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

Percentage Accurate: 100.0% → 100.0%

Time: 6.9s

Alternatives: 8

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: 87.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2 - \left(x + y\right)}\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{+14}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1520000000000:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 2.0 (+ x y)))))
   (if (<= x -8.5e+14)
     t_0
     (if (<= x 1520000000000.0) (/ (- x y) (- 2.0 y)) t_0))))

C

double code(double x, double y) {
	double t_0 = x / (2.0 - (x + y));
	double tmp;
	if (x <= -8.5e+14) {
		tmp = t_0;
	} else if (x <= 1520000000000.0) {
		tmp = (x - y) / (2.0 - y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x / (2.0d0 - (x + y))
    if (x <= (-8.5d+14)) then
        tmp = t_0
    else if (x <= 1520000000000.0d0) then
        tmp = (x - y) / (2.0d0 - y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (2.0 - (x + y));
	double tmp;
	if (x <= -8.5e+14) {
		tmp = t_0;
	} else if (x <= 1520000000000.0) {
		tmp = (x - y) / (2.0 - y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (2.0 - (x + y))
	tmp = 0
	if x <= -8.5e+14:
		tmp = t_0
	elif x <= 1520000000000.0:
		tmp = (x - y) / (2.0 - y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(2.0 - Float64(x + y)))
	tmp = 0.0
	if (x <= -8.5e+14)
		tmp = t_0;
	elseif (x <= 1520000000000.0)
		tmp = Float64(Float64(x - y) / Float64(2.0 - y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (2.0 - (x + y));
	tmp = 0.0;
	if (x <= -8.5e+14)
		tmp = t_0;
	elseif (x <= 1520000000000.0)
		tmp = (x - y) / (2.0 - y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.5e+14], t$95$0, If[LessEqual[x, 1520000000000.0], N[(N[(x - y), $MachinePrecision] / N[(2.0 - y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.5e14 or 1.52e12 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{\_.f64}\left(2, \mathsf{+.f64}\left(x, y\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 79.4%

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

   if -8.5e14 < x < 1.52e12

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \color{blue}{\left(2 - y\right)}\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 98.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(2, \color{blue}{y}\right)\right) \]

   5. Simplified 98.2%

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

Alternative 3: 87.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+42}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+41}:\\ \;\;\;\;\frac{x - y}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.15e+42) 1.0 (if (<= y 3.3e+41) (/ (- x y) (- 2.0 x)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.15e+42) {
		tmp = 1.0;
	} else if (y <= 3.3e+41) {
		tmp = (x - y) / (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 (y <= (-2.15d+42)) then
        tmp = 1.0d0
    else if (y <= 3.3d+41) then
        tmp = (x - y) / (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 (y <= -2.15e+42) {
		tmp = 1.0;
	} else if (y <= 3.3e+41) {
		tmp = (x - y) / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.15e+42:
		tmp = 1.0
	elif y <= 3.3e+41:
		tmp = (x - y) / (2.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.15e+42)
		tmp = 1.0;
	elseif (y <= 3.3e+41)
		tmp = Float64(Float64(x - y) / Float64(2.0 - x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.15e+42)
		tmp = 1.0;
	elseif (y <= 3.3e+41)
		tmp = (x - y) / (2.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.15e+42], 1.0, If[LessEqual[y, 3.3e+41], N[(N[(x - y), $MachinePrecision] / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1499999999999999e42 or 3.3e41 < 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 73.6%

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

   if -2.1499999999999999e42 < y < 3.3e41

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \color{blue}{\left(2 - x\right)}\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 93.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(2, \color{blue}{x}\right)\right) \]

   5. Simplified 93.3%

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

Alternative 4: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2 - \left(x + y\right)}\\ \mathbf{if}\;x \leq -6.4 \cdot 10^{-33}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-49}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 2.0 (+ x y)))))
   (if (<= x -6.4e-33) t_0 (if (<= x 2.8e-49) (/ y (+ y -2.0)) t_0))))

C

double code(double x, double y) {
	double t_0 = x / (2.0 - (x + y));
	double tmp;
	if (x <= -6.4e-33) {
		tmp = t_0;
	} else if (x <= 2.8e-49) {
		tmp = y / (y + -2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x / (2.0d0 - (x + y))
    if (x <= (-6.4d-33)) then
        tmp = t_0
    else if (x <= 2.8d-49) then
        tmp = y / (y + (-2.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (2.0 - (x + y));
	double tmp;
	if (x <= -6.4e-33) {
		tmp = t_0;
	} else if (x <= 2.8e-49) {
		tmp = y / (y + -2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (2.0 - (x + y))
	tmp = 0
	if x <= -6.4e-33:
		tmp = t_0
	elif x <= 2.8e-49:
		tmp = y / (y + -2.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(2.0 - Float64(x + y)))
	tmp = 0.0
	if (x <= -6.4e-33)
		tmp = t_0;
	elseif (x <= 2.8e-49)
		tmp = Float64(y / Float64(y + -2.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (2.0 - (x + y));
	tmp = 0.0;
	if (x <= -6.4e-33)
		tmp = t_0;
	elseif (x <= 2.8e-49)
		tmp = y / (y + -2.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.4e-33], t$95$0, If[LessEqual[x, 2.8e-49], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.39999999999999954e-33 or 2.79999999999999997e-49 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{\_.f64}\left(2, \mathsf{+.f64}\left(x, y\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 76.8%

