Average Error: 31.8 → 0.0

Time: 1.4s

Precision: binary64

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

↓

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

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

↓

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

(FPCore (x y) :precision binary64 (sqrt (+ (* x x) (* y y))))

↓

(FPCore (x y) :precision binary64 (hypot x y))

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	31.8
Target	17.4
Herbie	0.0

\[\begin{array}{l} \mathbf{if}\;x < -1.1236950826599826 \cdot 10^{+145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x < 1.116557621183362 \cdot 10^{+93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Derivation

Initial program 31.8
\[\sqrt{x \cdot x + y \cdot y} \]
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 2021275 
(FPCore (x y)
  :name "Data.Octree.Internal:octantDistance  from Octree-0.5.4.2"
  :precision binary64

  :herbie-target
  (if (< x -1.1236950826599826e+145) (- x) (if (< x 1.116557621183362e+93) (sqrt (+ (* x x) (* y y))) x))

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