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

Percentage Accurate: 99.8% → 99.8%

Time: 6.2s

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, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 0.5 * fma(y, sqrt(z), x);
}

Julia

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

Wolfram

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

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

   2. +-commutative 99.8%

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

   3. fma-def 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 73.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+24}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-50} \lor \neg \left(x \leq 29500000000\right) \land x \leq 2.3 \cdot 10^{+45}:\\ \;\;\;\;0.5 \cdot \frac{y}{{z}^{-0.5}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.35e+24)
   (* 0.5 x)
   (if (or (<= x 2e-50) (and (not (<= x 29500000000.0)) (<= x 2.3e+45)))
     (* 0.5 (/ y (pow z -0.5)))
     (* 0.5 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.35e+24) {
		tmp = 0.5 * x;
	} else if ((x <= 2e-50) || (!(x <= 29500000000.0) && (x <= 2.3e+45))) {
		tmp = 0.5 * (y / pow(z, -0.5));
	} 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) :: tmp
    if (x <= (-1.35d+24)) then
        tmp = 0.5d0 * x
    else if ((x <= 2d-50) .or. (.not. (x <= 29500000000.0d0)) .and. (x <= 2.3d+45)) then
        tmp = 0.5d0 * (y / (z ** (-0.5d0)))
    else
        tmp = 0.5d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.35e+24) {
		tmp = 0.5 * x;
	} else if ((x <= 2e-50) || (!(x <= 29500000000.0) && (x <= 2.3e+45))) {
		tmp = 0.5 * (y / Math.pow(z, -0.5));
	} else {
		tmp = 0.5 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.35e+24:
		tmp = 0.5 * x
	elif (x <= 2e-50) or (not (x <= 29500000000.0) and (x <= 2.3e+45)):
		tmp = 0.5 * (y / math.pow(z, -0.5))
	else:
		tmp = 0.5 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.35e+24)
		tmp = Float64(0.5 * x);
	elseif ((x <= 2e-50) || (!(x <= 29500000000.0) && (x <= 2.3e+45)))
		tmp = Float64(0.5 * Float64(y / (z ^ -0.5)));
	else
		tmp = Float64(0.5 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.35e+24)
		tmp = 0.5 * x;
	elseif ((x <= 2e-50) || (~((x <= 29500000000.0)) && (x <= 2.3e+45)))
		tmp = 0.5 * (y / (z ^ -0.5));
	else
		tmp = 0.5 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.35e+24], N[(0.5 * x), $MachinePrecision], If[Or[LessEqual[x, 2e-50], And[N[Not[LessEqual[x, 29500000000.0]], $MachinePrecision], LessEqual[x, 2.3e+45]]], N[(0.5 * N[(y / N[Power[z, -0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.35e24 or 2.00000000000000002e-50 < x < 2.95e10 or 2.30000000000000012e45 < x

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 77.5%

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

   if -1.35e24 < x < 2.00000000000000002e-50 or 2.95e10 < x < 2.30000000000000012e45

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. +-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. add-sqr-sqrt 99.2%

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

      4. associate-*l* 99.3%

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

      5. fma-def 99.2%

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

      6. pow1/2 99.2%

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

      7. sqrt-pow1 99.4%

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

      8. metadata-eval 99.4%

         \[\leadsto 0.5 \cdot \mathsf{fma}\left({z}^{\color{blue}{0.25}}, \sqrt{\sqrt{z}} \cdot y, x\right) \]

      9. pow1/2 99.4%

         \[\leadsto 0.5 \cdot \mathsf{fma}\left({z}^{0.25}, \sqrt{\color{blue}{{z}^{0.5}}} \cdot y, x\right) \]

      10. sqrt-pow1 99.3%

          \[\leadsto 0.5 \cdot \mathsf{fma}\left({z}^{0.25}, \color{blue}{{z}^{\left(\frac{0.5}{2}\right)}} \cdot y, x\right) \]

      11. metadata-eval 99.3%

          \[\leadsto 0.5 \cdot \mathsf{fma}\left({z}^{0.25}, {z}^{\color{blue}{0.25}} \cdot y, x\right) \]

   5. Applied egg-rr 99.3%

      \[\leadsto 0.5 \cdot \color{blue}{\mathsf{fma}\left({z}^{0.25}, {z}^{0.25} \cdot y, x\right)} \]

   7. Applied egg-rr 99.5%

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

   8. Taylor expanded in y around inf 79.1%

      \[\leadsto 0.5 \cdot \frac{1}{\color{blue}{\frac{1}{y} \cdot \sqrt{\frac{1}{z}}}} \]
   9. Step-by-step derivation

      1. expm1-log1p-u 52.9%

         \[\leadsto 0.5 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{\frac{1}{y} \cdot \sqrt{\frac{1}{z}}}\right)\right)} \]

      2. expm1-udef 29.8%

         \[\leadsto 0.5 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{1}{\frac{1}{y} \cdot \sqrt{\frac{1}{z}}}\right)} - 1\right)} \]

      3. associate-*l/ 29.8%

         \[\leadsto 0.5 \cdot \left(e^{\mathsf{log1p}\left(\frac{1}{\color{blue}{\frac{1 \cdot \sqrt{\frac{1}{z}}}{y}}}\right)} - 1\right) \]

