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

Percentage Accurate: 99.8% → 99.8%

Time: 5.4s

Alternatives: 5

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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

   1. +-commutative 99.5%

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

   2. distribute-lft-in 99.5%

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

   3. *-commutative 99.5%

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

   4. associate-*l* 99.8%

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

5. Applied egg-rr 99.8%

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

6. Final simplification 99.8%

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

Alternative 2: 76.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \sqrt{z}\\ \mathbf{if}\;t_0 \leq -0.05 \lor \neg \left(t_0 \leq 10^{+49}\right):\\ \;\;\;\;0.5 \cdot t_0\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (sqrt z))))
   (if (or (<= t_0 -0.05) (not (<= t_0 1e+49))) (* 0.5 t_0) (* 0.5 x))))

C

double code(double x, double y, double z) {
	double t_0 = y * sqrt(z);
	double tmp;
	if ((t_0 <= -0.05) || !(t_0 <= 1e+49)) {
		tmp = 0.5 * t_0;
	} else {
		tmp = 0.5 * x;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = y * sqrt(z)
    if ((t_0 <= (-0.05d0)) .or. (.not. (t_0 <= 1d+49))) then
        tmp = 0.5d0 * t_0
    else
        tmp = 0.5d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * Math.sqrt(z);
	double tmp;
	if ((t_0 <= -0.05) || !(t_0 <= 1e+49)) {
		tmp = 0.5 * t_0;
	} else {
		tmp = 0.5 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * math.sqrt(z)
	tmp = 0
	if (t_0 <= -0.05) or not (t_0 <= 1e+49):
		tmp = 0.5 * t_0
	else:
		tmp = 0.5 * x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * sqrt(z))
	tmp = 0.0
	if ((t_0 <= -0.05) || !(t_0 <= 1e+49))
		tmp = Float64(0.5 * t_0);
	else
		tmp = Float64(0.5 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * sqrt(z);
	tmp = 0.0;
	if ((t_0 <= -0.05) || ~((t_0 <= 1e+49)))
		tmp = 0.5 * t_0;
	else
		tmp = 0.5 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -0.05], N[Not[LessEqual[t$95$0, 1e+49]], $MachinePrecision]], N[(0.5 * t$95$0), $MachinePrecision], N[(0.5 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (sqrt.f64 z)) < -0.050000000000000003 or 9.99999999999999946e48 < (*.f64 y (sqrt.f64 z))

   1. Initial program 99.0%

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

      1. metadata-eval 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in x around 0 85.5%

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

   if -0.050000000000000003 < (*.f64 y (sqrt.f64 z)) < 9.99999999999999946e48

   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. Taylor expanded in x around inf 83.1%

      \[\leadsto \color{blue}{0.5 \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \sqrt{z} \leq -0.05 \lor \neg \left(y \cdot \sqrt{z} \leq 10^{+49}\right):\\ \;\;\;\;0.5 \cdot \left(y \cdot \sqrt{z}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot x\\ \end{array} \]

Alternative 3: 76.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \sqrt{z}\\ \mathbf{if}\;t_0 \leq -0.05:\\ \;\;\;\;\sqrt{z} \cdot \left(y \cdot 0.5\right)\\ \mathbf{elif}\;t_0 \leq 10^{+49}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (sqrt z))))
   (if (<= t_0 -0.05)
     (* (sqrt z) (* y 0.5))
     (if (<= t_0 1e+49) (* 0.5 x) (* 0.5 t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = y * sqrt(z);
	double tmp;
	if (t_0 <= -0.05) {
		tmp = sqrt(z) * (y * 0.5);
	} else if (t_0 <= 1e+49) {
		tmp = 0.5 * x;
	} else {
		tmp = 0.5 * t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = y * sqrt(z)
    if (t_0 <= (-0.05d0)) then
        tmp = sqrt(z) * (y * 0.5d0)
    else if (t_0 <= 1d+49) then
        tmp = 0.5d0 * x
    else
        tmp = 0.5d0 * t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * Math.sqrt(z);
	double tmp;
	if (t_0 <= -0.05) {
		tmp = Math.sqrt(z) * (y * 0.5);
	} else if (t_0 <= 1e+49) {
		tmp = 0.5 * x;
	} else {
		tmp = 0.5 * t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * math.sqrt(z)
	tmp = 0
	if t_0 <= -0.05:
		tmp = math.sqrt(z) * (y * 0.5)
	elif t_0 <= 1e+49:
		tmp = 0.5 * x
	else:
		tmp = 0.5 * t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * sqrt(z))
	tmp = 0.0
	if (t_0 <= -0.05)
		tmp = Float64(sqrt(z) * Float64(y * 0.5));
	elseif (t_0 <= 1e+49)
		tmp = Float64(0.5 * x);
	else
		tmp = Float64(0.5 * t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * sqrt(z);
	tmp = 0.0;
	if (t_0 <= -0.05)
		tmp = sqrt(z) * (y * 0.5);
	elseif (t_0 <= 1e+49)
		tmp = 0.5 * x;
	else
		tmp = 0.5 * t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.05], N[(N[Sqrt[z], $MachinePrecision] * N[(y * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1e+49], N[(0.5 * x), $MachinePrecision], N[(0.5 * t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y (sqrt.f64 z)) < -0.050000000000000003

   1. Initial program 98.3%

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

      1. metadata-eval 98.3%

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

   3. Simplified 98.3%

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

      1. *-commutative 98.3%

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

      2. flip-+ 37.7%

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

      3. associate-*l/ 37.7%

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

      4. *-commutative 37.7%

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

      5. *-commutative 37.7%

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

      6. swap-sqr 27.3%

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

      7. add-sqr-sqrt 27.2%

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

   5. Applied egg-rr 27.2%

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

   6. Taylor expanded in x around 0 25.3%

      \[\leadsto \frac{\color{blue}{\left(-1 \cdot \left({y}^{2} \cdot z\right)\right)} \cdot 0.5}{x - y \cdot \sqrt{z}} \]
   7. Step-by-step derivation

      1. unpow2 25.3%

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

      2. associate-*r* 25.3%

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

      3. neg-mul-1 25.3%

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

      4. distribute-rgt-neg-out 25.3%

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

      5. associate-*r* 35.4%

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

   8. Simplified 35.4%

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

   9. Taylor expanded in y around inf 82.9%

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

       1. associate-*r* 84.3%

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

       2. *-commutative 84.3%

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

   11. Simplified 84.3%

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

   if -0.050000000000000003 < (*.f64 y (sqrt.f64 z)) < 9.99999999999999946e48

   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. Taylor expanded in x around inf 83.1%

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

   if 9.99999999999999946e48 < (*.f64 y (sqrt.f64 z))

   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. Taylor expanded in x around 0 87.9%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \sqrt{z} \leq -0.05:\\ \;\;\;\;\sqrt{z} \cdot \left(y \cdot 0.5\right)\\ \mathbf{elif}\;y \cdot \sqrt{z} \leq 10^{+49}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \sqrt{z}\right)\\ \end{array} \]

Alternative 4: 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 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

4. Final simplification 99.5%

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

Alternative 5: 50.4% 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 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

4. Taylor expanded in x around inf 52.5%

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

5. Final simplification 52.5%

   \[\leadsto 0.5 \cdot x \]

Reproduce

herbie shell --seed 2023215 
(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)))))