FRP.Yampa.Vector3:vector3Rho from Yampa-0.10.2

Percentage Accurate: 45.9% → 100.0%

Time: 10.8s

Alternatives: 3

Speedup: 1.1×

Specification

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]

Initial Program: 45.9% accurate, 1.0× 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]

Alternative 1: 100.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \mathsf{hypot}\left(\mathsf{hypot}\left(z, y\right), x\right) \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z)
	return hypot(hypot(z, y), x)
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[Sqrt[N[Sqrt[z ^ 2 + y ^ 2], $MachinePrecision] ^ 2 + x ^ 2], $MachinePrecision]

Derivation

1. Initial program 36.4%

   \[\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z} \]
2. Step-by-step derivation

   1. associate-+l+ 36.4%

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

   2. +-commutative 36.4%

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

   3. add-sqr-sqrt 36.4%

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

   4. hypot-def 52.5%

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

   5. hypot-def 100.0%

      \[\leadsto \mathsf{hypot}\left(\color{blue}{\mathsf{hypot}\left(y, z\right)}, x\right) \]

3. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\mathsf{hypot}\left(\mathsf{hypot}\left(y, z\right), x\right)} \]
4. Step-by-step derivation

   1. hypot-def 52.5%

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

   2. +-commutative 52.5%

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

   3. hypot-def 100.0%

      \[\leadsto \mathsf{hypot}\left(\color{blue}{\mathsf{hypot}\left(z, y\right)}, x\right) \]

5. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{hypot}\left(\mathsf{hypot}\left(z, y\right), x\right)} \]

6. Final simplification 100.0%

   \[\leadsto \mathsf{hypot}\left(\mathsf{hypot}\left(z, y\right), x\right) \]

Alternative 2: 67.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{hypot}\left(z, y\right) \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z)
	return hypot(z, y)
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[Sqrt[z ^ 2 + y ^ 2], $MachinePrecision]

Derivation

1. Initial program 36.4%

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

2. Taylor expanded in x around 0 26.1%

   \[\leadsto \color{blue}{\sqrt{{z}^{2} + {y}^{2}}} \]
3. Step-by-step derivation

   1. unpow2 26.1%

      \[\leadsto \sqrt{\color{blue}{z \cdot z} + {y}^{2}} \]

   2. unpow2 26.1%

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

   3. hypot-def 66.4%

      \[\leadsto \color{blue}{\mathsf{hypot}\left(z, y\right)} \]

4. Simplified 66.4%

   \[\leadsto \color{blue}{\mathsf{hypot}\left(z, y\right)} \]

5. Final simplification 66.4%

   \[\leadsto \mathsf{hypot}\left(z, y\right) \]

Alternative 3: 18.1% accurate, 111.0× speedup

Math

\[\begin{array}{l} \\ z \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return 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 = z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 36.4%

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

2. Taylor expanded in z around inf 19.2%

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

3. Final simplification 19.2%

   \[\leadsto z \]

Developer target: 62.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023278 
(FPCore (x y z)
  :name "FRP.Yampa.Vector3:vector3Rho from Yampa-0.10.2"
  :precision binary64

  :herbie-target
  (if (< z -6.396479394109776e+136) (- z) (if (< z 7.320293694404182e+117) (sqrt (+ (+ (* z z) (* x x)) (* y y))) z))

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