Data.Array.Repa.Algorithms.Pixel:doubleRmsOfRGB8 from repa-algorithms-3.4.0.1

Percentage Accurate: 45.0% → 45.0%

Time: 1.8s

Alternatives: 8

Speedup: 1.0×

Specification

\[\mathsf{TRUE}\left(\right)\]

Math

\[\begin{array}{l} \\ \sqrt{\frac{\left(x \cdot x + y \cdot y\right) + z \cdot z}{3}} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)))

C

double code(double x, double y, double z) {
	return sqrt(((((x * x) + (y * y)) + (z * z)) / 3.0));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = sqrt(((((x * x) + (y * y)) + (z * z)) / 3.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return Math.sqrt(((((x * x) + (y * y)) + (z * z)) / 3.0));
}

Python

def code(x, y, z):
	return math.sqrt(((((x * x) + (y * y)) + (z * z)) / 3.0))

Julia

function code(x, y, z)
	return sqrt(Float64(Float64(Float64(Float64(x * x) + Float64(y * y)) + Float64(z * z)) / 3.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = sqrt(((((x * x) + (y * y)) + (z * z)) / 3.0));
end

Wolfram

code[x_, y_, z_] := N[Sqrt[N[(N[(N[(N[(x * x), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision] + N[(z * z), $MachinePrecision]), $MachinePrecision] / 3.0), $MachinePrecision]], $MachinePrecision]

Initial Program: 45.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sqrt{\frac{\left(x \cdot x + y \cdot y\right) + z \cdot z}{3}} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)))

C

double code(double x, double y, double z) {
	return sqrt(((((x * x) + (y * y)) + (z * z)) / 3.0));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = sqrt(((((x * x) + (y * y)) + (z * z)) / 3.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return Math.sqrt(((((x * x) + (y * y)) + (z * z)) / 3.0));
}

Python

def code(x, y, z):
	return math.sqrt(((((x * x) + (y * y)) + (z * z)) / 3.0))

Julia

function code(x, y, z)
	return sqrt(Float64(Float64(Float64(Float64(x * x) + Float64(y * y)) + Float64(z * z)) / 3.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = sqrt(((((x * x) + (y * y)) + (z * z)) / 3.0));
end

Wolfram

code[x_, y_, z_] := N[Sqrt[N[(N[(N[(N[(x * x), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision] + N[(z * z), $MachinePrecision]), $MachinePrecision] / 3.0), $MachinePrecision]], $MachinePrecision]

Alternative 1: 45.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sqrt{\frac{\left(x \cdot x + y \cdot y\right) + z \cdot z}{3}} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)))

C

double code(double x, double y, double z) {
	return sqrt(((((x * x) + (y * y)) + (z * z)) / 3.0));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = sqrt(((((x * x) + (y * y)) + (z * z)) / 3.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return Math.sqrt(((((x * x) + (y * y)) + (z * z)) / 3.0));
}

Python

def code(x, y, z):
	return math.sqrt(((((x * x) + (y * y)) + (z * z)) / 3.0))

Julia

function code(x, y, z)
	return sqrt(Float64(Float64(Float64(Float64(x * x) + Float64(y * y)) + Float64(z * z)) / 3.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = sqrt(((((x * x) + (y * y)) + (z * z)) / 3.0));
end

Wolfram

code[x_, y_, z_] := N[Sqrt[N[(N[(N[(N[(x * x), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision] + N[(z * z), $MachinePrecision]), $MachinePrecision] / 3.0), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 48.5%

   \[\sqrt{\frac{\left(x \cdot x + y \cdot y\right) + z \cdot z}{3}} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 12.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (sqrt (+ (+ (* x x) (* y y)) (* z z))))

C

double code(double x, double y, double z) {
	return sqrt((((x * x) + (y * y)) + (z * z)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = sqrt((((x * x) + (y * y)) + (z * z)))
end function

Java

public static double code(double x, double y, double z) {
	return Math.sqrt((((x * x) + (y * y)) + (z * z)));
}

Python

def code(x, y, z):
	return math.sqrt((((x * x) + (y * y)) + (z * z)))

Julia

function code(x, y, z)
	return sqrt(Float64(Float64(Float64(x * x) + Float64(y * y)) + Float64(z * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = sqrt((((x * x) + (y * y)) + (z * z)));
end

Wolfram

code[x_, y_, z_] := N[Sqrt[N[(N[(N[(x * x), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision] + N[(z * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 48.5%

   \[\sqrt{\frac{\left(x \cdot x + y \cdot y\right) + z \cdot z}{3}} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \sqrt{\color{blue}{\frac{1}{3} \cdot \left({y}^{2} + {z}^{2}\right)}} \]

