Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B

Percentage Accurate: 99.8% → 99.8%

Time: 7.9s

Alternatives: 4

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))

C

double code(double x, double y, double z) {
	return (1.0 / 2.0) * (x + (y * sqrt(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 = (1.0d0 / 2.0d0) * (x + (y * sqrt(z)))
end function

Java

public static double code(double x, double y, double z) {
	return (1.0 / 2.0) * (x + (y * Math.sqrt(z)));
}

Python

def code(x, y, z):
	return (1.0 / 2.0) * (x + (y * math.sqrt(z)))

Julia

function code(x, y, z)
	return Float64(Float64(1.0 / 2.0) * Float64(x + Float64(y * sqrt(z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (1.0 / 2.0) * (x + (y * sqrt(z)));
end

Wolfram

code[x_, y_, z_] := N[(N[(1.0 / 2.0), $MachinePrecision] * N[(x + N[(y * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))

C

double code(double x, double y, double z) {
	return (1.0 / 2.0) * (x + (y * sqrt(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 = (1.0d0 / 2.0d0) * (x + (y * sqrt(z)))
end function

Java

public static double code(double x, double y, double z) {
	return (1.0 / 2.0) * (x + (y * Math.sqrt(z)));
}

Python

def code(x, y, z):
	return (1.0 / 2.0) * (x + (y * math.sqrt(z)))

Julia

function code(x, y, z)
	return Float64(Float64(1.0 / 2.0) * Float64(x + Float64(y * sqrt(z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (1.0 / 2.0) * (x + (y * sqrt(z)));
end

Wolfram

code[x_, y_, z_] := N[(N[(1.0 / 2.0), $MachinePrecision] * N[(x + N[(y * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \left(x + \frac{y}{{z}^{-0.5}}\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* 0.5 (+ x (/ y (pow z -0.5)))))

C

double code(double x, double y, double z) {
	return 0.5 * (x + (y / pow(z, -0.5)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 0.5d0 * (x + (y / (z ** (-0.5d0))))
end function

Java

public static double code(double x, double y, double z) {
	return 0.5 * (x + (y / Math.pow(z, -0.5)));
}

Python

def code(x, y, z):
	return 0.5 * (x + (y / math.pow(z, -0.5)))

Julia

function code(x, y, z)
	return Float64(0.5 * Float64(x + Float64(y / (z ^ -0.5))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.5 * (x + (y / (z ^ -0.5)));
end

Wolfram

code[x_, y_, z_] := N[(0.5 * N[(x + N[(y / N[Power[z, -0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]
2. Step-by-step derivation

   1. metadata-eval 99.8%

      \[\leadsto \color{blue}{0.5} \cdot \left(x + y \cdot \sqrt{z}\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{0.5 \cdot \left(x + y \cdot \sqrt{z}\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. add0 99.8%

      \[\leadsto 0.5 \cdot \left(x + \color{blue}{\left(y \cdot \sqrt{z} + 0\right)}\right) \]

   2. flip-+ 70.1%

      \[\leadsto 0.5 \cdot \left(x + \color{blue}{\frac{\left(y \cdot \sqrt{z}\right) \cdot \left(y \cdot \sqrt{z}\right) - 0 \cdot 0}{y \cdot \sqrt{z} - 0}}\right) \]

   3. metadata-eval 70.1%

      \[\leadsto 0.5 \cdot \left(x + \frac{\left(y \cdot \sqrt{z}\right) \cdot \left(y \cdot \sqrt{z}\right) - \color{blue}{0}}{y \cdot \sqrt{z} - 0}\right) \]

   4. fma-neg 70.1%

      \[\leadsto 0.5 \cdot \left(x + \frac{\color{blue}{\mathsf{fma}\left(y \cdot \sqrt{z}, y \cdot \sqrt{z}, -0\right)}}{y \cdot \sqrt{z} - 0}\right) \]

   5. metadata-eval 70.1%

      \[\leadsto 0.5 \cdot \left(x + \frac{\mathsf{fma}\left(y \cdot \sqrt{z}, y \cdot \sqrt{z}, \color{blue}{0}\right)}{y \cdot \sqrt{z} - 0}\right) \]

   6. fma-define 70.1%

      \[\leadsto 0.5 \cdot \left(x + \frac{\color{blue}{\left(y \cdot \sqrt{z}\right) \cdot \left(y \cdot \sqrt{z}\right) + 0}}{y \cdot \sqrt{z} - 0}\right) \]

   7. add0 70.1%

      \[\leadsto 0.5 \cdot \left(x + \frac{\color{blue}{\left(y \cdot \sqrt{z}\right) \cdot \left(y \cdot \sqrt{z}\right)}}{y \cdot \sqrt{z} - 0}\right) \]