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

   if -6.39999999999999954e-33 < x < 2.79999999999999997e-49

   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

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(-1 \cdot \left(2 - y\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\mathsf{neg}\left(\left(2 - y\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\mathsf{neg}\left(\left(2 + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + 2\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(-1 \cdot \left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(-1 \cdot \left(-1 \cdot y\right) + \left(\mathsf{neg}\left(2\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(\left(-1 \cdot -1\right) \cdot y + \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(1 \cdot y + \left(\mathsf{neg}\left(2\right)\right)\right)\right) \]

      13. *-lft-identity N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(y + \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right) \]

      15. metadata-eval 79.2%

          \[\leadsto \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(y, -2\right)\right) \]

   5. Simplified 79.2%

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

Alternative 5: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{-37}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-92}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 2.0 x))))
   (if (<= x -9.5e-37) t_0 (if (<= x 4.6e-92) (/ y (+ y -2.0)) t_0))))

C

double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (x <= -9.5e-37) {
		tmp = t_0;
	} else if (x <= 4.6e-92) {
		tmp = y / (y + -2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x / (2.0d0 - x)
    if (x <= (-9.5d-37)) then
        tmp = t_0
    else if (x <= 4.6d-92) then
        tmp = y / (y + (-2.0d0))
    else
        tmp = t_0
    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 (x <= -9.5e-37) {
		tmp = t_0;
	} else if (x <= 4.6e-92) {
		tmp = y / (y + -2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (2.0 - x)
	tmp = 0
	if x <= -9.5e-37:
		tmp = t_0
	elif x <= 4.6e-92:
		tmp = y / (y + -2.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(2.0 - x))
	tmp = 0.0
	if (x <= -9.5e-37)
		tmp = t_0;
	elseif (x <= 4.6e-92)
		tmp = Float64(y / Float64(y + -2.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (2.0 - x);
	tmp = 0.0;
	if (x <= -9.5e-37)
		tmp = t_0;
	elseif (x <= 4.6e-92)
		tmp = y / (y + -2.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.5e-37], t$95$0, If[LessEqual[x, 4.6e-92], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.49999999999999927e-37 or 4.60000000000000032e-92 < x

   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

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(2 - x\right)}\right) \]

      2. --lowering--.f64 75.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(2, \color{blue}{x}\right)\right) \]

   5. Simplified 75.3%

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

   if -9.49999999999999927e-37 < x < 4.60000000000000032e-92

   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

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(-1 \cdot \left(2 - y\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\mathsf{neg}\left(\left(2 - y\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\mathsf{neg}\left(\left(2 + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + 2\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(-1 \cdot \left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(-1 \cdot \left(-1 \cdot y\right) + \left(\mathsf{neg}\left(2\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(\left(-1 \cdot -1\right) \cdot y + \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(1 \cdot y + \left(\mathsf{neg}\left(2\right)\right)\right)\right) \]

      13. *-lft-identity N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(y + \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right) \]

      15. metadata-eval 80.7%

          \[\leadsto \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(y, -2\right)\right) \]

   5. Simplified 80.7%

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

Alternative 6: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+42}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.3e+42) 1.0 (if (<= y 3e+44) (/ x (- 2.0 x)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.3e+42) {
		tmp = 1.0;
	} else if (y <= 3e+44) {
		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 (y <= (-2.3d+42)) then
        tmp = 1.0d0
    else if (y <= 3d+44) 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 (y <= -2.3e+42) {
		tmp = 1.0;
	} else if (y <= 3e+44) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.3e+42:
		tmp = 1.0
	elif y <= 3e+44:
		tmp = x / (2.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.3e+42)
		tmp = 1.0;
	elseif (y <= 3e+44)
		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 (y <= -2.3e+42)
		tmp = 1.0;
	elseif (y <= 3e+44)
		tmp = x / (2.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.3e+42], 1.0, If[LessEqual[y, 3e+44], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3e42 or 2.99999999999999987e44 < 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 74.0%

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

   if -2.3e42 < y < 2.99999999999999987e44

   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

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(2 - x\right)}\right) \]

      2. --lowering--.f64 72.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(2, \color{blue}{x}\right)\right) \]

   5. Simplified 72.3%

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

Alternative 7: 62.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -17200000000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -17200000000000.0) -1.0 (if (<= x 2.4e+19) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -17200000000000.0) {
		tmp = -1.0;
	} else if (x <= 2.4e+19) {
		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 <= (-17200000000000.0d0)) then
        tmp = -1.0d0
    else if (x <= 2.4d+19) 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 <= -17200000000000.0) {
		tmp = -1.0;
	} else if (x <= 2.4e+19) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -17200000000000.0:
		tmp = -1.0
	elif x <= 2.4e+19:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -17200000000000.0)
		tmp = -1.0;
	elseif (x <= 2.4e+19)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -17200000000000.0)
		tmp = -1.0;
	elseif (x <= 2.4e+19)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -17200000000000.0], -1.0, If[LessEqual[x, 2.4e+19], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.72e13 or 2.4e19 < x

   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 79.2%

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

   if -1.72e13 < x < 2.4e19

   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 54.0%

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

Alternative 8: 37.7% 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. Add Preprocessing

3. Taylor expanded in x around inf

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

5. Simplified 39.6%

   \[\leadsto \color{blue}{-1} \]
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 2024145 
(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))))