Average Error: 31.6 → 0.0

Time: 464.0ms

Precision: 64

\[\sqrt{x \cdot x + y \cdot y}\]

↓

\[\mathsf{hypot}\left(x, y\right)\]

\sqrt{x \cdot x + y \cdot y}

↓

\mathsf{hypot}\left(x, y\right)

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

↓

double code(double x, double y) {
	return hypot(x, y);
}

Error

The X axis uses an exponential scale — Bits error versus `x`

Try it out

In
Out

Enter valid numbers for all inputs

Target

Original	31.6
Target	17.8
Herbie	0.0

\[\begin{array}{l} \mathbf{if}\;x \lt -1.123695082659983 \cdot 10^{145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \lt 1.11655762118336204 \cdot 10^{93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Derivation

Initial program 31.6
\[\sqrt{x \cdot x + y \cdot y}\]
Simplified0.0
\[\leadsto \color{blue}{\mathsf{hypot}\left(x, y\right)}\]
Final simplification0.0
\[\leadsto \mathsf{hypot}\left(x, y\right)\]

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(FPCore (x y)
  :name "Data.Octree.Internal:octantDistance  from Octree-0.5.4.2"
  :precision binary64

  :herbie-target
  (if (< x -1.123695082659983e+145) (- x) (if (< x 1.116557621183362e+93) (sqrt (+ (* x x) (* y y))) x))

  (sqrt (+ (* x x) (* y y))))