Linear.Quaternion:$c/ from linear-1.19.1.3, A

Percentage Accurate: 98.5% → 98.6%

Time: 4.2s

Alternatives: 6

Speedup: 1.7×

• 34.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.6% accurate, 0.0× speedup

Math

\[\begin{array}{l} z = |z|\\ \\ \mathsf{fma}\left(\left(z \cdot 3\right) \cdot \sqrt{z}, \sqrt{z}, x \cdot y\right) \end{array} \]

FPCore

NOTE: z should be positive before calling this function
(FPCore (x y z)
 :precision binary64
 (fma (* (* z 3.0) (sqrt z)) (sqrt z) (* x y)))

C

z = abs(z);
double code(double x, double y, double z) {
	return fma(((z * 3.0) * sqrt(z)), sqrt(z), (x * y));
}

Julia

z = abs(z)
function code(x, y, z)
	return fma(Float64(Float64(z * 3.0) * sqrt(z)), sqrt(z), Float64(x * y))
end

Wolfram

NOTE: z should be positive before calling this function
code[x_, y_, z_] := N[(N[(N[(z * 3.0), $MachinePrecision] * N[Sqrt[z], $MachinePrecision]), $MachinePrecision] * N[Sqrt[z], $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.1%

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

   1. associate-+l+ 99.1%

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

   2. associate-+l+ 99.1%

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

   3. fma-def 99.1%

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

   4. count-2 99.1%

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

   5. distribute-rgt1-in 99.1%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(2 + 1\right) \cdot \left(z \cdot z\right)}\right) \]

   6. *-commutative 99.1%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(z \cdot z\right) \cdot \left(2 + 1\right)}\right) \]

   7. associate-*l* 99.1%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(z \cdot \left(2 + 1\right)\right)}\right) \]

   8. metadata-eval 99.1%

      \[\leadsto \mathsf{fma}\left(x, y, z \cdot \left(z \cdot \color{blue}{3}\right)\right) \]

3. Simplified 99.1%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(z \cdot 3\right)\right)} \]
4. Step-by-step derivation

   1. fma-udef 99.1%

      \[\leadsto \color{blue}{x \cdot y + z \cdot \left(z \cdot 3\right)} \]

   2. +-commutative 99.1%

      \[\leadsto \color{blue}{z \cdot \left(z \cdot 3\right) + x \cdot y} \]

5. Applied egg-rr 99.1%

   \[\leadsto \color{blue}{z \cdot \left(z \cdot 3\right) + x \cdot y} \]
6. Step-by-step derivation

   1. associate-*r* 99.1%

      \[\leadsto \color{blue}{\left(z \cdot z\right) \cdot 3} + x \cdot y \]

   2. *-commutative 99.1%

      \[\leadsto \color{blue}{3 \cdot \left(z \cdot z\right)} + x \cdot y \]

   3. associate-*r* 99.1%

      \[\leadsto \color{blue}{\left(3 \cdot z\right) \cdot z} + x \cdot y \]

   4. *-commutative 99.1%

      \[\leadsto \color{blue}{\left(z \cdot 3\right)} \cdot z + x \cdot y \]

   5. add-sqr-sqrt 50.3%

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

   6. associate-*r* 50.3%

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

   7. fma-def 50.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot 3\right) \cdot \sqrt{z}, \sqrt{z}, x \cdot y\right)} \]

7. Applied egg-rr 50.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot 3\right) \cdot \sqrt{z}, \sqrt{z}, x \cdot y\right)} \]

8. Final simplification 50.7%

   \[\leadsto \mathsf{fma}\left(\left(z \cdot 3\right) \cdot \sqrt{z}, \sqrt{z}, x \cdot y\right) \]

Alternative 2: 99.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} z = |z|\\ \\ \mathsf{fma}\left(z, z, \mathsf{fma}\left(x, y, z \cdot \left(z + z\right)\right)\right) \end{array} \]

FPCore

NOTE: z should be positive before calling this function
(FPCore (x y z) :precision binary64 (fma z z (fma x y (* z (+ z z)))))