      4. *-un-lft-identity 29.8%

         \[\leadsto 0.5 \cdot \left(e^{\mathsf{log1p}\left(\frac{1}{\frac{\color{blue}{\sqrt{\frac{1}{z}}}}{y}}\right)} - 1\right) \]

      5. clear-num 29.8%

         \[\leadsto 0.5 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\sqrt{\frac{1}{z}}}}\right)} - 1\right) \]

      6. inv-pow 29.8%

         \[\leadsto 0.5 \cdot \left(e^{\mathsf{log1p}\left(\frac{y}{\sqrt{\color{blue}{{z}^{-1}}}}\right)} - 1\right) \]

      7. sqrt-pow1 29.8%

         \[\leadsto 0.5 \cdot \left(e^{\mathsf{log1p}\left(\frac{y}{\color{blue}{{z}^{\left(\frac{-1}{2}\right)}}}\right)} - 1\right) \]

      8. metadata-eval 29.8%

         \[\leadsto 0.5 \cdot \left(e^{\mathsf{log1p}\left(\frac{y}{{z}^{\color{blue}{-0.5}}}\right)} - 1\right) \]

   10. Applied egg-rr 29.8%

       \[\leadsto 0.5 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{{z}^{-0.5}}\right)} - 1\right)} \]
   11. Step-by-step derivation

       1. expm1-def 53.0%

          \[\leadsto 0.5 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{{z}^{-0.5}}\right)\right)} \]

       2. expm1-log1p 79.3%

          \[\leadsto 0.5 \cdot \color{blue}{\frac{y}{{z}^{-0.5}}} \]

   12. Simplified 79.3%

       \[\leadsto 0.5 \cdot \color{blue}{\frac{y}{{z}^{-0.5}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+24}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-50} \lor \neg \left(x \leq 29500000000\right) \land x \leq 2.3 \cdot 10^{+45}:\\ \;\;\;\;0.5 \cdot \frac{y}{{z}^{-0.5}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot x\\ \end{array} \]

Alternative 3: 72.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{+83}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-56} \lor \neg \left(x \leq 33000000000\right) \land x \leq 2.6 \cdot 10^{+40}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \sqrt{z}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.4e+83)
   (* 0.5 x)
   (if (or (<= x 1.95e-56) (and (not (<= x 33000000000.0)) (<= x 2.6e+40)))
     (* 0.5 (* y (sqrt z)))
     (* 0.5 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.4e+83) {
		tmp = 0.5 * x;
	} else if ((x <= 1.95e-56) || (!(x <= 33000000000.0) && (x <= 2.6e+40))) {
		tmp = 0.5 * (y * sqrt(z));
	} 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) :: tmp
    if (x <= (-8.4d+83)) then
        tmp = 0.5d0 * x
    else if ((x <= 1.95d-56) .or. (.not. (x <= 33000000000.0d0)) .and. (x <= 2.6d+40)) then
        tmp = 0.5d0 * (y * sqrt(z))
    else
        tmp = 0.5d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.4e+83) {
		tmp = 0.5 * x;
	} else if ((x <= 1.95e-56) || (!(x <= 33000000000.0) && (x <= 2.6e+40))) {
		tmp = 0.5 * (y * Math.sqrt(z));
	} else {
		tmp = 0.5 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8.4e+83:
		tmp = 0.5 * x
	elif (x <= 1.95e-56) or (not (x <= 33000000000.0) and (x <= 2.6e+40)):
		tmp = 0.5 * (y * math.sqrt(z))
	else:
		tmp = 0.5 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.4e+83)
		tmp = Float64(0.5 * x);
	elseif ((x <= 1.95e-56) || (!(x <= 33000000000.0) && (x <= 2.6e+40)))
		tmp = Float64(0.5 * Float64(y * sqrt(z)));
	else
		tmp = Float64(0.5 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -8.4e+83)
		tmp = 0.5 * x;
	elseif ((x <= 1.95e-56) || (~((x <= 33000000000.0)) && (x <= 2.6e+40)))
		tmp = 0.5 * (y * sqrt(z));
	else
		tmp = 0.5 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.4e+83], N[(0.5 * x), $MachinePrecision], If[Or[LessEqual[x, 1.95e-56], And[N[Not[LessEqual[x, 33000000000.0]], $MachinePrecision], LessEqual[x, 2.6e+40]]], N[(0.5 * N[(y * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.4000000000000001e83 or 1.95e-56 < x < 3.3e10 or 2.6000000000000001e40 < x

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 80.5%

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

   if -8.4000000000000001e83 < x < 1.95e-56 or 3.3e10 < x < 2.6000000000000001e40

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 76.5%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{+83}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-56} \lor \neg \left(x \leq 33000000000\right) \land x \leq 2.6 \cdot 10^{+40}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \sqrt{z}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot x\\ \end{array} \]

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 99.8%

   \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]
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. Final simplification 99.8%

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

Alternative 5: 50.0% 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. Taylor expanded in x around inf 49.9%

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

5. Final simplification 49.9%

   \[\leadsto 0.5 \cdot x \]

Reproduce

herbie shell --seed 2023214 
(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)))))