (- 2.0 x))
     (if (<= t_0 0.01) (/ (- x y) 2.0) (/ y (+ y -2.0))))))

C

double code(double x, double y) {
	double t_0 = (x - y) / (2.0 - (x + y));
	double tmp;
	if (t_0 <= -0.5) {
		tmp = x / (2.0 - x);
	} else if (t_0 <= 0.01) {
		tmp = (x - y) / 2.0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = (x - y) / (2.0d0 - (x + y))
    if (t_0 <= (-0.5d0)) then
        tmp = x / (2.0d0 - x)
    else if (t_0 <= 0.01d0) then
        tmp = (x - y) / 2.0d0
    else
        tmp = y / (y + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x - y) / (2.0 - (x + y));
	double tmp;
	if (t_0 <= -0.5) {
		tmp = x / (2.0 - x);
	} else if (t_0 <= 0.01) {
		tmp = (x - y) / 2.0;
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x - y) / (2.0 - (x + y))
	tmp = 0
	if t_0 <= -0.5:
		tmp = x / (2.0 - x)
	elif t_0 <= 0.01:
		tmp = (x - y) / 2.0
	else:
		tmp = y / (y + -2.0)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
	tmp = 0.0
	if (t_0 <= -0.5)
		tmp = Float64(x / Float64(2.0 - x));
	elseif (t_0 <= 0.01)
		tmp = Float64(Float64(x - y) / 2.0);
	else
		tmp = Float64(y / Float64(y + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x - y) / (2.0 - (x + y));
	tmp = 0.0;
	if (t_0 <= -0.5)
		tmp = x / (2.0 - x);
	elseif (t_0 <= 0.01)
		tmp = (x - y) / 2.0;
	else
		tmp = y / (y + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.5], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.01], N[(N[(x - y), $MachinePrecision] / 2.0), $MachinePrecision], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < -0.5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 98.5

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

   5. Simplified 98.5%

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

   if -0.5 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < 0.0100000000000000002

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. --lowering--.f64 98.4

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

   5. Simplified 98.4%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 97.5%

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

   if 0.0100000000000000002 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y)))

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. mul-1-neg N/A

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

      11. associate-*r* N/A

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

      12. metadata-eval N/A

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

      13. *-lft-identity N/A

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

      14. +-lowering-+.f64 N/A

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

      15. metadata-eval 98.4

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

   5. Simplified 98.4%

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

Alternative 7: 84.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{2 - \left(x + y\right)}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-8}:\\ \;\;\;\;-1\\ \mathbf{elif}\;t\_0 \leq 0.01:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- x y) (- 2.0 (+ x y)))))
   (if (<= t_0 -5e-8) -1.0 (if (<= t_0 0.01) (* x 0.5) 1.0))))

C

double code(double x, double y) {
	double t_0 = (x - y) / (2.0 - (x + y));
	double tmp;
	if (t_0 <= -5e-8) {
		tmp = -1.0;
	} else if (t_0 <= 0.01) {
		tmp = x * 0.5;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x - y) / (2.0d0 - (x + y))
    if (t_0 <= (-5d-8)) then
        tmp = -1.0d0
    else if (t_0 <= 0.01d0) then
        tmp = x * 0.5d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x - y) / (2.0 - (x + y));
	double tmp;
	if (t_0 <= -5e-8) {
		tmp = -1.0;
	} else if (t_0 <= 0.01) {
		tmp = x * 0.5;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x - y) / (2.0 - (x + y))
	tmp = 0
	if t_0 <= -5e-8:
		tmp = -1.0
	elif t_0 <= 0.01:
		tmp = x * 0.5
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
	tmp = 0.0
	if (t_0 <= -5e-8)
		tmp = -1.0;
	elseif (t_0 <= 0.01)
		tmp = Float64(x * 0.5);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x - y) / (2.0 - (x + y));
	tmp = 0.0;
	if (t_0 <= -5e-8)
		tmp = -1.0;
	elseif (t_0 <= 0.01)
		tmp = x * 0.5;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e-8], -1.0, If[LessEqual[t$95$0, 0.01], N[(x * 0.5), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < -4.9999999999999998e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1} \]
   4. Step-by-step derivation

   5. Simplified 96.0%

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

   if -4.9999999999999998e-8 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < 0.0100000000000000002

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 50.3

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

   5. Simplified 50.3%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 48.7

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

   8. Simplified 48.7%

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

   if 0.0100000000000000002 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y)))

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 96.5%

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

Alternative 8: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 - \left(x + y\right)\\ \mathbf{if}\;\frac{x - y}{t\_0} \leq -0.5:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 2.0 (+ x y))))
   (if (<= (/ (- x y) t_0) -0.5) (/ x t_0) (/ (- x y) (- 2.0 y)))))

