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

Percentage Accurate: 100.0% → 100.0%

Time: 1.9s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (/ (- 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)
use fmin_fmax_functions
    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]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	(x - y) / ((2) - (x + y))
END code

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (/ (- 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)
use fmin_fmax_functions
    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]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	(x - y) / ((2) - (x + y))
END code

Alternative 1: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{2 - \left(x + y\right)} \leq 0.005:\\ \;\;\;\;\frac{x - y}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= (/ (- x y) (- 2.0 (+ x y))) 0.005)
  (/ (- x y) (- 2.0 x))
  (/ (- x y) (- 2.0 y))))

C

double code(double x, double y) {
	double tmp;
	if (((x - y) / (2.0 - (x + y))) <= 0.005) {
		tmp = (x - y) / (2.0 - x);
	} else {
		tmp = (x - y) / (2.0 - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (((x - y) / (2.0d0 - (x + y))) <= 0.005d0) then
        tmp = (x - y) / (2.0d0 - x)
    else
        tmp = (x - y) / (2.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((x - y) / (2.0 - (x + y))) <= 0.005) {
		tmp = (x - y) / (2.0 - x);
	} else {
		tmp = (x - y) / (2.0 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((x - y) / (2.0 - (x + y))) <= 0.005:
		tmp = (x - y) / (2.0 - x)
	else:
		tmp = (x - y) / (2.0 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(x - y) / Float64(2.0 - Float64(x + y))) <= 0.005)
		tmp = Float64(Float64(x - y) / Float64(2.0 - x));
	else
		tmp = Float64(Float64(x - y) / Float64(2.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((x - y) / (2.0 - (x + y))) <= 0.005)
		tmp = (x - y) / (2.0 - x);
	else
		tmp = (x - y) / (2.0 - y);
	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], 0.005], N[(N[(x - y), $MachinePrecision] / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / N[(2.0 - y), $MachinePrecision]), $MachinePrecision]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp = IF (((x - y) / ((2) - (x + y))) <= (5000000000000000104083408558608425664715468883514404296875e-60)) THEN ((x - y) / ((2) - x)) ELSE ((x - y) / ((2) - y)) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < 0.0050000000000000001

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 63.5%

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

   if 0.0050000000000000001 < (/.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. Taylor expanded in x around 0

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

   4. Applied rewrites 62.2%

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

Alternative 2: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{2 - \left(x + y\right)} \leq 0.005:\\ \;\;\;\;\frac{x - y}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= (/ (- x y) (- 2.0 (+ x y))) 0.005) (/ (- x y) (- 2.0 x)) 1.0))

C

double code(double x, double y) {
	double tmp;
	if (((x - y) / (2.0 - (x + y))) <= 0.005) {
		tmp = (x - y) / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (((x - y) / (2.0d0 - (x + y))) <= 0.005d0) 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 (((x - y) / (2.0 - (x + y))) <= 0.005) {
		tmp = (x - y) / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((x - y) / (2.0 - (x + y))) <= 0.005:
		tmp = (x - y) / (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))) <= 0.005)
		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 (((x - y) / (2.0 - (x + y))) <= 0.005)
		tmp = (x - y) / (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], 0.005], N[(N[(x - y), $MachinePrecision] / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp = IF (((x - y) / ((2) - (x + y))) <= (5000000000000000104083408558608425664715468883514404296875e-60)) THEN ((x - y) / ((2) - x)) ELSE (1) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < 0.0050000000000000001

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 63.5%

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

   if 0.0050000000000000001 < (/.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. Taylor expanded in y around inf

      \[\leadsto 1 \]
   3. Step-by-step derivation

   4. Applied rewrites 37.3%

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

Alternative 3: 97.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \frac{x - y}{2 - \left(x + y\right)}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;t\_0 \leq 0.005:\\ \;\;\;\;\frac{x - y}{2}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (/ (- x y) (- 2.0 (+ x y)))))
  (if (<= t_0 -2e-7)
    (/ x (- 2.0 x))
    (if (<= t_0 0.005) (/ (- x y) 2.0) 1.0))))

C

double code(double x, double y) {
	double t_0 = (x - y) / (2.0 - (x + y));
	double tmp;
	if (t_0 <= -2e-7) {
		tmp = x / (2.0 - x);
	} else if (t_0 <= 0.005) {
		tmp = (x - y) / 2.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    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 <= (-2d-7)) then
        tmp = x / (2.0d0 - x)
    else if (t_0 <= 0.005d0) then
        tmp = (x - y) / 2.0d0
    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 <= -2e-7) {
		tmp = x / (2.0 - x);
	} else if (t_0 <= 0.005) {
		tmp = (x - y) / 2.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x - y) / (2.0 - (x + y))
	tmp = 0
	if t_0 <= -2e-7:
		tmp = x / (2.0 - x)
	elif t_0 <= 0.005:
		tmp = (x - y) / 2.0
	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 <= -2e-7)
		tmp = Float64(x / Float64(2.0 - x));
	elseif (t_0 <= 0.005)
		tmp = Float64(Float64(x - y) / 2.0);
	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 <= -2e-7)
		tmp = x / (2.0 - x);
	elseif (t_0 <= 0.005)
		tmp = (x - y) / 2.0;
	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, -2e-7], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.005], N[(N[(x - y), $MachinePrecision] / 2.0), $MachinePrecision], 1.0]]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET t_0 = ((x - y) / ((2) - (x + y))) IN
		LET tmp_1 = IF (t_0 <= (5000000000000000104083408558608425664715468883514404296875e-60)) THEN ((x - y) / (2)) ELSE (1) ENDIF IN
		LET tmp = IF (t_0 <= (-199999999999999990949622365177251737122787744738161563873291015625e-72)) THEN (x / ((2) - x)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < -1.9999999999999999e-7

