Data.Colour.CIE.Chromaticity:chromaCoords from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 1.1s

Alternatives: 4

Speedup: 1.0×

Specification

Math

\[\left(1 - x\right) - y \]

FPCore

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

C

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

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - x) - y
end function

Java

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

Python

def code(x, y):
	return (1.0 - x) - y

Julia

function code(x, y)
	return Float64(Float64(1.0 - x) - y)
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - x) - y;
end

Wolfram

code[x_, y_] := N[(N[(1.0 - x), $MachinePrecision] - y), $MachinePrecision]

ReFlow

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\left(1 - x\right) - y \]

FPCore

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

C

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

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - x) - y
end function

Java

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

Python

def code(x, y):
	return (1.0 - x) - y

Julia

function code(x, y)
	return Float64(Float64(1.0 - x) - y)
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - x) - y;
end

Wolfram

code[x_, y_] := N[(N[(1.0 - x), $MachinePrecision] - y), $MachinePrecision]

ReFlow

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

Alternative 1: 99.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := 1 - \mathsf{min}\left(x, y\right)\\ \mathbf{if}\;t\_0 - \mathsf{max}\left(x, y\right) \leq 0.9999999999999998:\\ \;\;\;\;1 - \mathsf{max}\left(x, y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (- 1.0 (fmin x y))))
  (if (<= (- t_0 (fmax x y)) 0.9999999999999998)
    (- 1.0 (fmax x y))
    t_0)))

C

double code(double x, double y) {
	double t_0 = 1.0 - fmin(x, y);
	double tmp;
	if ((t_0 - fmax(x, y)) <= 0.9999999999999998) {
		tmp = 1.0 - fmax(x, y);
	} else {
		tmp = t_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 = 1.0d0 - fmin(x, y)
    if ((t_0 - fmax(x, y)) <= 0.9999999999999998d0) then
        tmp = 1.0d0 - fmax(x, y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 - fmin(x, y);
	double tmp;
	if ((t_0 - fmax(x, y)) <= 0.9999999999999998) {
		tmp = 1.0 - fmax(x, y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - fmin(x, y)
	tmp = 0
	if (t_0 - fmax(x, y)) <= 0.9999999999999998:
		tmp = 1.0 - fmax(x, y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - fmin(x, y))
	tmp = 0.0
	if (Float64(t_0 - fmax(x, y)) <= 0.9999999999999998)
		tmp = Float64(1.0 - fmax(x, y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - min(x, y);
	tmp = 0.0;
	if ((t_0 - max(x, y)) <= 0.9999999999999998)
		tmp = 1.0 - max(x, y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 - N[Min[x, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$0 - N[Max[x, y], $MachinePrecision]), $MachinePrecision], 0.9999999999999998], N[(1.0 - N[Max[x, y], $MachinePrecision]), $MachinePrecision], t$95$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) THEN x ELSE y ENDIF IN
	LET t_0 = ((1) - tmp) IN
		LET tmp_3 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_4 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_2 = IF ((t_0 - tmp_3) <= (9999999999999997779553950749686919152736663818359375e-52)) THEN ((1) - tmp_4) ELSE t_0 ENDIF IN
	tmp_2
END code

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 #s(literal 1 binary64) x) y) < 0.99999999999999978

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 62.9%

      \[\leadsto 1 - y \]

   if 0.99999999999999978 < (-.f64 (-.f64 #s(literal 1 binary64) x) y)

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 62.8%

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

Alternative 2: 61.8% accurate, 0.9× speedup

Math

\[1 - \mathsf{min}\left(x, y\right) \]

FPCore

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

C

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

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0 - fmin(x, y)
end function

Java

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

Python

def code(x, y):
	return 1.0 - fmin(x, y)

Julia

function code(x, y)
	return Float64(1.0 - fmin(x, y))
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0 - min(x, y);
end

Wolfram

code[x_, y_] := N[(1.0 - N[Min[x, 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) THEN x ELSE y ENDIF IN
	(1) - tmp
END code

Derivation

1. Initial program 100.0%

   \[\left(1 - x\right) - y \]

2. Taylor expanded in y around 0

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

4. Applied rewrites 62.8%

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

Alternative 3: 26.4% accurate, 6.2× 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%

   \[\left(1 - x\right) - y \]

2. Taylor expanded in y around 0

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

4. Applied rewrites 62.8%

   \[\leadsto 1 - x \]

5. Taylor expanded in x around 0

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

7. Applied rewrites 26.4%

   \[\leadsto 1 \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y)
  :name "Data.Colour.CIE.Chromaticity:chromaCoords from colour-2.3.3"
  :precision binary64
  (- (- 1.0 x) y))