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

Average Error: 0.02% → 0.02%

Time: 5.3s

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 0.02

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

2. Final simplification 0.02

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

Alternatives

Alternative 1
Error	38.81%
Cost	1248

\[\begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-164}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-280}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-166}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-100}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-37}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.78 \cdot 10^{+124}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Error	18.73%
Cost	1112

\[\begin{array}{l} t_0 := x + \frac{y}{z}\\ t_1 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{-164}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-283}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-167}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-38}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	10.81%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -9.4 \cdot 10^{-95} \lor \neg \left(y \leq 9.5 \cdot 10^{-160}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \]

Alternative 4
Error	38.72%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.78 \cdot 10^{+124}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Error	54.33%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023089 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))