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

Average Error: 0.0 → 0.0

Time: 7.5s

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. Simplified 0.0

   \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	13.8
Cost	848

\[\begin{array}{l} t_0 := x + \frac{y}{z}\\ t_1 := \frac{-x}{z}\\ \mathbf{if}\;y \leq -3.352107844179885 \cdot 10^{-290}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.6645356111221677 \cdot 10^{-242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.119267278529334 \cdot 10^{-185}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.2971969880538484 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	23.6
Cost	720

\[\begin{array}{l} \mathbf{if}\;z \leq -1.798997311531756 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-292}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 0.0011290443335734708:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 4.380123430700242 \cdot 10^{+48}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Error	7.2
Cost	584

\[\begin{array}{l} t_0 := x + \frac{y}{z}\\ \mathbf{if}\;y \leq -1.7361442744847176 \cdot 10^{-109}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.2792598538232 \cdot 10^{-65}:\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	0.9
Cost	584

\[\begin{array}{l} t_0 := x + \frac{y}{z}\\ \mathbf{if}\;z \leq -11173254449.201303:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.0011290443335734708:\\ \;\;\;\;\frac{y - x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	24.1
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.798997311531756 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.380123430700242 \cdot 10^{+48}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	35.1
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022325 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))