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

Average Error: 0.03% → 0.03%

Time: 5.1s

Precision: binary64

Cost: 576

Math

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

↓

\[\frac{y}{z} - \left(\frac{x}{z} - x\right) \]

FPCore

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

↓

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

C

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

↓

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

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 = (y / z) - ((x / z) - x)
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 (y / z) - ((x / z) - x);
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.03

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

2. Applied egg-rr 0.03

   \[\leadsto \color{blue}{\frac{y}{z} - \left(\frac{x}{z} - x\right)} \]

3. Final simplification 0.03

   \[\leadsto \frac{y}{z} - \left(\frac{x}{z} - x\right) \]

Alternatives

Alternative 1
Error	36.69%
Cost	916

\[\begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -0.39:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-265}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-92}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-46}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Error	17.07%
Cost	850

\[\begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+50} \lor \neg \left(x \leq 3.6 \cdot 10^{-183} \lor \neg \left(x \leq 1.5 \cdot 10^{-91}\right) \land x \leq 1.5 \cdot 10^{-69}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} + x\\ \end{array} \]

Alternative 3
Error	1.67%
Cost	716

\[\begin{array}{l} t_0 := \frac{y}{z} + x\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-6}:\\ \;\;\;\;\frac{y - x}{z}\\ \mathbf{elif}\;z \leq 18000:\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	17.64%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq 4.1 \cdot 10^{-265} \lor \neg \left(z \leq 1.36 \cdot 10^{-93}\right):\\ \;\;\;\;\frac{y}{z} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \]

Alternative 5
Error	40.05%
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-194}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	0.03%
Cost	448

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

Alternative 7
Error	53.75%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023121 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))