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

Percentage Accurate: 100.0% → 100.0%

Time: 1.7s

Alternatives: 6

Speedup: 1.0×

Specification

Math

\[\frac{x - y}{x + y} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (/ (- x y) (+ x y)))

C

double code(double x, double y) {
	return (x - y) / (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) / (x + y)
end function

Java

public static double code(double x, double y) {
	return (x - y) / (x + y);
}

Python

def code(x, y):
	return (x - y) / (x + y)

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (x + y);
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]

ReFlow

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\frac{x - y}{x + y} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (/ (- x y) (+ x y)))

C

double code(double x, double y) {
	return (x - y) / (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) / (x + y)
end function

Java

public static double code(double x, double y) {
	return (x - y) / (x + y);
}

Python

def code(x, y):
	return (x - y) / (x + y)

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (x + y);
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]

ReFlow

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

Alternative 1: 98.2% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], -1.0], N[(N[(x / y), $MachinePrecision] * 2.0 + -1.0), $MachinePrecision], N[(N[(y / x), $MachinePrecision] * -2.0 + 1.0), $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) / (x + y)) <= (-1)) THEN (((x / y) * (2)) + (-1)) ELSE (((y / x) * (-2)) + (1)) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (+.f64 x y)) < -1

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 51.3%

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

   6. Applied rewrites 51.3%

      \[\leadsto \mathsf{fma}\left(\frac{x}{y}, 2, -1\right) \]

   if -1 < (/.f64 (-.f64 x y) (+.f64 x y))

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 50.8%

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

   6. Applied rewrites 50.8%

      \[\leadsto \mathsf{fma}\left(\frac{y}{x}, -2, 1\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 98.0% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

ReFlow

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (+.f64 x y)) < -1

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 51.3%

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

   6. Applied rewrites 51.3%

      \[\leadsto \mathsf{fma}\left(\frac{x}{y}, 2, -1\right) \]

   if -1 < (/.f64 (-.f64 x y) (+.f64 x y))

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 49.5%

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

Alternative 3: 97.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{x + y} \leq -1:\\ \;\;\;\;\frac{x - y}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if (((x - y) / (x + y)) <= -1.0) {
		tmp = (x - y) / y;
	} 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) / (x + y)) <= (-1.0d0)) then
        tmp = (x - y) / y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], -1.0], N[(N[(x - y), $MachinePrecision] / y), $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) / (x + y)) <= (-1)) THEN ((x - y) / y) ELSE (1) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (+.f64 x y)) < -1

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 50.8%

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

   if -1 < (/.f64 (-.f64 x y) (+.f64 x y))

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 49.5%

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

Alternative 4: 97.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{x + y} \leq 6.758573732548052 \cdot 10^{-79}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= (/ (- x y) (+ x y)) 6.758573732548052e-79) -1.0 1.0))

C

double code(double x, double y) {
	double tmp;
	if (((x - y) / (x + y)) <= 6.758573732548052e-79) {
		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) / (x + y)) <= 6.758573732548052d-79) 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) / (x + y)) <= 6.758573732548052e-79) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((x - y) / (x + y)) <= 6.758573732548052e-79:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(x - y) / Float64(x + y)) <= 6.758573732548052e-79)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((x - y) / (x + y)) <= 6.758573732548052e-79)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], 6.758573732548052e-79], -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) / (x + y)) <= (67585737325480524122593017784783224281129036479529979170791439070932276332156772635614123730730560729694865766693754440503840626982182983204595483746874952097657820593720196064259884245482346877553769814994666376151144504547119140625e-311)) THEN (-1) ELSE (1) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (+.f64 x y)) < 6.7585737325480524e-79

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 50.1%

      \[\leadsto -1 \]

   if 6.7585737325480524e-79 < (/.f64 (-.f64 x y) (+.f64 x y))

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 49.5%

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

Alternative 5: 50.1% accurate, 10.0× 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%

   \[\frac{x - y}{x + y} \]

2. Taylor expanded in x around 0

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

4. Applied rewrites 50.1%

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

Reproduce

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