Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2

Percentage Accurate: 99.9% → 99.9%

Time: 5.5s

Alternatives: 5

Speedup: 1.0×

• 25.0% 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, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 2: 82.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(y \cdot z\right)\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{+60} \lor \neg \left(t_0 \leq 10^{-254}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* y z))))
   (if (or (<= t_0 -1e+60) (not (<= t_0 1e-254))) t_0 x)))

C

double code(double x, double y, double z) {
	double t_0 = z * (y * z);
	double tmp;
	if ((t_0 <= -1e+60) || !(t_0 <= 1e-254)) {
		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 * (y * z)
    if ((t_0 <= (-1d+60)) .or. (.not. (t_0 <= 1d-254))) 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 * (y * z);
	double tmp;
	if ((t_0 <= -1e+60) || !(t_0 <= 1e-254)) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y * z)
	tmp = 0
	if (t_0 <= -1e+60) or not (t_0 <= 1e-254):
		tmp = t_0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y * z))
	tmp = 0.0
	if ((t_0 <= -1e+60) || !(t_0 <= 1e-254))
		tmp = t_0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (y * z);
	tmp = 0.0;
	if ((t_0 <= -1e+60) || ~((t_0 <= 1e-254)))
		tmp = t_0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -1e+60], N[Not[LessEqual[t$95$0, 1e-254]], $MachinePrecision]], t$95$0, x]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y z) z) < -9.9999999999999995e59 or 9.9999999999999991e-255 < (*.f64 (*.f64 y z) z)

   1. Initial program 99.9%

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

      1. associate-*l* 89.6%

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

   3. Simplified 89.6%

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

      1. +-commutative 89.6%

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

      2. associate-*r* 99.9%

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

      3. add-sqr-sqrt 40.7%

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

      4. associate-*r* 40.6%

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

      5. fma-def 40.6%

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

   5. Applied egg-rr 40.6%

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

   7. Applied egg-rr 99.8%

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

   8. Taylor expanded in z around inf 75.0%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{y \cdot {z}^{2}}}} \]
   9. Step-by-step derivation

      1. unpow2 75.0%

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

      2. associate-/r* 75.0%

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{1}{y}}{z \cdot z}}} \]

   10. Simplified 75.0%

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

       1. associate-/r/ 75.0%

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

       2. remove-double-div 75.1%

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

       3. associate-*r* 82.9%

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

   12. Applied egg-rr 82.9%

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

   if -9.9999999999999995e59 < (*.f64 (*.f64 y z) z) < 9.9999999999999991e-255

   1. Initial program 99.9%

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

      1. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 88.9%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(y \cdot z\right) \leq -1 \cdot 10^{+60} \lor \neg \left(z \cdot \left(y \cdot z\right) \leq 10^{-254}\right):\\ \;\;\;\;z \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 77.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-19} \lor \neg \left(z \leq 2.6 \cdot 10^{-45}\right):\\ \;\;\;\;y \cdot \left(z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.02e-19) (not (<= z 2.6e-45))) (* y (* z z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.02e-19) || !(z <= 2.6e-45)) {
		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 <= (-1.02d-19)) .or. (.not. (z <= 2.6d-45))) 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 <= -1.02e-19) || !(z <= 2.6e-45)) {
		tmp = y * (z * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.02e-19) or not (z <= 2.6e-45):
		tmp = y * (z * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.02e-19) || !(z <= 2.6e-45))
		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 <= -1.02e-19) || ~((z <= 2.6e-45)))
		tmp = y * (z * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.02e-19], N[Not[LessEqual[z, 2.6e-45]], $MachinePrecision]], N[(y * N[(z * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.02000000000000004e-19 or 2.59999999999999987e-45 < z