5. Applied rewrites 6.7%

   \[\leadsto \sqrt{\color{blue}{x \cdot x}} \]

6. Taylor expanded in x around 0

   \[\leadsto \sqrt{{x}^{\color{blue}{2}}} \]

8. Applied rewrites 12.7%

   \[\leadsto \sqrt{\left(x \cdot x + y \cdot y\right) + \color{blue}{z \cdot z}} \]
9. Add Preprocessing

Alternative 3: 9.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot y \leq 1.32 \cdot 10^{-37}:\\ \;\;\;\;\sqrt{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{y \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* y y) 1.32e-37) (sqrt (* x x)) (sqrt (* y y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * y) <= 1.32e-37) {
		tmp = sqrt((x * x));
	} else {
		tmp = sqrt((y * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y * y) <= 1.32d-37) then
        tmp = sqrt((x * x))
    else
        tmp = sqrt((y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y * y) <= 1.32e-37) {
		tmp = Math.sqrt((x * x));
	} else {
		tmp = Math.sqrt((y * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y * y) <= 1.32e-37:
		tmp = math.sqrt((x * x))
	else:
		tmp = math.sqrt((y * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y * y) <= 1.32e-37)
		tmp = sqrt(Float64(x * x));
	else
		tmp = sqrt(Float64(y * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * y) <= 1.32e-37)
		tmp = sqrt((x * x));
	else
		tmp = sqrt((y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y * y), $MachinePrecision], 1.32e-37], N[Sqrt[N[(x * x), $MachinePrecision]], $MachinePrecision], N[Sqrt[N[(y * y), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y y) < 1.3200000000000001e-37

   1. Initial program 63.8%

      \[\sqrt{\frac{\left(x \cdot x + y \cdot y\right) + z \cdot z}{3}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \sqrt{\color{blue}{\frac{1}{3} \cdot \left({y}^{2} + {z}^{2}\right)}} \]

   5. Applied rewrites 8.6%

      \[\leadsto \sqrt{\color{blue}{x \cdot x}} \]

   if 1.3200000000000001e-37 < (*.f64 y y)

   1. Initial program 36.8%

      \[\sqrt{\frac{\left(x \cdot x + y \cdot y\right) + z \cdot z}{3}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \sqrt{\color{blue}{\frac{1}{3} \cdot \left({y}^{2} + {z}^{2}\right) + \frac{1}{3} \cdot {x}^{2}}} \]

   5. Applied rewrites 9.6%

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

Alternative 4: 9.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \sqrt{x \cdot x + z \cdot z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (sqrt (+ (* x x) (* z z))))

C

double code(double x, double y, double z) {
	return sqrt(((x * x) + (z * z)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = sqrt(((x * x) + (z * z)))
end function

Java

public static double code(double x, double y, double z) {
	return Math.sqrt(((x * x) + (z * z)));
}

Python

def code(x, y, z):
	return math.sqrt(((x * x) + (z * z)))

Julia

function code(x, y, z)
	return sqrt(Float64(Float64(x * x) + Float64(z * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = sqrt(((x * x) + (z * z)));
end

Wolfram

code[x_, y_, z_] := N[Sqrt[N[(N[(x * x), $MachinePrecision] + N[(z * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 48.5%

   \[\sqrt{\frac{\left(x \cdot x + y \cdot y\right) + z \cdot z}{3}} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \sqrt{\color{blue}{\frac{1}{3} \cdot \left({y}^{2} + {z}^{2}\right)}} \]

5. Applied rewrites 6.7%

   \[\leadsto \sqrt{\color{blue}{x \cdot x}} \]

6. Taylor expanded in x around 0

   \[\leadsto \sqrt{{x}^{\color{blue}{2}}} \]

8. Applied rewrites 12.7%

   \[\leadsto \sqrt{\left(x \cdot x + y \cdot y\right) + \color{blue}{z \cdot z}} \]

9. Taylor expanded in x around inf

   \[\leadsto \sqrt{\color{blue}{\frac{1}{3} \cdot {x}^{2}}} \]

11. Applied rewrites 8.7%

    \[\leadsto \sqrt{\color{blue}{\sqrt{x \cdot x} + z \cdot z}} \]

12. Taylor expanded in x around 0

    \[\leadsto \sqrt{\left({x}^{2} + {y}^{2}\right) + \color{blue}{z} \cdot z} \]

14. Applied rewrites 10.4%

    \[\leadsto \sqrt{x \cdot x + \color{blue}{z} \cdot z} \]
15. Add Preprocessing

Alternative 5: 6.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \sqrt{x \cdot x} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (sqrt (* x x)))

C

double code(double x, double y, double z) {
	return sqrt((x * x));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = sqrt((x * x))
end function

