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

Average Accuracy: 100.0% → 100.0%

Time: 6.3s

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 100.0%

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

2. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	62.4%
Cost	852

\[\begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+14}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-59}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+28}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Accuracy	61.3%
Cost	720

\[\begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+15}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+28}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Accuracy	80.7%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-5} \lor \neg \left(z \leq 1.3 \cdot 10^{-55}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \]

Alternative 4
Accuracy	88.3%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-109} \lor \neg \left(y \leq 1.08 \cdot 10^{-47}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \]

Alternative 5
Accuracy	98.0%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 4.5 \cdot 10^{-17}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \]

Alternative 6
Accuracy	45.3%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023135 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))