Average Error: 31.3 → 17.2
Time: 1.5s
Precision: binary64
\[\sqrt{x \cdot x + y \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \leq -4.8534135319298755 \cdot 10^{+120}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -1.7561694933647637 \cdot 10^{-223}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \leq -1.6733231477544338 \cdot 10^{-305}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.6023651145839193 \cdot 10^{+102}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
\sqrt{x \cdot x + y \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;x \leq -4.8534135319298755 \cdot 10^{+120}:\\
\;\;\;\;-x\\

\mathbf{elif}\;x \leq -1.7561694933647637 \cdot 10^{-223}:\\
\;\;\;\;\sqrt{x \cdot x + y \cdot y}\\

\mathbf{elif}\;x \leq -1.6733231477544338 \cdot 10^{-305}:\\
\;\;\;\;y\\

\mathbf{elif}\;x \leq 1.6023651145839193 \cdot 10^{+102}:\\
\;\;\;\;\sqrt{x \cdot x + y \cdot y}\\

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

\end{array}
(FPCore (x y) :precision binary64 (sqrt (+ (* x x) (* y y))))
↓
(FPCore (x y)
 :precision binary64
 (if (<= x -4.8534135319298755e+120)
   (- x)
   (if (<= x -1.7561694933647637e-223)
     (sqrt (+ (* x x) (* y y)))
     (if (<= x -1.6733231477544338e-305)
       y
       (if (<= x 1.6023651145839193e+102) (sqrt (+ (* x x) (* y y))) x)))))
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 <= -4.8534135319298755e+120)) {
		VAR = ((double) -(x));
	} else {
		double VAR_1;
		if ((x <= -1.7561694933647637e-223)) {
			VAR_1 = ((double) sqrt(((double) (((double) (x * x)) + ((double) (y * y))))));
		} else {
			double VAR_2;
			if ((x <= -1.6733231477544338e-305)) {
				VAR_2 = y;
			} else {
				double VAR_3;
				if ((x <= 1.6023651145839193e+102)) {
					VAR_3 = ((double) sqrt(((double) (((double) (x * x)) + ((double) (y * y))))));
				} else {
					VAR_3 = x;
				}
				VAR_2 = VAR_3;
			}
			VAR_1 = VAR_2;
		}
		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

Original31.3
Target17.1
Herbie17.2
\[\begin{array}{l} \mathbf{if}\;x < -1.1236950826599826 \cdot 10^{+145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x < 1.116557621183362 \cdot 10^{+93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if x < -4.8534135319298755e120

    1. Initial program 55.8

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

    2. Taylor expanded around -inf 9.3

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

    3. Simplified9.3

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

    if -4.8534135319298755e120 < x < -1.75616949336476367e-223 or -1.6733231477544338e-305 < x < 1.602365114583919e102

    1. Initial program 19.3

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

    if -1.75616949336476367e-223 < x < -1.6733231477544338e-305

    1. Initial program 30.8

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

    2. Taylor expanded around 0 32.6

      \[\leadsto \color{blue}{y}\]

    if 1.602365114583919e102 < x

    1. Initial program 53.0

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

    2. Taylor expanded around inf 10.8

      \[\leadsto \color{blue}{x}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification17.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8534135319298755 \cdot 10^{+120}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -1.7561694933647637 \cdot 10^{-223}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \leq -1.6733231477544338 \cdot 10^{-305}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.6023651145839193 \cdot 10^{+102}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Reproduce

herbie shell --seed 2020198 
(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))))