Average Error: 32.1 → 17.8
Time: 1.9s
Precision: binary64
\[\sqrt{x \cdot x + y \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.00706805242326439 \cdot 10^{130}:\\ \;\;\;\;-1 \cdot x\\ \mathbf{elif}\;x \le 7.17250003621042806 \cdot 10^{119}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
\sqrt{x \cdot x + y \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.00706805242326439 \cdot 10^{130}:\\
\;\;\;\;-1 \cdot x\\

\mathbf{elif}\;x \le 7.17250003621042806 \cdot 10^{119}:\\
\;\;\;\;\sqrt{x \cdot x + y \cdot y}\\

\mathbf{else}:\\
\;\;\;\;x\\

\end{array}
double code(double x, double y) {
	return ((double) sqrt(((double) (((double) (x * x)) + ((double) (y * y))))));
}
↓
double code(double x, double y) {
	double VAR;
	if ((x <= -1.0070680524232644e+130)) {
		VAR = ((double) (-1.0 * x));
	} else {
		double VAR_1;
		if ((x <= 7.172500036210428e+119)) {
			VAR_1 = ((double) sqrt(((double) (((double) (x * x)) + ((double) (y * y))))));
		} else {
			VAR_1 = x;
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.1
Target17.8
Herbie17.8
\[\begin{array}{l} \mathbf{if}\;x \lt -1.123695082659983 \cdot 10^{145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \lt 1.11655762118336204 \cdot 10^{93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -1.00706805242326439e130

    1. Initial program 58.2

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

    2. Taylor expanded around -inf 9.0

      \[\leadsto \color{blue}{-1 \cdot x}\]

    if -1.00706805242326439e130 < x < 7.17250003621042806e119

    1. Initial program 21.5

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

    if 7.17250003621042806e119 < x

    1. Initial program 55.1

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

    2. Taylor expanded around inf 9.4

      \[\leadsto \color{blue}{x}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification17.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.00706805242326439 \cdot 10^{130}:\\ \;\;\;\;-1 \cdot x\\ \mathbf{elif}\;x \le 7.17250003621042806 \cdot 10^{119}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Reproduce

herbie shell --seed 2020177 
(FPCore (x y)
  :name "Data.Octree.Internal:octantDistance  from Octree-0.5.4.2"
  :precision binary64

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

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