Java

public static double code(double x, double y, double z) {
	return Math.sqrt((x * x));
}

Python

def code(x, y, z):
	return math.sqrt((x * x))

Julia

function code(x, y, z)
	return sqrt(Float64(x * x))
end

MATLAB

function tmp = code(x, y, z)
	tmp = sqrt((x * x));
end

Wolfram

code[x_, y_, z_] := N[Sqrt[N[(x * x), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 48.5%

   \[\sqrt{\frac{\left(x \cdot x + y \cdot y\right) + z \cdot z}{3}} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \sqrt{\color{blue}{\frac{1}{3} \cdot \left({y}^{2} + {z}^{2}\right)}} \]

5. Applied rewrites 6.7%

   \[\leadsto \sqrt{\color{blue}{x \cdot x}} \]
6. Add Preprocessing

Alternative 6: 6.5% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ x \cdot x + z \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x x) (* z z)))

C

double code(double x, double y, double z) {
	return (x * x) + (z * z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * x) + (z * z)
end function

Java

public static double code(double x, double y, double z) {
	return (x * x) + (z * z);
}

Python

def code(x, y, z):
	return (x * x) + (z * z)

Julia

function code(x, y, z)
	return Float64(Float64(x * x) + Float64(z * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * x) + (z * z);
end

Wolfram

code[x_, y_, z_] := N[(N[(x * x), $MachinePrecision] + N[(z * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 48.5%

   \[\sqrt{\frac{\left(x \cdot x + y \cdot y\right) + z \cdot z}{3}} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\sqrt{\frac{1}{3}} \cdot \sqrt{{y}^{2} + {z}^{2}} + {x}^{2} \cdot \left(\frac{-1}{8} \cdot \left(\left({x}^{2} \cdot \sqrt{\frac{1}{3}}\right) \cdot \sqrt{\frac{1}{{\left({y}^{2} + {z}^{2}\right)}^{3}}}\right) + \frac{1}{2} \cdot \left(\sqrt{\frac{1}{3}} \cdot \sqrt{\frac{1}{{y}^{2} + {z}^{2}}}\right)\right)} \]

5. Applied rewrites 7.0%

   \[\leadsto \color{blue}{\left(x \cdot x + y \cdot y\right) + z \cdot z} \]

6. Taylor expanded in x around 0

   \[\leadsto \left({x}^{2} + {y}^{2}\right) + \color{blue}{z} \cdot z \]

8. Applied rewrites 6.5%

   \[\leadsto x \cdot x + \color{blue}{z} \cdot z \]
9. Add Preprocessing

Alternative 7: 5.3% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ y \cdot y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* y y))

C

double code(double x, double y, double z) {
	return y * y;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = y * y
end function

Java

public static double code(double x, double y, double z) {
	return y * y;
}

Python

def code(x, y, z):
	return y * y

Julia

function code(x, y, z)
	return Float64(y * y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = y * y;
end

Wolfram

code[x_, y_, z_] := N[(y * y), $MachinePrecision]

Derivation

1. Initial program 48.5%

   \[\sqrt{\frac{\left(x \cdot x + y \cdot y\right) + z \cdot z}{3}} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \sqrt{\color{blue}{\frac{1}{3} \cdot \left({y}^{2} + {z}^{2}\right) + \frac{1}{3} \cdot {x}^{2}}} \]

5. Applied rewrites 7.3%

   \[\leadsto \sqrt{\color{blue}{y \cdot y}} \]

6. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\sqrt{\frac{1}{3}} \cdot \sqrt{{y}^{2} + {z}^{2}} + {x}^{2} \cdot \left(\frac{-1}{8} \cdot \left(\left({x}^{2} \cdot \sqrt{\frac{1}{3}}\right) \cdot \sqrt{\frac{1}{{\left({y}^{2} + {z}^{2}\right)}^{3}}}\right) + \frac{1}{2} \cdot \left(\sqrt{\frac{1}{3}} \cdot \sqrt{\frac{1}{{y}^{2} + {z}^{2}}}\right)\right)} \]

8. Applied rewrites 5.4%

   \[\leadsto \color{blue}{y \cdot y} \]
9. Add Preprocessing

Alternative 8: 5.2% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ x \cdot x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x x))

C

double code(double x, double y, double z) {
	return x * x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * x
end function

Java

public static double code(double x, double y, double z) {
	return x * x;
}

Python

def code(x, y, z):
	return x * x

Julia

function code(x, y, z)
	return Float64(x * x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * x;
end

Wolfram

code[x_, y_, z_] := N[(x * x), $MachinePrecision]

