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

Average Accuracy: 100.0% → 100.0%

Time: 6.0s

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 100.0%

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

2. Applied egg-rr 100.0%

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

   [Start] 100.0	\[ x + \frac{y - x}{z} \]
   +-commutative [=>] 100.0	\[ \color{blue}{\frac{y - x}{z} + x} \]
   div-sub [=>] 100.0	\[ \color{blue}{\left(\frac{y}{z} - \frac{x}{z}\right)} + x \]
   associate-+l- [=>] 100.0	\[ \color{blue}{\frac{y}{z} - \left(\frac{x}{z} - x\right)} \]

3. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	79.9%
Cost	1112

\[\begin{array}{l} t_0 := \frac{y}{z} + x\\ t_1 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -0.0075:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-156}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-148}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Accuracy	62.1%
Cost	852

\[\begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-227}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-146}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-55}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+57}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Accuracy	88.6%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-118} \lor \neg \left(y \leq 2.5 \cdot 10^{-109}\right):\\ \;\;\;\;\frac{y}{z} + x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \]

Alternative 4
Accuracy	98.4%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 6.2 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{y}{z} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \]

Alternative 5
Accuracy	62.3%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1450000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+61}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Accuracy	100.0%
Cost	448

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

Alternative 7
Accuracy	45.4%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023133 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))