Average Error: 31.5 → 17.7
Time: 1.0s
Precision: 64
\[\sqrt{x \cdot x + y \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -3.2448676667043955 \cdot 10^{94}:\\ \;\;\;\;-1 \cdot x\\ \mathbf{elif}\;x \le 3.30012455476501778 \cdot 10^{108}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
\sqrt{x \cdot x + y \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -3.2448676667043955 \cdot 10^{94}:\\
\;\;\;\;-1 \cdot x\\

\mathbf{elif}\;x \le 3.30012455476501778 \cdot 10^{108}:\\
\;\;\;\;\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 <= -3.2448676667043955e+94)) {
		VAR = (-1.0 * x);
	} else {
		double VAR_1;
		if ((x <= 3.300124554765018e+108)) {
			VAR_1 = sqrt(((x * x) + (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

Original31.5
Target17.6
Herbie17.7
\[\begin{array}{l} \mathbf{if}\;x \lt -1.123695082659983 \cdot 10^{145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \lt 1.11655762118336204 \cdot 10^{93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -3.2448676667043955e+94

    1. Initial program 50.7

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

    2. Taylor expanded around -inf 10.8

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

    if -3.2448676667043955e+94 < x < 3.300124554765018e+108

    1. Initial program 21.3

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

    if 3.300124554765018e+108 < x

    1. Initial program 54.0

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

    2. Taylor expanded around inf 9.8

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

  4. Final simplification17.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.2448676667043955 \cdot 10^{94}:\\ \;\;\;\;-1 \cdot x\\ \mathbf{elif}\;x \le 3.30012455476501778 \cdot 10^{108}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Reproduce

herbie shell --seed 2020105 
(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))))