Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2

Average Error: 0.1 → 0.1

Time: 7.0s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z) :precision binary64 (+ x (* 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) {
	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 + ((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
    code = x + (z * (y * z))
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) {
	return x + (z * (y * z));
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.1

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

2. Final simplification 0.1

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

Alternatives

Alternative 1
Error	14.2
Cost	848

\[\begin{array}{l} t_0 := z \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+30}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.835410107184495 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.5265754225361245 \cdot 10^{-60}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	14.2
Cost	848

\[\begin{array}{l} t_0 := z \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+30}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.835410107184495 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.5265754225361245 \cdot 10^{-60}:\\ \;\;\;\;y \cdot \left(z \cdot z\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	21.0
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022317 
(FPCore (x y z)
  :name "Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2"
  :precision binary64
  (+ x (* (* y z) z)))