Derivation

1. Initial program 48.5%

   \[\sqrt{\frac{\left(x \cdot x + y \cdot y\right) + z \cdot z}{3}} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\sqrt{\frac{1}{3}} \cdot \sqrt{{y}^{2} + {z}^{2}} + {x}^{2} \cdot \left(\frac{1}{2} \cdot \left(\sqrt{\frac{1}{3}} \cdot \sqrt{\frac{1}{{y}^{2} + {z}^{2}}}\right) + {x}^{2} \cdot \left(\frac{-1}{8} \cdot \left(\sqrt{\frac{1}{3}} \cdot \sqrt{\frac{1}{{\left({y}^{2} + {z}^{2}\right)}^{3}}}\right) + \frac{1}{16} \cdot \left(\left({x}^{2} \cdot \sqrt{\frac{1}{3}}\right) \cdot \sqrt{\frac{1}{{\left({y}^{2} + {z}^{2}\right)}^{5}}}\right)\right)\right)} \]

5. Applied rewrites 6.4%

   \[\leadsto \color{blue}{x \cdot x + y \cdot y} \]

6. Taylor expanded in x around 0

   \[\leadsto {x}^{2} + \color{blue}{{y}^{2}} \]

8. Applied rewrites 5.1%

   \[\leadsto x \cdot \color{blue}{x} \]
9. Add Preprocessing

Developer Target 1: 62.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z < -6.396479394109776 \cdot 10^{+136}:\\ \;\;\;\;\frac{-z}{\sqrt{3}}\\ \mathbf{elif}\;z < 7.320293694404182 \cdot 10^{+117}:\\ \;\;\;\;\frac{\sqrt{\left(z \cdot z + x \cdot x\right) + y \cdot y}}{\sqrt{3}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{0.3333333333333333} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (< z -6.396479394109776e+136)
   (/ (- z) (sqrt 3.0))
   (if (< z 7.320293694404182e+117)
     (/ (sqrt (+ (+ (* z z) (* x x)) (* y y))) (sqrt 3.0))
     (* (sqrt 0.3333333333333333) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z < -6.396479394109776e+136) {
		tmp = -z / sqrt(3.0);
	} else if (z < 7.320293694404182e+117) {
		tmp = sqrt((((z * z) + (x * x)) + (y * y))) / sqrt(3.0);
	} else {
		tmp = sqrt(0.3333333333333333) * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z < (-6.396479394109776d+136)) then
        tmp = -z / sqrt(3.0d0)
    else if (z < 7.320293694404182d+117) then
        tmp = sqrt((((z * z) + (x * x)) + (y * y))) / sqrt(3.0d0)
    else
        tmp = sqrt(0.3333333333333333d0) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z < -6.396479394109776e+136) {
		tmp = -z / Math.sqrt(3.0);
	} else if (z < 7.320293694404182e+117) {
		tmp = Math.sqrt((((z * z) + (x * x)) + (y * y))) / Math.sqrt(3.0);
	} else {
		tmp = Math.sqrt(0.3333333333333333) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z < -6.396479394109776e+136:
		tmp = -z / math.sqrt(3.0)
	elif z < 7.320293694404182e+117:
		tmp = math.sqrt((((z * z) + (x * x)) + (y * y))) / math.sqrt(3.0)
	else:
		tmp = math.sqrt(0.3333333333333333) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z < -6.396479394109776e+136)
		tmp = Float64(Float64(-z) / sqrt(3.0));
	elseif (z < 7.320293694404182e+117)
		tmp = Float64(sqrt(Float64(Float64(Float64(z * z) + Float64(x * x)) + Float64(y * y))) / sqrt(3.0));
	else
		tmp = Float64(sqrt(0.3333333333333333) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z < -6.396479394109776e+136)
		tmp = -z / sqrt(3.0);
	elseif (z < 7.320293694404182e+117)
		tmp = sqrt((((z * z) + (x * x)) + (y * y))) / sqrt(3.0);
	else
		tmp = sqrt(0.3333333333333333) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Less[z, -6.396479394109776e+136], N[((-z) / N[Sqrt[3.0], $MachinePrecision]), $MachinePrecision], If[Less[z, 7.320293694404182e+117], N[(N[Sqrt[N[(N[(N[(z * z), $MachinePrecision] + N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[Sqrt[3.0], $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[0.3333333333333333], $MachinePrecision] * z), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024321 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.Pixel:doubleRmsOfRGB8 from repa-algorithms-3.4.0.1"
  :precision binary64
  :pre (TRUE)

  :alt
  (! :herbie-platform default (if (< z -63964793941097760000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- z) (sqrt 3)) (if (< z 7320293694404182000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (sqrt (+ (+ (* z z) (* x x)) (* y y))) (sqrt 3)) (* (sqrt 3333333333333333/10000000000000000) z))))

  (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)))