   1. Initial program 99.9%

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

      1. associate-*l* 92.2%

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

   3. Simplified 92.2%

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

      1. +-commutative 92.2%

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

      2. flip-+ 22.6%

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

      3. pow2 22.6%

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

      4. add-sqr-sqrt 8.0%

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

      5. pow-prod-down 8.0%

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

      6. pow-prod-up 8.0%

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

      7. *-commutative 8.0%

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

      8. sqrt-prod 7.9%

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

      9. sqrt-prod 2.3%

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

      10. add-sqr-sqrt 7.9%

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

      11. metadata-eval 7.9%

          \[\leadsto \frac{{\left(z \cdot \sqrt{y}\right)}^{\color{blue}{4}} - x \cdot x}{y \cdot \left(z \cdot z\right) - x} \]

      12. associate-*r* 9.0%

          \[\leadsto \frac{{\left(z \cdot \sqrt{y}\right)}^{4} - x \cdot x}{\color{blue}{\left(y \cdot z\right) \cdot z} - x} \]

      13. *-commutative 9.0%

          \[\leadsto \frac{{\left(z \cdot \sqrt{y}\right)}^{4} - x \cdot x}{\color{blue}{z \cdot \left(y \cdot z\right)} - x} \]

   5. Applied egg-rr 9.0%

      \[\leadsto \color{blue}{\frac{{\left(z \cdot \sqrt{y}\right)}^{4} - x \cdot x}{z \cdot \left(y \cdot z\right) - x}} \]

   6. Taylor expanded in z around inf 80.6%

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

      1. unpow2 80.6%

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

   8. Simplified 80.6%

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

   if -1.02000000000000004e-19 < z < 2.59999999999999987e-45

   1. Initial program 99.9%

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

      1. associate-*l* 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in x around inf 85.2%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-19} \lor \neg \left(z \leq 2.6 \cdot 10^{-45}\right):\\ \;\;\;\;y \cdot \left(z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 95.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+154}:\\ \;\;\;\;z \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.5e+154) (* z (* y z)) (+ x (* y (* z z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.5e+154) {
		tmp = z * (y * z);
	} else {
		tmp = x + (y * (z * 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 (z <= (-2.5d+154)) then
        tmp = z * (y * z)
    else
        tmp = x + (y * (z * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.5e+154) {
		tmp = z * (y * z);
	} else {
		tmp = x + (y * (z * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.5e+154:
		tmp = z * (y * z)
	else:
		tmp = x + (y * (z * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.5e+154)
		tmp = Float64(z * Float64(y * z));
	else
		tmp = Float64(x + Float64(y * Float64(z * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.5e+154)
		tmp = z * (y * z);
	else
		tmp = x + (y * (z * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.5e+154], N[(z * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.50000000000000002e154

   1. Initial program 100.0%

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

      1. associate-*l* 78.1%

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

   3. Simplified 78.1%

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

      1. +-commutative 78.1%

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

      2. associate-*r* 100.0%

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

      3. add-sqr-sqrt 0.0%

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

      4. associate-*r* 0.0%

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

      5. fma-def 0.0%

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

   5. Applied egg-rr 0.0%

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

   7. Applied egg-rr 100.0%

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

   8. Taylor expanded in z around inf 78.1%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{y \cdot {z}^{2}}}} \]
   9. Step-by-step derivation

      1. unpow2 78.1%

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

      2. associate-/r* 78.1%

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{1}{y}}{z \cdot z}}} \]

   10. Simplified 78.1%

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

       1. associate-/r/ 78.1%

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

       2. remove-double-div 78.1%

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

       3. associate-*r* 91.9%

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

   12. Applied egg-rr 91.9%

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

   if -2.50000000000000002e154 < z

   1. Initial program 99.9%

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

      1. associate-*l* 96.5%

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

   3. Simplified 96.5%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+154}:\\ \;\;\;\;z \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z \cdot z\right)\\ \end{array} \]

Alternative 5: 50.6% 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* 94.0%

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

3. Simplified 94.0%

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

4. Taylor expanded in x around inf 48.0%

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

5. Final simplification 48.0%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023192 
(FPCore (x y z)
  :name "Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2"
  :precision binary64
  (+ x (* (* y z) z)))