   8. *-commutative 70.1%

      \[\leadsto 0.5 \cdot \left(x + \frac{\color{blue}{\left(\sqrt{z} \cdot y\right)} \cdot \left(y \cdot \sqrt{z}\right)}{y \cdot \sqrt{z} - 0}\right) \]

   9. *-commutative 70.1%

      \[\leadsto 0.5 \cdot \left(x + \frac{\left(\sqrt{z} \cdot y\right) \cdot \color{blue}{\left(\sqrt{z} \cdot y\right)}}{y \cdot \sqrt{z} - 0}\right) \]

   10. swap-sqr 61.2%

       \[\leadsto 0.5 \cdot \left(x + \frac{\color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right) \cdot \left(y \cdot y\right)}}{y \cdot \sqrt{z} - 0}\right) \]

   11. add-sqr-sqrt 61.2%

       \[\leadsto 0.5 \cdot \left(x + \frac{\color{blue}{z} \cdot \left(y \cdot y\right)}{y \cdot \sqrt{z} - 0}\right) \]

   12. pow2 61.2%

       \[\leadsto 0.5 \cdot \left(x + \frac{z \cdot \color{blue}{{y}^{2}}}{y \cdot \sqrt{z} - 0}\right) \]

   13. fma-neg 61.2%

       \[\leadsto 0.5 \cdot \left(x + \frac{z \cdot {y}^{2}}{\color{blue}{\mathsf{fma}\left(y, \sqrt{z}, -0\right)}}\right) \]

   14. metadata-eval 61.2%

       \[\leadsto 0.5 \cdot \left(x + \frac{z \cdot {y}^{2}}{\mathsf{fma}\left(y, \sqrt{z}, \color{blue}{0}\right)}\right) \]

   15. fma-define 61.2%

       \[\leadsto 0.5 \cdot \left(x + \frac{z \cdot {y}^{2}}{\color{blue}{y \cdot \sqrt{z} + 0}}\right) \]

   16. add0 61.2%

       \[\leadsto 0.5 \cdot \left(x + \frac{z \cdot {y}^{2}}{\color{blue}{y \cdot \sqrt{z}}}\right) \]

6. Applied egg-rr 61.2%

   \[\leadsto 0.5 \cdot \left(x + \color{blue}{\frac{z \cdot {y}^{2}}{y \cdot \sqrt{z}}}\right) \]
7. Step-by-step derivation

   1. associate-/l* 68.4%

      \[\leadsto 0.5 \cdot \left(x + \color{blue}{\frac{z}{\frac{y \cdot \sqrt{z}}{{y}^{2}}}}\right) \]

   2. unpow2 68.4%

      \[\leadsto 0.5 \cdot \left(x + \frac{z}{\frac{y \cdot \sqrt{z}}{\color{blue}{y \cdot y}}}\right) \]

   3. times-frac 92.2%

      \[\leadsto 0.5 \cdot \left(x + \frac{z}{\color{blue}{\frac{y}{y} \cdot \frac{\sqrt{z}}{y}}}\right) \]

   4. *-inverses 92.2%

      \[\leadsto 0.5 \cdot \left(x + \frac{z}{\color{blue}{1} \cdot \frac{\sqrt{z}}{y}}\right) \]

   5. associate-*r/ 92.2%

      \[\leadsto 0.5 \cdot \left(x + \frac{z}{\color{blue}{\frac{1 \cdot \sqrt{z}}{y}}}\right) \]

   6. *-lft-identity 92.2%

      \[\leadsto 0.5 \cdot \left(x + \frac{z}{\frac{\color{blue}{\sqrt{z}}}{y}}\right) \]

8. Simplified 92.2%

   \[\leadsto 0.5 \cdot \left(x + \color{blue}{\frac{z}{\frac{\sqrt{z}}{y}}}\right) \]
9. Step-by-step derivation

   1. clear-num 92.2%

      \[\leadsto 0.5 \cdot \left(x + \color{blue}{\frac{1}{\frac{\frac{\sqrt{z}}{y}}{z}}}\right) \]

   2. associate-/r/ 91.5%

      \[\leadsto 0.5 \cdot \left(x + \color{blue}{\frac{1}{\frac{\sqrt{z}}{y}} \cdot z}\right) \]

   3. clear-num 91.5%

      \[\leadsto 0.5 \cdot \left(x + \color{blue}{\frac{y}{\sqrt{z}}} \cdot z\right) \]

10. Applied egg-rr 91.5%

    \[\leadsto 0.5 \cdot \left(x + \color{blue}{\frac{y}{\sqrt{z}} \cdot z}\right) \]
11. Step-by-step derivation

    1. associate-*l/ 92.7%

       \[\leadsto 0.5 \cdot \left(x + \color{blue}{\frac{y \cdot z}{\sqrt{z}}}\right) \]

