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

Percentage Accurate: 100.0% → 100.0%

Time: 6.5s

Alternatives: 6

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{x + y} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    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]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{x + y} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    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]

Alternative 1: 100.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{x + y}{x - y}} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ 1.0 (/ (+ x y) (- x y))))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. clear-num 100.0%

      \[\leadsto \color{blue}{\frac{1}{\frac{x + y}{x - y}}} \]

   2. inv-pow 100.0%

      \[\leadsto \color{blue}{{\left(\frac{x + y}{x - y}\right)}^{-1}} \]

4. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{{\left(\frac{x + y}{x - y}\right)}^{-1}} \]
5. Step-by-step derivation

   1. unpow-1 100.0%

      \[\leadsto \color{blue}{\frac{1}{\frac{x + y}{x - y}}} \]

6. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\frac{1}{\frac{x + y}{x - y}}} \]

7. Final simplification 100.0%

   \[\leadsto \frac{1}{\frac{x + y}{x - y}} \]
8. Add Preprocessing

Alternative 2: 74.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4200 \lor \neg \left(x \leq 6.6 \cdot 10^{-66} \lor \neg \left(x \leq 1.02 \cdot 10^{+44}\right) \land x \leq 1.5 \cdot 10^{+63}\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4200.0)
         (not (or (<= x 6.6e-66) (and (not (<= x 1.02e+44)) (<= x 1.5e+63)))))
   (+ 1.0 (* -2.0 (/ y x)))
   -1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4200.0) || !((x <= 6.6e-66) || (!(x <= 1.02e+44) && (x <= 1.5e+63)))) {
		tmp = 1.0 + (-2.0 * (y / 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 <= (-4200.0d0)) .or. (.not. (x <= 6.6d-66) .or. (.not. (x <= 1.02d+44)) .and. (x <= 1.5d+63))) then
        tmp = 1.0d0 + ((-2.0d0) * (y / x))
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -4200.0) || !((x <= 6.6e-66) || (!(x <= 1.02e+44) && (x <= 1.5e+63)))) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -4200.0) or not ((x <= 6.6e-66) or (not (x <= 1.02e+44) and (x <= 1.5e+63))):
		tmp = 1.0 + (-2.0 * (y / x))
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -4200.0) || !((x <= 6.6e-66) || (!(x <= 1.02e+44) && (x <= 1.5e+63))))
		tmp = Float64(1.0 + Float64(-2.0 * Float64(y / x)));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -4200.0) || ~(((x <= 6.6e-66) || (~((x <= 1.02e+44)) && (x <= 1.5e+63)))))
		tmp = 1.0 + (-2.0 * (y / x));
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -4200.0], N[Not[Or[LessEqual[x, 6.6e-66], And[N[Not[LessEqual[x, 1.02e+44]], $MachinePrecision], LessEqual[x, 1.5e+63]]]], $MachinePrecision]], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0]

Derivation

1. Split input into 2 regimes

2. if x < -4200 or 6.5999999999999998e-66 < x < 1.01999999999999999e44 or 1.5e63 < x

