Statistics.Sample:$swelfordMean from math-functions-0.1.5.2

Average Error: 0.0 → 0.0

Time: 7.0s

Precision: binary64

Cost: 448

Math

\[x + \frac{y - x}{z} \]

↓

\[x + \frac{y - x}{z} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (/ (- y x) z)))

↓

(FPCore (x y z) :precision binary64 (+ x (/ (- y x) z)))

C

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

↓

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

Java

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

↓

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

Python

def code(x, y, z):
	return x + ((y - x) / z)

↓

def code(x, y, z):
	return x + ((y - x) / z)

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

   \[x + \frac{y - x}{z} \]

2. Final simplification 0.0

   \[\leadsto x + \frac{y - x}{z} \]

Alternatives

Alternative 1
Error	33.4
Cost	1512

\[\begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{-79}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-123}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-175}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-291}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-112}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-43}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-25}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.0085:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+45}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z}\\ \end{array} \]

Alternative 2
Error	12.4
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-286} \lor \neg \left(z \leq 6.8 \cdot 10^{-144}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \]

Alternative 3
Error	6.8
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-85} \lor \neg \left(y \leq 4.6 \cdot 10^{-99}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \]

Alternative 4
Error	0.9
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -300 \lor \neg \left(z \leq 1.15 \cdot 10^{-5}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \]

Alternative 5
Error	25.4
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+21}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	35.0
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023031 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))