C

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

Julia

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

Wolfram

NOTE: z should be positive before calling this function
code[x_, y_, z_] := N[(z * z + N[(x * y + N[(z * N[(z + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.1%

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

   1. +-commutative 99.1%

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

   2. fma-def 99.2%

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

   3. associate-+l+ 99.2%

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

   4. fma-def 99.2%

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

   5. distribute-lft-out 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

   \[\leadsto \mathsf{fma}\left(z, z, \mathsf{fma}\left(x, y, z \cdot \left(z + z\right)\right)\right) \]

Alternative 3: 81.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} z = |z|\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{-153} \lor \neg \left(z \cdot z \leq 5 \cdot 10^{+19}\right) \land z \cdot z \leq 2 \cdot 10^{+90}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(z \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z should be positive before calling this function
(FPCore (x y z)
 :precision binary64
 (if (or (<= (* z z) 5e-153) (and (not (<= (* z z) 5e+19)) (<= (* z z) 2e+90)))
   (* x y)
   (* 3.0 (* z z))))

C

z = abs(z);
double code(double x, double y, double z) {
	double tmp;
	if (((z * z) <= 5e-153) || (!((z * z) <= 5e+19) && ((z * z) <= 2e+90))) {
		tmp = x * y;
	} else {
		tmp = 3.0 * (z * z);
	}
	return tmp;
}

Fortran

NOTE: z should be positive before calling this function
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 * z) <= 5d-153) .or. (.not. ((z * z) <= 5d+19)) .and. ((z * z) <= 2d+90)) then
        tmp = x * y
    else
        tmp = 3.0d0 * (z * z)
    end if
    code = tmp
end function

Java

z = Math.abs(z);
public static double code(double x, double y, double z) {
	double tmp;
	if (((z * z) <= 5e-153) || (!((z * z) <= 5e+19) && ((z * z) <= 2e+90))) {
		tmp = x * y;
	} else {
		tmp = 3.0 * (z * z);
	}
	return tmp;
}

Python

z = abs(z)
def code(x, y, z):
	tmp = 0
	if ((z * z) <= 5e-153) or (not ((z * z) <= 5e+19) and ((z * z) <= 2e+90)):
		tmp = x * y
	else:
		tmp = 3.0 * (z * z)
	return tmp

Julia

z = abs(z)
function code(x, y, z)
	tmp = 0.0
	if ((Float64(z * z) <= 5e-153) || (!(Float64(z * z) <= 5e+19) && (Float64(z * z) <= 2e+90)))
		tmp = Float64(x * y);
	else
		tmp = Float64(3.0 * Float64(z * z));
	end
	return tmp
end

MATLAB

z = abs(z)
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((z * z) <= 5e-153) || (~(((z * z) <= 5e+19)) && ((z * z) <= 2e+90)))
		tmp = x * y;
	else
		tmp = 3.0 * (z * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z should be positive before calling this function
code[x_, y_, z_] := If[Or[LessEqual[N[(z * z), $MachinePrecision], 5e-153], And[N[Not[LessEqual[N[(z * z), $MachinePrecision], 5e+19]], $MachinePrecision], LessEqual[N[(z * z), $MachinePrecision], 2e+90]]], N[(x * y), $MachinePrecision], N[(3.0 * N[(z * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 5.00000000000000033e-153 or 5e19 < (*.f64 z z) < 1.99999999999999993e90

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 93.6%

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

   if 5.00000000000000033e-153 < (*.f64 z z) < 5e19 or 1.99999999999999993e90 < (*.f64 z z)

   1. Initial program 98.4%

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

   2. Taylor expanded in x around 0 82.8%

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

      1. unpow2 82.8%

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

      2. unpow2 82.8%

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

      3. distribute-rgt1-in 82.8%

         \[\leadsto \color{blue}{\left(2 + 1\right) \cdot \left(z \cdot z\right)} \]

      4. metadata-eval 82.8%

         \[\leadsto \color{blue}{3} \cdot \left(z \cdot z\right) \]