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 75.3%

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

   if -4200 < x < 6.5999999999999998e-66 or 1.01999999999999999e44 < x < 1.5e63

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 78.3%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4200 \lor \neg \left(x \leq 6.6 \cdot 10^{-66} \lor \neg \left(x \leq 1.02 \cdot 10^{+44}\right) \land x \leq 1.5 \cdot 10^{+63}\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + -2 \cdot \frac{y}{x}\\ \mathbf{if}\;x \leq -4400:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-53}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+44} \lor \neg \left(x \leq 1.85 \cdot 10^{+61}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* -2.0 (/ y x)))))
   (if (<= x -4400.0)
     t_0
     (if (<= x 1.35e-53)
       (+ (* 2.0 (/ x y)) -1.0)
       (if (or (<= x 1.16e+44) (not (<= x 1.85e+61))) t_0 -1.0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (-2.0 * (y / x));
	double tmp;
	if (x <= -4400.0) {
		tmp = t_0;
	} else if (x <= 1.35e-53) {
		tmp = (2.0 * (x / y)) + -1.0;
	} else if ((x <= 1.16e+44) || !(x <= 1.85e+61)) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 + ((-2.0d0) * (y / x))
    if (x <= (-4400.0d0)) then
        tmp = t_0
    else if (x <= 1.35d-53) then
        tmp = (2.0d0 * (x / y)) + (-1.0d0)
    else if ((x <= 1.16d+44) .or. (.not. (x <= 1.85d+61))) then
        tmp = t_0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 + (-2.0 * (y / x));
	double tmp;
	if (x <= -4400.0) {
		tmp = t_0;
	} else if (x <= 1.35e-53) {
		tmp = (2.0 * (x / y)) + -1.0;
	} else if ((x <= 1.16e+44) || !(x <= 1.85e+61)) {
		tmp = t_0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (-2.0 * (y / x))
	tmp = 0
	if x <= -4400.0:
		tmp = t_0
	elif x <= 1.35e-53:
		tmp = (2.0 * (x / y)) + -1.0
	elif (x <= 1.16e+44) or not (x <= 1.85e+61):
		tmp = t_0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(-2.0 * Float64(y / x)))
	tmp = 0.0
	if (x <= -4400.0)
		tmp = t_0;
	elseif (x <= 1.35e-53)
		tmp = Float64(Float64(2.0 * Float64(x / y)) + -1.0);
	elseif ((x <= 1.16e+44) || !(x <= 1.85e+61))
		tmp = t_0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (-2.0 * (y / x));
	tmp = 0.0;
	if (x <= -4400.0)
		tmp = t_0;
	elseif (x <= 1.35e-53)
		tmp = (2.0 * (x / y)) + -1.0;
	elseif ((x <= 1.16e+44) || ~((x <= 1.85e+61)))
		tmp = t_0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4400.0], t$95$0, If[LessEqual[x, 1.35e-53], N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision], If[Or[LessEqual[x, 1.16e+44], N[Not[LessEqual[x, 1.85e+61]], $MachinePrecision]], t$95$0, -1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4400 or 1.35e-53 < x < 1.1600000000000001e44 or 1.85000000000000001e61 < x

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 75.7%

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

   if -4400 < x < 1.35e-53

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 77.7%

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

   if 1.1600000000000001e44 < x < 1.85000000000000001e61

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 100.0%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4400:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-53}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+44} \lor \neg \left(x \leq 1.85 \cdot 10^{+61}\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -120:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{-65}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+43}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+61}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -120.0)
   1.0
   (if (<= x 1.06e-65) -1.0 (if (<= x 7e+43) 1.0 (if (<= x 2e+61) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -120.0) {
		tmp = 1.0;
	} else if (x <= 1.06e-65) {
		tmp = -1.0;
	} else if (x <= 7e+43) {
		tmp = 1.0;
	} else if (x <= 2e+61) {
		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 <= (-120.0d0)) then
        tmp = 1.0d0
    else if (x <= 1.06d-65) then
        tmp = -1.0d0
    else if (x <= 7d+43) then
        tmp = 1.0d0
    else if (x <= 2d+61) 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 <= -120.0) {
		tmp = 1.0;
	} else if (x <= 1.06e-65) {
		tmp = -1.0;
	} else if (x <= 7e+43) {
		tmp = 1.0;
	} else if (x <= 2e+61) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -120.0:
		tmp = 1.0
	elif x <= 1.06e-65:
		tmp = -1.0
	elif x <= 7e+43:
		tmp = 1.0
	elif x <= 2e+61:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -120.0)
		tmp = 1.0;
	elseif (x <= 1.06e-65)
		tmp = -1.0;
	elseif (x <= 7e+43)
		tmp = 1.0;
	elseif (x <= 2e+61)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -120.0)
		tmp = 1.0;
	elseif (x <= 1.06e-65)
		tmp = -1.0;
	elseif (x <= 7e+43)
		tmp = 1.0;
	elseif (x <= 2e+61)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -120.0], 1.0, If[LessEqual[x, 1.06e-65], -1.0, If[LessEqual[x, 7e+43], 1.0, If[LessEqual[x, 2e+61], -1.0, 1.0]]]]

Derivation

1. Split input into 2 regimes

2. if x < -120 or 1.0600000000000001e-65 < x < 7.0000000000000002e43 or 1.9999999999999999e61 < x

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 74.2%

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

   if -120 < x < 1.0600000000000001e-65 or 7.0000000000000002e43 < x < 1.9999999999999999e61

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 78.3%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -120:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{-65}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+43}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+61}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{x + y} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    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]

Derivation

1. Initial program 99.9%

   \[\frac{x - y}{x + y} \]
2. Add Preprocessing

3. Final simplification 99.9%

   \[\leadsto \frac{x - y}{x + y} \]
4. Add Preprocessing

Alternative 6: 50.5% accurate, 7.0× 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 99.9%

   \[\frac{x - y}{x + y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0 48.8%

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

4. Final simplification 48.8%

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

Developer target: 100.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \frac{x}{x + y} - \frac{y}{x + y} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x / (x + y)) - (y / (x + y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024039 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

  :herbie-target
  (- (/ x (+ x y)) (/ y (+ x y)))

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