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

      \[\leadsto \frac{x}{2 - x} \]
   3. Step-by-step derivation

   4. Applied rewrites 51.7%

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

   if -1.9999999999999999e-7 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < 0.0050000000000000001

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 63.5%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 26.4%

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

   if 0.0050000000000000001 < (/.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. Taylor expanded in y around inf

      \[\leadsto 1 \]
   3. Step-by-step derivation

   4. Applied rewrites 37.3%

      \[\leadsto 1 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 86.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{2 - \left(x + y\right)} \leq 0.005:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= (/ (- x y) (- 2.0 (+ x y))) 0.005) (/ x (- 2.0 x)) 1.0))

C

double code(double x, double y) {
	double tmp;
	if (((x - y) / (2.0 - (x + y))) <= 0.005) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (((x - y) / (2.0d0 - (x + y))) <= 0.005d0) 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))) <= 0.005) {
		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))) <= 0.005:
		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))) <= 0.005)
		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))) <= 0.005)
		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], 0.005], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp = IF (((x - y) / ((2) - (x + y))) <= (5000000000000000104083408558608425664715468883514404296875e-60)) THEN (x / ((2) - x)) ELSE (1) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < 0.0050000000000000001

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

      \[\leadsto \frac{x}{2 - x} \]
   3. Step-by-step derivation

   4. Applied rewrites 51.7%

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

   if 0.0050000000000000001 < (/.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. Taylor expanded in y around inf

      \[\leadsto 1 \]
   3. Step-by-step derivation

   4. Applied rewrites 37.3%

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

Alternative 5: 85.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := \frac{x - y}{2 - \left(x + y\right)}\\ \mathbf{if}\;t\_0 \leq -0.5:\\ \;\;\;\;-1\\ \mathbf{elif}\;t\_0 \leq 0.005:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (/ (- x y) (- 2.0 (+ x y)))))
  (if (<= t_0 -0.5) -1.0 (if (<= t_0 0.005) (* 0.5 x) 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 <= 0.005) {
		tmp = 0.5 * x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    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 <= 0.005d0) then
        tmp = 0.5d0 * x
    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 <= 0.005) {
		tmp = 0.5 * x;
	} 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 <= 0.005:
		tmp = 0.5 * x
	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 <= 0.005)
		tmp = Float64(0.5 * x);
	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 <= 0.005)
		tmp = 0.5 * x;
	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, 0.005], N[(0.5 * x), $MachinePrecision], 1.0]]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET t_0 = ((x - y) / ((2) - (x + y))) IN
		LET tmp_1 = IF (t_0 <= (5000000000000000104083408558608425664715468883514404296875e-60)) THEN ((5e-1) * x) ELSE (1) ENDIF IN
		LET tmp = IF (t_0 <= (-5e-1)) THEN (-1) ELSE tmp_1 ENDIF IN
	tmp
END code

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. Taylor expanded in x around inf

      \[\leadsto -1 \]
   3. Step-by-step derivation

   4. Applied rewrites 38.6%

      \[\leadsto -1 \]

   if -0.5 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < 0.0050000000000000001

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

      \[\leadsto \frac{x}{2 - x} \]
   3. Step-by-step derivation

   4. Applied rewrites 51.7%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 15.1%

      \[\leadsto 0.5 \cdot x \]

   if 0.0050000000000000001 < (/.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. Taylor expanded in y around inf

      \[\leadsto 1 \]
   3. Step-by-step derivation

   4. Applied rewrites 37.3%

      \[\leadsto 1 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{2 - \left(x + y\right)} \leq 1.2423345892717348 \cdot 10^{-287}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= (/ (- x y) (- 2.0 (+ x y))) 1.2423345892717348e-287) -1.0 1.0))

C

double code(double x, double y) {
	double tmp;
	if (((x - y) / (2.0 - (x + y))) <= 1.2423345892717348e-287) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (((x - y) / (2.0d0 - (x + y))) <= 1.2423345892717348d-287) 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))) <= 1.2423345892717348e-287) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((x - y) / (2.0 - (x + y))) <= 1.2423345892717348e-287:
		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))) <= 1.2423345892717348e-287)
		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))) <= 1.2423345892717348e-287)
		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], 1.2423345892717348e-287], -1.0, 1.0]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp = IF (((x - y) / ((2) - (x + y))) <= (1242334589271734766694965026517907720287440807835919262790717453718264796586232870372742219313993639126732271887653312891673217485764275913935208689788400991999425081684233369133967092053600591711271565009616305561755793329555419578904695226767333125048876406319501324407047827118955270741031890851361457221001975359953622888113881968686396988159422708259137900394205831693205730602502096063680098810999724250314232074827573860718884208569997659215263730395847721814035768566635675449346359019778049325138083304927054078954017120551506776185727842591748845651099572271896389078801269178897586440719058896315829702125368319145544851777972247625557177649505143600781948884891059403656754511757753789424896240234375e-998)) THEN (-1) ELSE (1) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < 1.2423345892717348e-287

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto -1 \]
   3. Step-by-step derivation

   4. Applied rewrites 38.6%

      \[\leadsto -1 \]

   if 1.2423345892717348e-287 < (/.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. Taylor expanded in y around inf

      \[\leadsto 1 \]
   3. Step-by-step derivation

   4. Applied rewrites 37.3%

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

Alternative 7: 38.6% accurate, 12.6× speedup

Math

\[-1 \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  -1.0)

C

double code(double x, double y) {
	return -1.0;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    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

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	-1
END code

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around inf

   \[\leadsto -1 \]
3. Step-by-step derivation

4. Applied rewrites 38.6%

   \[\leadsto -1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64
  (/ (- x y) (- 2.0 (+ x y))))