Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2

Average Error: 0.1 → 0.1

Time: 1.4min

Precision: binary64

Cost: 708

Math

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

↓

\[x + \begin{array}{l} \mathbf{if}\;z \ne 0:\\ \;\;\;\;\frac{z \cdot y}{\frac{1}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot z\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (+ x (if (!= z 0.0) (/ (* z y) (/ 1.0 z)) (* (* z y) z))))

C

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

↓

double code(double x, double y, double z) {
	double tmp;
	if (z != 0.0) {
		tmp = (z * y) / (1.0 / z);
	} else {
		tmp = (z * y) * z;
	}
	return x + tmp;
}

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

↓

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 /= 0.0d0) then
        tmp = (z * y) / (1.0d0 / z)
    else
        tmp = (z * y) * z
    end if
    code = x + tmp
end function

Java

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

↓

public static double code(double x, double y, double z) {
	double tmp;
	if (z != 0.0) {
		tmp = (z * y) / (1.0 / z);
	} else {
		tmp = (z * y) * z;
	}
	return x + tmp;
}

Python

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

↓

def code(x, y, z):
	tmp = 0
	if z != 0.0:
		tmp = (z * y) / (1.0 / z)
	else:
		tmp = (z * y) * z
	return x + tmp

Julia

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

↓

function code(x, y, z)
	tmp = 0.0
	if (z != 0.0)
		tmp = Float64(Float64(z * y) / Float64(1.0 / z));
	else
		tmp = Float64(Float64(z * y) * z);
	end
	return Float64(x + tmp)
end

MATLAB

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

↓

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z ~= 0.0)
		tmp = (z * y) / (1.0 / z);
	else
		tmp = (z * y) * z;
	end
	tmp_2 = x + tmp;
end

Wolfram

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

↓

code[x_, y_, z_] := N[(x + If[Unequal[z, 0.0], N[(N[(z * y), $MachinePrecision] / N[(1.0 / z), $MachinePrecision]), $MachinePrecision], N[(N[(z * y), $MachinePrecision] * z), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Initial program 0.1

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

2. Applied egg-rr 0.1

   \[\leadsto x + \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;z \ne 0:\\ \;\;\;\;\frac{y \cdot z}{{z}^{-1}}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot z\\ } \end{array}} \]

3. Simplified 0.1

   \[\leadsto x + \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;z \ne 0:\\ \;\;\;\;\frac{z \cdot y}{\frac{1}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot z\\ } \end{array}} \]
   Proof

Alternatives

Alternative 1
Error	14.7
Cost	584

\[\begin{array}{l} t_0 := z \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{-9}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+68}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	0.1
Cost	448

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

Alternative 3
Error	21.0
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023033 
(FPCore (x y z)
  :name "Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2"
  :precision binary64
  (+ x (* (* y z) z)))