    2. associate-/l* 99.7%

       \[\leadsto 0.5 \cdot \left(x + \color{blue}{\frac{y}{\frac{\sqrt{z}}{z}}}\right) \]

12. Applied egg-rr 99.7%

    \[\leadsto 0.5 \cdot \left(x + \color{blue}{\frac{y}{\frac{\sqrt{z}}{z}}}\right) \]
13. Step-by-step derivation

    1. *-un-lft-identity 99.7%

       \[\leadsto 0.5 \cdot \left(x + \frac{\color{blue}{1 \cdot y}}{\frac{\sqrt{z}}{z}}\right) \]

    2. add-sqr-sqrt 99.4%

       \[\leadsto 0.5 \cdot \left(x + \frac{1 \cdot y}{\color{blue}{\sqrt{\frac{\sqrt{z}}{z}} \cdot \sqrt{\frac{\sqrt{z}}{z}}}}\right) \]

    3. times-frac 99.5%

       \[\leadsto 0.5 \cdot \left(x + \color{blue}{\frac{1}{\sqrt{\frac{\sqrt{z}}{z}}} \cdot \frac{y}{\sqrt{\frac{\sqrt{z}}{z}}}}\right) \]

    4. pow1/2 99.5%

       \[\leadsto 0.5 \cdot \left(x + \frac{1}{\sqrt{\frac{\color{blue}{{z}^{0.5}}}{z}}} \cdot \frac{y}{\sqrt{\frac{\sqrt{z}}{z}}}\right) \]

    5. pow1 99.5%

       \[\leadsto 0.5 \cdot \left(x + \frac{1}{\sqrt{\frac{{z}^{0.5}}{\color{blue}{{z}^{1}}}}} \cdot \frac{y}{\sqrt{\frac{\sqrt{z}}{z}}}\right) \]

    6. pow-div 99.5%

       \[\leadsto 0.5 \cdot \left(x + \frac{1}{\sqrt{\color{blue}{{z}^{\left(0.5 - 1\right)}}}} \cdot \frac{y}{\sqrt{\frac{\sqrt{z}}{z}}}\right) \]

    7. metadata-eval 99.5%

       \[\leadsto 0.5 \cdot \left(x + \frac{1}{\sqrt{{z}^{\color{blue}{-0.5}}}} \cdot \frac{y}{\sqrt{\frac{\sqrt{z}}{z}}}\right) \]

    8. pow1/2 99.5%

       \[\leadsto 0.5 \cdot \left(x + \frac{1}{\sqrt{{z}^{-0.5}}} \cdot \frac{y}{\sqrt{\frac{\color{blue}{{z}^{0.5}}}{z}}}\right) \]

    9. pow1 99.5%

       \[\leadsto 0.5 \cdot \left(x + \frac{1}{\sqrt{{z}^{-0.5}}} \cdot \frac{y}{\sqrt{\frac{{z}^{0.5}}{\color{blue}{{z}^{1}}}}}\right) \]

    10. pow-div 99.5%

        \[\leadsto 0.5 \cdot \left(x + \frac{1}{\sqrt{{z}^{-0.5}}} \cdot \frac{y}{\sqrt{\color{blue}{{z}^{\left(0.5 - 1\right)}}}}\right) \]

    11. metadata-eval 99.5%

        \[\leadsto 0.5 \cdot \left(x + \frac{1}{\sqrt{{z}^{-0.5}}} \cdot \frac{y}{\sqrt{{z}^{\color{blue}{-0.5}}}}\right) \]

14. Applied egg-rr 99.5%

    \[\leadsto 0.5 \cdot \left(x + \color{blue}{\frac{1}{\sqrt{{z}^{-0.5}}} \cdot \frac{y}{\sqrt{{z}^{-0.5}}}}\right) \]
15. Step-by-step derivation

    1. associate-*l/ 99.5%

       \[\leadsto 0.5 \cdot \left(x + \color{blue}{\frac{1 \cdot \frac{y}{\sqrt{{z}^{-0.5}}}}{\sqrt{{z}^{-0.5}}}}\right) \]

    2. *-lft-identity 99.5%

       \[\leadsto 0.5 \cdot \left(x + \frac{\color{blue}{\frac{y}{\sqrt{{z}^{-0.5}}}}}{\sqrt{{z}^{-0.5}}}\right) \]

    3. associate-/r* 99.5%

       \[\leadsto 0.5 \cdot \left(x + \color{blue}{\frac{y}{\sqrt{{z}^{-0.5}} \cdot \sqrt{{z}^{-0.5}}}}\right) \]

    4. rem-square-sqrt 99.8%

       \[\leadsto 0.5 \cdot \left(x + \frac{y}{\color{blue}{{z}^{-0.5}}}\right) \]

