Average Error: 31.1 → 17.3
Time: 1.5s
Precision: 64
\[\sqrt{x \cdot x + y \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -7.4585822033812435 \cdot 10^{103}:\\ \;\;\;\;-1 \cdot x\\ \mathbf{elif}\;x \le 2.56439878537218745 \cdot 10^{-244}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le 2.9654757473955426 \cdot 10^{-173}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 1.556390230884587 \cdot 10^{144}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
\sqrt{x \cdot x + y \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -7.4585822033812435 \cdot 10^{103}:\\
\;\;\;\;-1 \cdot x\\

\mathbf{elif}\;x \le 2.56439878537218745 \cdot 10^{-244}:\\
\;\;\;\;\sqrt{x \cdot x + y \cdot y}\\

\mathbf{elif}\;x \le 2.9654757473955426 \cdot 10^{-173}:\\
\;\;\;\;y\\

\mathbf{elif}\;x \le 1.556390230884587 \cdot 10^{144}:\\
\;\;\;\;\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 <= -7.458582203381243e+103)) {
		VAR = (-1.0 * x);
	} else {
		double VAR_1;
		if ((x <= 2.5643987853721874e-244)) {
			VAR_1 = sqrt(((x * x) + (y * y)));
		} else {
			double VAR_2;
			if ((x <= 2.9654757473955426e-173)) {
				VAR_2 = y;
			} else {
				double VAR_3;
				if ((x <= 1.5563902308845874e+144)) {
					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
Target17.0
Herbie17.3
\[\begin{array}{l} \mathbf{if}\;x \lt -1.123695082659983 \cdot 10^{145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \lt 1.11655762118336204 \cdot 10^{93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if x < -7.458582203381243e+103

    1. Initial program 52.4

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

    2. Taylor expanded around -inf 10.5

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

    if -7.458582203381243e+103 < x < 2.5643987853721874e-244 or 2.9654757473955426e-173 < x < 1.5563902308845874e+144

    1. Initial program 19.7

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

    if 2.5643987853721874e-244 < x < 2.9654757473955426e-173

    1. Initial program 31.4

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

    2. Taylor expanded around 0 35.6

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

    if 1.5563902308845874e+144 < x

    1. Initial program 61.2

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

    2. Taylor expanded around inf 6.2

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

  4. Final simplification17.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -7.4585822033812435 \cdot 10^{103}:\\ \;\;\;\;-1 \cdot x\\ \mathbf{elif}\;x \le 2.56439878537218745 \cdot 10^{-244}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le 2.9654757473955426 \cdot 10^{-173}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 1.556390230884587 \cdot 10^{144}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Reproduce

herbie shell --seed 2020075 
(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))))