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

Average Error: 0.0 → 0.0

Time: 1.9s

Precision: binary64

Math

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

↓

\[\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{x + y}\right)\right) \]

FPCore

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

↓

(FPCore (x y) :precision binary64 (log1p (expm1 (/ x (+ x y)))))

C

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

↓

double code(double x, double y) {
	return log1p(expm1((x / (x + y))));
}

Java

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

↓

public static double code(double x, double y) {
	return Math.log1p(Math.expm1((x / (x + y))));
}

Python

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

↓

def code(x, y):
	return math.log1p(math.expm1((x / (x + y))))

Julia

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

↓

function code(x, y)
	return log1p(expm1(Float64(x / Float64(x + y))))
end

Wolfram

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

↓

code[x_, y_] := N[Log[1 + N[(Exp[N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision]

Error

Bits error versus x

Bits error versus y

Derivation

1. Initial program 0.0

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

2. Applied log1p-expm1-u_binary64 0.0

   \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{y + x}\right)\right)} \]

3. Final simplification 0.0

   \[\leadsto \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{x + y}\right)\right) \]

Reproduce

herbie shell --seed 2022131 
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, B"
  :precision binary64
  (/ x (+ y x)))