AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, A

Average Error: 0.02% → 0.02%

Time: 3.8s

Precision: binary64

Cost: 320

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x / (x + y)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x / (x + y)
end function

Java

public static double code(double x, double y) {
	return x / (x + y);
}

↓

public static double code(double x, double y) {
	return x / (x + y);
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.02

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

2. Final simplification 0.02

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

Alternatives

Alternative 1
Error	26.91%
Cost	984

\[\begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-40}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-57}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+53}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 2
Error	26.72%
Cost	720

\[\begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-57}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+51}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 3
Error	49.27%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023090 
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, A"
  :precision binary64
  (/ x (+ x y)))