Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2

Percentage Accurate: 99.9% → 99.9%

Time: 8.5s

Alternatives: 6

Speedup: 1.0×

• 24.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. *-commutative 99.9%

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

   3. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 86.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(z \cdot y\right)\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{+81} \lor \neg \left(t_0 \leq 4 \cdot 10^{+47}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* z y))))
   (if (or (<= t_0 -5e+81) (not (<= t_0 4e+47))) t_0 x)))

C

double code(double x, double y, double z) {
	double t_0 = z * (z * y);
	double tmp;
	if ((t_0 <= -5e+81) || !(t_0 <= 4e+47)) {
		tmp = t_0;
	} else {
		tmp = 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 = z * (z * y)
    if ((t_0 <= (-5d+81)) .or. (.not. (t_0 <= 4d+47))) then
        tmp = t_0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (z * y);
	double tmp;
	if ((t_0 <= -5e+81) || !(t_0 <= 4e+47)) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (z * y)
	tmp = 0
	if (t_0 <= -5e+81) or not (t_0 <= 4e+47):
		tmp = t_0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(z * y))
	tmp = 0.0
	if ((t_0 <= -5e+81) || !(t_0 <= 4e+47))
		tmp = t_0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (z * y);
	tmp = 0.0;
	if ((t_0 <= -5e+81) || ~((t_0 <= 4e+47)))
		tmp = t_0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -5e+81], N[Not[LessEqual[t$95$0, 4e+47]], $MachinePrecision]], t$95$0, x]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y z) z) < -4.9999999999999998e81 or 4.0000000000000002e47 < (*.f64 (*.f64 y z) z)

   1. Initial program 99.8%

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

      1. associate-*l* 81.7%

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

   3. Simplified 81.7%

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

      1. +-commutative 81.7%

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

      2. associate-*r* 99.8%

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

      3. add-sqr-sqrt 42.9%

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

      4. associate-*r* 42.9%

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

      5. fma-def 42.9%

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

   5. Applied egg-rr 42.9%

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

   6. Taylor expanded in y around inf 75.6%

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

      1. unpow2 75.6%

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

   8. Simplified 75.6%

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

      1. add-cube-cbrt 75.3%

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

      2. pow3 75.3%

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

      3. associate-*r* 90.4%

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

      4. *-commutative 90.4%

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

   10. Applied egg-rr 90.4%

       \[\leadsto \color{blue}{{\left(\sqrt[3]{z \cdot \left(y \cdot z\right)}\right)}^{3}} \]
   11. Step-by-step derivation

       1. rem-cube-cbrt 91.0%

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

       2. *-commutative 91.0%

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

   12. Applied egg-rr 91.0%

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

   if -4.9999999999999998e81 < (*.f64 (*.f64 y z) z) < 4.0000000000000002e47

   1. Initial program 100.0%

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

      1. associate-*l* 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in x around inf 86.8%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(z \cdot y\right) \leq -5 \cdot 10^{+81} \lor \neg \left(z \cdot \left(z \cdot y\right) \leq 4 \cdot 10^{+47}\right):\\ \;\;\;\;z \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 64.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.7 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+47} \lor \neg \left(z \leq 3.5 \cdot 10^{+71}\right):\\ \;\;\;\;y \cdot \left(z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 2.7e+24)
   x
   (if (or (<= z 2.8e+47) (not (<= z 3.5e+71))) (* y (* z z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 2.7e+24) {
		tmp = x;
	} else if ((z <= 2.8e+47) || !(z <= 3.5e+71)) {
		tmp = y * (z * z);
	} else {
		tmp = 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 (z <= 2.7d+24) then
        tmp = x
    else if ((z <= 2.8d+47) .or. (.not. (z <= 3.5d+71))) then
        tmp = y * (z * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 2.7e+24) {
		tmp = x;
	} else if ((z <= 2.8e+47) || !(z <= 3.5e+71)) {
		tmp = y * (z * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 2.7e+24:
		tmp = x
	elif (z <= 2.8e+47) or not (z <= 3.5e+71):
		tmp = y * (z * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 2.7e+24)
		tmp = x;
	elseif ((z <= 2.8e+47) || !(z <= 3.5e+71))
		tmp = Float64(y * Float64(z * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 2.7e+24)
		tmp = x;
	elseif ((z <= 2.8e+47) || ~((z <= 3.5e+71)))
		tmp = y * (z * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 2.7e+24], x, If[Or[LessEqual[z, 2.8e+47], N[Not[LessEqual[z, 3.5e+71]], $MachinePrecision]], N[(y * N[(z * z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < 2.7e24 or 2.79999999999999988e47 < z < 3.4999999999999999e71

