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

Percentage Accurate: 99.8% → 99.8%

Time: 5.6s

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 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 74.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \sqrt{z}\\ \mathbf{if}\;t_0 \leq -7.2 \cdot 10^{+19} \lor \neg \left(t_0 \leq 2 \cdot 10^{-68}\right) \land \left(t_0 \leq 1.1 \cdot 10^{+102} \lor \neg \left(t_0 \leq 8.2 \cdot 10^{+142}\right)\right):\\ \;\;\;\;0.5 \cdot t_0\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (sqrt z))))
   (if (or (<= t_0 -7.2e+19)
           (and (not (<= t_0 2e-68))
                (or (<= t_0 1.1e+102) (not (<= t_0 8.2e+142)))))
     (* 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 <= -7.2e+19) || (!(t_0 <= 2e-68) && ((t_0 <= 1.1e+102) || !(t_0 <= 8.2e+142)))) {
		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 <= (-7.2d+19)) .or. (.not. (t_0 <= 2d-68)) .and. (t_0 <= 1.1d+102) .or. (.not. (t_0 <= 8.2d+142))) 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 <= -7.2e+19) || (!(t_0 <= 2e-68) && ((t_0 <= 1.1e+102) || !(t_0 <= 8.2e+142)))) {
		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 <= -7.2e+19) or (not (t_0 <= 2e-68) and ((t_0 <= 1.1e+102) or not (t_0 <= 8.2e+142))):
		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 <= -7.2e+19) || (!(t_0 <= 2e-68) && ((t_0 <= 1.1e+102) || !(t_0 <= 8.2e+142))))
		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 <= -7.2e+19) || (~((t_0 <= 2e-68)) && ((t_0 <= 1.1e+102) || ~((t_0 <= 8.2e+142)))))
		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, -7.2e+19], And[N[Not[LessEqual[t$95$0, 2e-68]], $MachinePrecision], Or[LessEqual[t$95$0, 1.1e+102], N[Not[LessEqual[t$95$0, 8.2e+142]], $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)) < -7.2e19 or 2.00000000000000013e-68 < (*.f64 y (sqrt.f64 z)) < 1.10000000000000004e102 or 8.19999999999999963e142 < (*.f64 y (sqrt.f64 z))

   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 0 81.2%

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

   if -7.2e19 < (*.f64 y (sqrt.f64 z)) < 2.00000000000000013e-68 or 1.10000000000000004e102 < (*.f64 y (sqrt.f64 z)) < 8.19999999999999963e142

   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 81.5%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \sqrt{z} \leq -7.2 \cdot 10^{+19} \lor \neg \left(y \cdot \sqrt{z} \leq 2 \cdot 10^{-68}\right) \land \left(y \cdot \sqrt{z} \leq 1.1 \cdot 10^{+102} \lor \neg \left(y \cdot \sqrt{z} \leq 8.2 \cdot 10^{+142}\right)\right):\\ \;\;\;\;0.5 \cdot \left(y \cdot \sqrt{z}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot x\\ \end{array} \]

