Average Error: 0.0 → 0.0
Time: 1.9s
Precision: binary64
\[\frac{x}{y + x} \]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{x + y}\right)\right) \]
\frac{x}{y + x}
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{x + y}\right)\right)

(FPCore (x y) :precision binary64 (/ x (+ y x)))
↓
(FPCore (x y) :precision binary64 (log1p (expm1 (/ x (+ x y)))))
double code(double x, double y) {
	return x / (y + x);
}
↓
double code(double x, double y) {
	return log1p(expm1(x / (x + y)));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  2. Applied log1p-expm1-u_binary640.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2021280 
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, B"
  :precision binary64
  (/ x (+ y x)))