Average Error: 31.1 → 18.9
Time: 947.0ms
Precision: 64
\[\sqrt{x \cdot x + y \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -8.1561596166685901 \cdot 10^{125}:\\ \;\;\;\;-1 \cdot x\\ \mathbf{elif}\;x \le -3.80996693730795831 \cdot 10^{-103}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le 2.33673518569970664 \cdot 10^{-296}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 1.0193327448038136 \cdot 10^{95}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
\sqrt{x \cdot x + y \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -8.1561596166685901 \cdot 10^{125}:\\
\;\;\;\;-1 \cdot x\\

\mathbf{elif}\;x \le -3.80996693730795831 \cdot 10^{-103}:\\
\;\;\;\;\sqrt{x \cdot x + y \cdot y}\\

\mathbf{elif}\;x \le 2.33673518569970664 \cdot 10^{-296}:\\
\;\;\;\;y\\

\mathbf{elif}\;x \le 1.0193327448038136 \cdot 10^{95}:\\
\;\;\;\;\sqrt{x \cdot x + y \cdot y}\\

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

\end{array}
double code(double x, double y) {
	return sqrt(((x * x) + (y * y)));
}
↓
double code(double x, double y) {
	double VAR;
	if ((x <= -8.15615961666859e+125)) {
		VAR = (-1.0 * x);
	} else {
		double VAR_1;
		if ((x <= -3.8099669373079583e-103)) {
			VAR_1 = sqrt(((x * x) + (y * y)));
		} else {
			double VAR_2;
			if ((x <= 2.3367351856997066e-296)) {
				VAR_2 = y;
			} else {
				double VAR_3;
				if ((x <= 1.0193327448038136e+95)) {
					VAR_3 = sqrt(((x * x) + (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

Original31.1
Target17.5
Herbie18.9
\[\begin{array}{l} \mathbf{if}\;x \lt -1.123695082659983 \cdot 10^{145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \lt 1.11655762118336204 \cdot 10^{93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if x < -8.15615961666859e+125

    1. Initial program 55.6

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

    2. Taylor expanded around -inf 9.1

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

    if -8.15615961666859e+125 < x < -3.8099669373079583e-103 or 2.3367351856997066e-296 < x < 1.0193327448038136e+95

    1. Initial program 18.9

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

    if -3.8099669373079583e-103 < x < 2.3367351856997066e-296

    1. Initial program 27.8

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

    2. Taylor expanded around 0 36.1

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

    if 1.0193327448038136e+95 < x

    1. Initial program 50.2

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

    2. Taylor expanded around inf 10.4

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

  4. Final simplification18.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -8.1561596166685901 \cdot 10^{125}:\\ \;\;\;\;-1 \cdot x\\ \mathbf{elif}\;x \le -3.80996693730795831 \cdot 10^{-103}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le 2.33673518569970664 \cdot 10^{-296}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 1.0193327448038136 \cdot 10^{95}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Reproduce

herbie shell --seed 2020100 
(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))))