Alternative 3: 74.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \sqrt{z}\\ t_1 := 0.5 \cdot t_0\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 10^{-68}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+98}:\\ \;\;\;\;0.5 \cdot \sqrt{y \cdot \left(y \cdot z\right)}\\ \mathbf{elif}\;t_0 \leq 10^{+143}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (sqrt z))) (t_1 (* 0.5 t_0)))
   (if (<= t_0 -2e+20)
     t_1
     (if (<= t_0 1e-68)
       (* 0.5 x)
       (if (<= t_0 5e+98)
         (* 0.5 (sqrt (* y (* y z))))
         (if (<= t_0 1e+143) (* 0.5 x) t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = y * sqrt(z);
	double t_1 = 0.5 * t_0;
	double tmp;
	if (t_0 <= -2e+20) {
		tmp = t_1;
	} else if (t_0 <= 1e-68) {
		tmp = 0.5 * x;
	} else if (t_0 <= 5e+98) {
		tmp = 0.5 * sqrt((y * (y * z)));
	} else if (t_0 <= 1e+143) {
		tmp = 0.5 * x;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = y * sqrt(z)
    t_1 = 0.5d0 * t_0
    if (t_0 <= (-2d+20)) then
        tmp = t_1
    else if (t_0 <= 1d-68) then
        tmp = 0.5d0 * x
    else if (t_0 <= 5d+98) then
        tmp = 0.5d0 * sqrt((y * (y * z)))
    else if (t_0 <= 1d+143) then
        tmp = 0.5d0 * x
    else
        tmp = t_1
    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 t_1 = 0.5 * t_0;
	double tmp;
	if (t_0 <= -2e+20) {
		tmp = t_1;
	} else if (t_0 <= 1e-68) {
		tmp = 0.5 * x;
	} else if (t_0 <= 5e+98) {
		tmp = 0.5 * Math.sqrt((y * (y * z)));
	} else if (t_0 <= 1e+143) {
		tmp = 0.5 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * math.sqrt(z)
	t_1 = 0.5 * t_0
	tmp = 0
	if t_0 <= -2e+20:
		tmp = t_1
	elif t_0 <= 1e-68:
		tmp = 0.5 * x
	elif t_0 <= 5e+98:
		tmp = 0.5 * math.sqrt((y * (y * z)))
	elif t_0 <= 1e+143:
		tmp = 0.5 * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * sqrt(z))
	t_1 = Float64(0.5 * t_0)
	tmp = 0.0
	if (t_0 <= -2e+20)
		tmp = t_1;
	elseif (t_0 <= 1e-68)
		tmp = Float64(0.5 * x);
	elseif (t_0 <= 5e+98)
		tmp = Float64(0.5 * sqrt(Float64(y * Float64(y * z))));
	elseif (t_0 <= 1e+143)
		tmp = Float64(0.5 * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * sqrt(z);
	t_1 = 0.5 * t_0;
	tmp = 0.0;
	if (t_0 <= -2e+20)
		tmp = t_1;
	elseif (t_0 <= 1e-68)
		tmp = 0.5 * x;
	elseif (t_0 <= 5e+98)
		tmp = 0.5 * sqrt((y * (y * z)));
	elseif (t_0 <= 1e+143)
		tmp = 0.5 * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(0.5 * t$95$0), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+20], t$95$1, If[LessEqual[t$95$0, 1e-68], N[(0.5 * x), $MachinePrecision], If[LessEqual[t$95$0, 5e+98], N[(0.5 * N[Sqrt[N[(y * N[(y * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1e+143], N[(0.5 * x), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y (sqrt.f64 z)) < -2e20 or 1e143 < (*.f64 y (sqrt.f64 z))

   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 0 85.0%

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

   if -2e20 < (*.f64 y (sqrt.f64 z)) < 1.00000000000000007e-68 or 4.9999999999999998e98 < (*.f64 y (sqrt.f64 z)) < 1e143

   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 81.5%

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

   if 1.00000000000000007e-68 < (*.f64 y (sqrt.f64 z)) < 4.9999999999999998e98

   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 67.2%

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

      1. add-sqr-sqrt 66.7%

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

      2. sqrt-unprod 67.2%

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

      3. pow1/2 67.2%

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

      4. *-commutative 67.2%

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

      5. *-commutative 67.2%

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

      6. swap-sqr 59.8%

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

      7. add-sqr-sqrt 60.0%

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

   6. Applied egg-rr 60.0%

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

      1. unpow1/2 60.0%

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

      2. *-commutative 60.0%

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

      3. associate-*l* 67.5%

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

   8. Simplified 67.5%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \sqrt{z} \leq -2 \cdot 10^{+20}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \sqrt{z}\right)\\ \mathbf{elif}\;y \cdot \sqrt{z} \leq 10^{-68}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;y \cdot \sqrt{z} \leq 5 \cdot 10^{+98}:\\ \;\;\;\;0.5 \cdot \sqrt{y \cdot \left(y \cdot z\right)}\\ \mathbf{elif}\;y \cdot \sqrt{z} \leq 10^{+143}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \sqrt{z}\right)\\ \end{array} \]

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 99.8%

   \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right) \]
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: 50.9% 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 51.9%

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

5. Final simplification 51.9%

   \[\leadsto 0.5 \cdot x \]

Reproduce

herbie shell --seed 2023176 
(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)))))