C

double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	double tmp;
	if (((x - y) / t_0) <= -0.5) {
		tmp = x / t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = 2.0d0 - (x + y)
    if (((x - y) / t_0) <= (-0.5d0)) then
        tmp = x / t_0
    else
        tmp = (x - y) / (2.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	double tmp;
	if (((x - y) / t_0) <= -0.5) {
		tmp = x / t_0;
	} else {
		tmp = (x - y) / (2.0 - y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 2.0 - (x + y)
	tmp = 0
	if ((x - y) / t_0) <= -0.5:
		tmp = x / t_0
	else:
		tmp = (x - y) / (2.0 - y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(2.0 - Float64(x + y))
	tmp = 0.0
	if (Float64(Float64(x - y) / t_0) <= -0.5)
		tmp = Float64(x / t_0);
	else
		tmp = Float64(Float64(x - y) / Float64(2.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 2.0 - (x + y);
	tmp = 0.0;
	if (((x - y) / t_0) <= -0.5)
		tmp = x / t_0;
	else
		tmp = (x - y) / (2.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(x - y), $MachinePrecision] / t$95$0), $MachinePrecision], -0.5], N[(x / t$95$0), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / N[(2.0 - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < -0.5

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 98.5%

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

   if -0.5 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y)))

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. --lowering--.f64 98.4

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

   5. Simplified 98.4%

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

Alternative 9: 85.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x - y}{2 - \left(x + y\right)} \leq -1 \cdot 10^{-189}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (/ (- x y) (- 2.0 (+ x y))) -1e-189)
   (/ x (- 2.0 x))
   (/ y (+ y -2.0))))

C

double code(double x, double y) {
	double tmp;
	if (((x - y) / (2.0 - (x + y))) <= -1e-189) {
		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 (((x - y) / (2.0d0 - (x + y))) <= (-1d-189)) 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 (((x - y) / (2.0 - (x + y))) <= -1e-189) {
		tmp = x / (2.0 - x);
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((x - y) / (2.0 - (x + y))) <= -1e-189:
		tmp = x / (2.0 - x)
	else:
		tmp = y / (y + -2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(x - y) / Float64(2.0 - Float64(x + y))) <= -1e-189)
		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 (((x - y) / (2.0 - (x + y))) <= -1e-189)
		tmp = x / (2.0 - x);
	else
		tmp = y / (y + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1e-189], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < -1.00000000000000007e-189

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 86.0

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

   5. Simplified 86.0%

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

   if -1.00000000000000007e-189 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y)))

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. mul-1-neg N/A

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

      11. associate-*r* N/A

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

      12. metadata-eval N/A

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

      13. *-lft-identity N/A

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

      14. +-lowering-+.f64 N/A

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

      15. metadata-eval 82.5

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

   5. Simplified 82.5%

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

Alternative 10: 85.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x - y}{2 - \left(x + y\right)} \leq 0.01:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (/ (- x y) (- 2.0 (+ x y))) 0.01) (/ x (- 2.0 x)) 1.0))

C

double code(double x, double y) {
	double tmp;
	if (((x - y) / (2.0 - (x + y))) <= 0.01) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (((x - y) / (2.0d0 - (x + y))) <= 0.01d0) then
        tmp = x / (2.0d0 - x)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((x - y) / (2.0 - (x + y))) <= 0.01) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((x - y) / (2.0 - (x + y))) <= 0.01:
		tmp = x / (2.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(x - y) / Float64(2.0 - Float64(x + y))) <= 0.01)
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((x - y) / (2.0 - (x + y))) <= 0.01)
		tmp = x / (2.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.01], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < 0.0100000000000000002

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 76.0

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

   5. Simplified 76.0%

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

   if 0.0100000000000000002 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y)))

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 96.5%

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

Alternative 11: 73.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x - y}{2 - \left(x + y\right)} \leq -2 \cdot 10^{-310}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (/ (- x y) (- 2.0 (+ x y))) -2e-310) -1.0 1.0))

C

double code(double x, double y) {
	double tmp;
	if (((x - y) / (2.0 - (x + y))) <= -2e-310) {
		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 - y) / (2.0d0 - (x + y))) <= (-2d-310)) 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 - y) / (2.0 - (x + y))) <= -2e-310) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((x - y) / (2.0 - (x + y))) <= -2e-310:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(x - y) / Float64(2.0 - Float64(x + y))) <= -2e-310)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((x - y) / (2.0 - (x + y))) <= -2e-310)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -2e-310], -1.0, 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < -1.999999999999994e-310

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1} \]
   4. Step-by-step derivation

   5. Simplified 69.4%

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

   if -1.999999999999994e-310 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y)))

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 69.5%

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

Alternative 12: 37.1% accurate, 21.0× 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. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{-1} \]
4. Step-by-step derivation

5. Simplified 35.8%

   \[\leadsto \color{blue}{-1} \]
6. Add Preprocessing

Developer Target 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]]

Reproduce

herbie shell --seed 2024199 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ x (- 2 (+ x y))) (/ y (- 2 (+ x y)))))

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