Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2

Percentage Accurate: 99.9% → 99.9%

Time: 6.0s

Alternatives: 6

Speedup: 1.0×

• 24.6% 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 99.8%

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

   1. +-commutative 99.8%

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

   2. *-commutative 99.8%

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

   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: 66.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.7 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 11.5:\\ \;\;\;\;y \cdot \left(z \cdot z\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 1.7e-49)
   x
   (if (<= z 11.5) (* y (* z z)) (if (<= z 1.05e+20) x (* z (* z y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.7e-49) {
		tmp = x;
	} else if (z <= 11.5) {
		tmp = y * (z * z);
	} else if (z <= 1.05e+20) {
		tmp = x;
	} 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 <= 1.7d-49) then
        tmp = x
    else if (z <= 11.5d0) then
        tmp = y * (z * z)
    else if (z <= 1.05d+20) then
        tmp = x
    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 <= 1.7e-49) {
		tmp = x;
	} else if (z <= 11.5) {
		tmp = y * (z * z);
	} else if (z <= 1.05e+20) {
		tmp = x;
	} else {
		tmp = z * (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.7e-49:
		tmp = x
	elif z <= 11.5:
		tmp = y * (z * z)
	elif z <= 1.05e+20:
		tmp = x
	else:
		tmp = z * (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.7e-49)
		tmp = x;
	elseif (z <= 11.5)
		tmp = Float64(y * Float64(z * z));
	elseif (z <= 1.05e+20)
		tmp = x;
	else
		tmp = Float64(z * Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1.7e-49)
		tmp = x;
	elseif (z <= 11.5)
		tmp = y * (z * z);
	elseif (z <= 1.05e+20)
		tmp = x;
	else
		tmp = z * (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.7e-49], x, If[LessEqual[z, 11.5], N[(y * N[(z * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e+20], x, N[(z * N[(z * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < 1.70000000000000002e-49 or 11.5 < z < 1.05e20

   1. Initial program 99.9%

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

      1. associate-*l* 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in x around inf 62.2%

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

   if 1.70000000000000002e-49 < z < 11.5

   1. Initial program 99.4%

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

      1. +-commutative 99.9%

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

      2. associate-*r* 99.4%

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

      3. add-sqr-sqrt 99.0%

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

      4. associate-*r* 99.2%

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

      5. fma-def 99.2%

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

   5. Applied egg-rr 99.2%

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

   6. Taylor expanded in y around inf 62.3%

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

      1. unpow2 62.3%

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

   8. Simplified 62.3%

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

   if 1.05e20 < z

   1. Initial program 99.8%

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

      1. associate-*l* 90.3%

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

   3. Simplified 90.3%

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

      1. +-commutative 90.3%

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

      2. associate-*r* 99.8%

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

      3. add-cbrt-cube 85.4%

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

      4. cbrt-prod 90.1%

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

      5. associate-*r* 90.1%

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

      6. fma-def 90.1%

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

      7. cbrt-prod 99.4%

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

      8. pow2 99.4%

         \[\leadsto \mathsf{fma}\left(\left(y \cdot z\right) \cdot \color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}, \sqrt[3]{z}, x\right) \]

   5. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y \cdot z\right) \cdot {\left(\sqrt[3]{z}\right)}^{2}, \sqrt[3]{z}, x\right)} \]

   6. Taylor expanded in y around inf 69.9%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(y \cdot {z}^{2}\right)} \]
   7. Step-by-step derivation

      1. pow-base-1 69.9%

         \[\leadsto \color{blue}{1} \cdot \left(y \cdot {z}^{2}\right) \]

      2. unpow2 69.9%

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

      3. *-commutative 69.9%

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

      4. associate-*r* 77.8%

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

      5. *-lft-identity 77.8%

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

   8. Simplified 77.8%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.7 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 11.5:\\ \;\;\;\;y \cdot \left(z \cdot z\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot y\right)\\ \end{array} \]

Alternative 3: 95.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x + y \cdot \left(z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 1.35e+154) (+ x (* y (* z z))) (* z (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.35e+154) {
		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 <= 1.35d+154) 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 <= 1.35e+154) {
		tmp = x + (y * (z * z));
	} else {
		tmp = z * (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.35e+154:
		tmp = x + (y * (z * z))
	else:
		tmp = z * (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.35e+154)
		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 <= 1.35e+154)
		tmp = x + (y * (z * z));
	else
		tmp = z * (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.35e+154], 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 < 1.35000000000000003e154

   1. Initial program 99.8%

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

      1. associate-*l* 94.3%

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

   3. Simplified 94.3%

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

   if 1.35000000000000003e154 < z

   1. Initial program 99.9%

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

      1. associate-*l* 80.7%

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

   3. Simplified 80.7%

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

      1. +-commutative 80.7%

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

      2. associate-*r* 99.9%

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

      3. add-cbrt-cube 80.7%

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

      4. cbrt-prod 80.7%

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

      5. associate-*r* 80.7%

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

      6. fma-def 80.7%

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

      7. cbrt-prod 99.7%

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

      8. pow2 99.7%

         \[\leadsto \mathsf{fma}\left(\left(y \cdot z\right) \cdot \color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}, \sqrt[3]{z}, x\right) \]

   5. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y \cdot z\right) \cdot {\left(\sqrt[3]{z}\right)}^{2}, \sqrt[3]{z}, x\right)} \]

   6. Taylor expanded in y around inf 80.7%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(y \cdot {z}^{2}\right)} \]
   7. Step-by-step derivation

      1. pow-base-1 80.7%

         \[\leadsto \color{blue}{1} \cdot \left(y \cdot {z}^{2}\right) \]

      2. unpow2 80.7%

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

      3. *-commutative 80.7%

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

      4. associate-*r* 96.6%

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

      5. *-lft-identity 96.6%

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

   8. Simplified 96.6%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x + y \cdot \left(z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot y\right)\\ \end{array} \]

Alternative 4: 63.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.7 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 1.7e-49) x (* y (* z z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.7e-49) {
		tmp = x;
	} else {
		tmp = 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 <= 1.7d-49) then
        tmp = x
    else
        tmp = y * (z * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.7e-49) {
		tmp = x;
	} else {
		tmp = y * (z * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.7e-49:
		tmp = x
	else:
		tmp = y * (z * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.7e-49)
		tmp = x;
	else
		tmp = Float64(y * Float64(z * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1.7e-49)
		tmp = x;
	else
		tmp = y * (z * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.7e-49], x, N[(y * N[(z * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.70000000000000002e-49

   1. Initial program 99.9%

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

      1. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in x around inf 62.3%

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

   if 1.70000000000000002e-49 < z

   1. Initial program 99.7%

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

      1. associate-*l* 92.4%

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

   3. Simplified 92.4%

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

      1. +-commutative 92.4%

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

      2. associate-*r* 99.7%

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

      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* 99.6%

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

      5. fma-def 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 66.5%

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

      1. unpow2 66.5%

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

   8. Simplified 66.5%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.7 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot z\right)\\ \end{array} \]

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 99.8%

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

2. Final simplification 99.8%

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

Alternative 6: 51.0% 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 99.8%

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

   1. associate-*l* 92.7%

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

3. Simplified 92.7%

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

4. Taylor expanded in x around inf 52.4%

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

5. Final simplification 52.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023275 
(FPCore (x y z)
  :name "Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2"
  :precision binary64
  (+ x (* (* y z) z)))