   1. Initial program 99.9%

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

      1. associate-*l* 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in x around inf 53.4%

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

   if 2.7e24 < z < 2.79999999999999988e47 or 3.4999999999999999e71 < z

   1. Initial program 99.9%

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

      1. associate-*l* 76.7%

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

   3. Simplified 76.7%

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

      1. +-commutative 76.7%

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

      2. associate-*r* 99.9%

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

      3. add-sqr-sqrt 99.6%

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

      4. associate-*r* 99.7%

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

      5. fma-def 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around inf 67.1%

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

      1. unpow2 67.1%

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

   8. Simplified 67.1%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.7 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+47} \lor \neg \left(z \leq 3.5 \cdot 10^{+71}\right):\\ \;\;\;\;y \cdot \left(z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 95.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.42 \cdot 10^{+142}:\\ \;\;\;\;x + y \cdot \left(z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 1.42e+142) (+ x (* y (* z z))) (* z (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.42e+142) {
		tmp = x + (y * (z * z));
	} else {
		tmp = z * (z * y);
	}
	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 (z <= 1.42d+142) then
        tmp = x + (y * (z * z))
    else
        tmp = z * (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.42e+142) {
		tmp = x + (y * (z * z));
	} else {
		tmp = z * (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.42e+142:
		tmp = x + (y * (z * z))
	else:
		tmp = z * (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.42e+142)
		tmp = Float64(x + Float64(y * Float64(z * z)));
	else
		tmp = Float64(z * Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1.42e+142)
		tmp = x + (y * (z * z));
	else
		tmp = z * (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.42e+142], N[(x + N[(y * N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.42e142

   1. Initial program 99.9%

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

      1. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   if 1.42e142 < z

   1. Initial program 99.9%

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

      1. associate-*l* 67.0%

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

   3. Simplified 67.0%

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

      1. +-commutative 67.0%

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

      2. associate-*r* 99.9%

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

      3. add-sqr-sqrt 99.7%

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

      4. associate-*r* 99.8%

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

      5. fma-def 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 67.0%

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

      1. unpow2 67.0%

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

   8. Simplified 67.0%

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

      1. add-cube-cbrt 67.0%

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

      2. pow3 67.0%

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

      3. associate-*r* 94.0%

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

      4. *-commutative 94.0%

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

   10. Applied egg-rr 94.0%

       \[\leadsto \color{blue}{{\left(\sqrt[3]{z \cdot \left(y \cdot z\right)}\right)}^{3}} \]
   11. Step-by-step derivation

       1. rem-cube-cbrt 94.7%

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

       2. *-commutative 94.7%

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

   12. Applied egg-rr 94.7%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.42 \cdot 10^{+142}:\\ \;\;\;\;x + y \cdot \left(z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot y\right)\\ \end{array} \]

Alternative 5: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (z * (z * y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 6: 51.5% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

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

   1. associate-*l* 88.8%

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

3. Simplified 88.8%

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

4. Taylor expanded in x around inf 45.8%

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

5. Final simplification 45.8%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023274 
(FPCore (x y z)
  :name "Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2"
  :precision binary64
  (+ x (* (* y z) z)))