   4. Simplified 82.8%

      \[\leadsto \color{blue}{3 \cdot \left(z \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{-153} \lor \neg \left(z \cdot z \leq 5 \cdot 10^{+19}\right) \land z \cdot z \leq 2 \cdot 10^{+90}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(z \cdot z\right)\\ \end{array} \]

Alternative 4: 98.5% accurate, 1.0× speedup

Math

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

FPCore

NOTE: z should be positive before calling this function
(FPCore (x y z)
 :precision binary64
 (+ (* z z) (+ (* z z) (+ (* x y) (* z z)))))

C

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

Fortran

NOTE: z should be positive before calling this function
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (z * z) + ((z * z) + ((x * y) + (z * z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: z should be positive before calling this function
code[x_, y_, z_] := N[(N[(z * z), $MachinePrecision] + N[(N[(z * z), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.1%

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

2. Final simplification 99.1%

   \[\leadsto z \cdot z + \left(z \cdot z + \left(x \cdot y + z \cdot z\right)\right) \]

Alternative 5: 98.5% accurate, 1.7× speedup

Math

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

FPCore

NOTE: z should be positive before calling this function
(FPCore (x y z) :precision binary64 (+ (* x y) (* z (* z 3.0))))

C

z = abs(z);
double code(double x, double y, double z) {
	return (x * y) + (z * (z * 3.0));
}

Fortran

NOTE: z should be positive before calling this function
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * y) + (z * (z * 3.0d0))
end function

Java

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

Python

z = abs(z)
def code(x, y, z):
	return (x * y) + (z * (z * 3.0))

Julia

z = abs(z)
function code(x, y, z)
	return Float64(Float64(x * y) + Float64(z * Float64(z * 3.0)))
end

MATLAB

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

Wolfram

NOTE: z should be positive before calling this function
code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(z * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.1%

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

   1. associate-+l+ 99.1%

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

   2. associate-+l+ 99.1%

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

   3. fma-def 99.1%

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

   4. count-2 99.1%

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

   5. distribute-rgt1-in 99.1%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(2 + 1\right) \cdot \left(z \cdot z\right)}\right) \]

   6. *-commutative 99.1%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(z \cdot z\right) \cdot \left(2 + 1\right)}\right) \]

   7. associate-*l* 99.1%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(z \cdot \left(2 + 1\right)\right)}\right) \]

   8. metadata-eval 99.1%

      \[\leadsto \mathsf{fma}\left(x, y, z \cdot \left(z \cdot \color{blue}{3}\right)\right) \]

3. Simplified 99.1%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(z \cdot 3\right)\right)} \]
4. Step-by-step derivation

   1. fma-udef 99.1%

      \[\leadsto \color{blue}{x \cdot y + z \cdot \left(z \cdot 3\right)} \]

   2. +-commutative 99.1%

      \[\leadsto \color{blue}{z \cdot \left(z \cdot 3\right) + x \cdot y} \]

5. Applied egg-rr 99.1%

   \[\leadsto \color{blue}{z \cdot \left(z \cdot 3\right) + x \cdot y} \]

6. Final simplification 99.1%

   \[\leadsto x \cdot y + z \cdot \left(z \cdot 3\right) \]

Alternative 6: 53.4% accurate, 5.0× speedup

Math

\[\begin{array}{l} z = |z|\\ \\ x \cdot y \end{array} \]

FPCore

NOTE: z should be positive before calling this function
(FPCore (x y z) :precision binary64 (* x y))

C

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

Fortran

NOTE: z should be positive before calling this function
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: z should be positive before calling this function
code[x_, y_, z_] := N[(x * y), $MachinePrecision]

Derivation

1. Initial program 99.1%

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

2. Taylor expanded in x around inf 55.4%

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

3. Final simplification 55.4%

   \[\leadsto x \cdot y \]

Developer target: 98.5% accurate, 1.7× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return ((3.0 * z) * z) + (y * 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 = ((3.0d0 * z) * z) + (y * x)
end function

Java

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

Python

def code(x, y, z):
	return ((3.0 * z) * z) + (y * x)

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023230 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (+ (* (* 3.0 z) z) (* y x))

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