16. Simplified 99.8%

    \[\leadsto 0.5 \cdot \left(x + \color{blue}{\frac{y}{{z}^{-0.5}}}\right) \]

17. Final simplification 99.8%

    \[\leadsto 0.5 \cdot \left(x + \frac{y}{{z}^{-0.5}}\right) \]
18. Add Preprocessing

Alternative 2: 72.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+16} \lor \neg \left(x \leq 9.5 \cdot 10^{-21}\right):\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \sqrt{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.8e+16) (not (<= x 9.5e-21)))
   (* 0.5 x)
   (* 0.5 (* y (sqrt z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.8e+16) || !(x <= 9.5e-21)) {
		tmp = 0.5 * x;
	} else {
		tmp = 0.5 * (y * sqrt(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 ((x <= (-6.8d+16)) .or. (.not. (x <= 9.5d-21))) then
        tmp = 0.5d0 * x
    else
        tmp = 0.5d0 * (y * sqrt(z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.8e+16) || !(x <= 9.5e-21)) {
		tmp = 0.5 * x;
	} else {
		tmp = 0.5 * (y * Math.sqrt(z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.8e+16) or not (x <= 9.5e-21):
		tmp = 0.5 * x
	else:
		tmp = 0.5 * (y * math.sqrt(z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.8e+16) || !(x <= 9.5e-21))
		tmp = Float64(0.5 * x);
	else
		tmp = Float64(0.5 * Float64(y * sqrt(z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.8e+16) || ~((x <= 9.5e-21)))
		tmp = 0.5 * x;
	else
		tmp = 0.5 * (y * sqrt(z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.8e+16], N[Not[LessEqual[x, 9.5e-21]], $MachinePrecision]], N[(0.5 * x), $MachinePrecision], N[(0.5 * N[(y * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.8e16 or 9.4999999999999994e-21 < x

   1. Initial program 99.9%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.9%

         \[\leadsto \color{blue}{0.5} \cdot \left(x + y \cdot \sqrt{z}\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{0.5 \cdot \left(x + y \cdot \sqrt{z}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 78.3%

      \[\leadsto 0.5 \cdot \color{blue}{x} \]

   if -6.8e16 < x < 9.4999999999999994e-21

   1. Initial program 99.7%

      \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.7%

         \[\leadsto \color{blue}{0.5} \cdot \left(x + y \cdot \sqrt{z}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{0.5 \cdot \left(x + y \cdot \sqrt{z}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 77.0%

      \[\leadsto 0.5 \cdot \color{blue}{\left(y \cdot \sqrt{z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+16} \lor \neg \left(x \leq 9.5 \cdot 10^{-21}\right):\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \sqrt{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \left(x + y \cdot \sqrt{z}\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* 0.5 (+ x (* y (sqrt z)))))

C

double code(double x, double y, double z) {
	return 0.5 * (x + (y * sqrt(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 = 0.5d0 * (x + (y * sqrt(z)))
end function

Java

public static double code(double x, double y, double z) {
	return 0.5 * (x + (y * Math.sqrt(z)));
}

Python

def code(x, y, z):
	return 0.5 * (x + (y * math.sqrt(z)))

Julia

function code(x, y, z)
	return Float64(0.5 * Float64(x + Float64(y * sqrt(z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.5 * (x + (y * sqrt(z)));
end

Wolfram

code[x_, y_, z_] := N[(0.5 * N[(x + N[(y * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]
2. Step-by-step derivation

   1. metadata-eval 99.8%

      \[\leadsto \color{blue}{0.5} \cdot \left(x + y \cdot \sqrt{z}\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{0.5 \cdot \left(x + y \cdot \sqrt{z}\right)} \]
4. Add Preprocessing

5. Final simplification 99.8%

   \[\leadsto 0.5 \cdot \left(x + y \cdot \sqrt{z}\right) \]
6. Add Preprocessing

Alternative 4: 50.6% accurate, 36.3× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* 0.5 x))

C

double code(double x, double y, double z) {
	return 0.5 * 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 = 0.5d0 * x
end function

Java

public static double code(double x, double y, double z) {
	return 0.5 * x;
}

Python

def code(x, y, z):
	return 0.5 * x

Julia

function code(x, y, z)
	return Float64(0.5 * x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.5 * x;
end

Wolfram

code[x_, y_, z_] := N[(0.5 * x), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]
2. Step-by-step derivation

   1. metadata-eval 99.8%

      \[\leadsto \color{blue}{0.5} \cdot \left(x + y \cdot \sqrt{z}\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{0.5 \cdot \left(x + y \cdot \sqrt{z}\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 51.3%

   \[\leadsto 0.5 \cdot \color{blue}{x} \]

6. Final simplification 51.3%

   \[\leadsto 0.5 \cdot x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024034 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))