Average Error: 32.3 → 18.0
Time: 2.3s
Precision: 64
\[\sqrt{x \cdot x + y \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -8.15024475259887937 \cdot 10^{153}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \le -9.52817244882649108 \cdot 10^{-265}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le 1.04745553524127593 \cdot 10^{-281}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 2.70835173311075 \cdot 10^{105}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
\sqrt{x \cdot x + y \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -8.15024475259887937 \cdot 10^{153}:\\
\;\;\;\;-x\\

\mathbf{elif}\;x \le -9.52817244882649108 \cdot 10^{-265}:\\
\;\;\;\;\sqrt{x \cdot x + y \cdot y}\\

\mathbf{elif}\;x \le 1.04745553524127593 \cdot 10^{-281}:\\
\;\;\;\;y\\

\mathbf{elif}\;x \le 2.70835173311075 \cdot 10^{105}:\\
\;\;\;\;\sqrt{x \cdot x + y \cdot y}\\

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

\end{array}
double f(double x, double y) {
        double r894517 = x;
        double r894518 = r894517 * r894517;
        double r894519 = y;
        double r894520 = r894519 * r894519;
        double r894521 = r894518 + r894520;
        double r894522 = sqrt(r894521);
        return r894522;
}
↓
double f(double x, double y) {
        double r894523 = x;
        double r894524 = -8.15024475259888e+153;
        bool r894525 = r894523 <= r894524;
        double r894526 = -r894523;
        double r894527 = -9.528172448826491e-265;
        bool r894528 = r894523 <= r894527;
        double r894529 = r894523 * r894523;
        double r894530 = y;
        double r894531 = r894530 * r894530;
        double r894532 = r894529 + r894531;
        double r894533 = sqrt(r894532);
        double r894534 = 1.047455535241276e-281;
        bool r894535 = r894523 <= r894534;
        double r894536 = 2.70835173311075e+105;
        bool r894537 = r894523 <= r894536;
        double r894538 = r894537 ? r894533 : r894523;
        double r894539 = r894535 ? r894530 : r894538;
        double r894540 = r894528 ? r894533 : r894539;
        double r894541 = r894525 ? r894526 : r894540;
        return r894541;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.3
Target17.9
Herbie18.0
\[\begin{array}{l} \mathbf{if}\;x \lt -1.123695082659983 \cdot 10^{145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \lt 1.11655762118336204 \cdot 10^{93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if x < -8.15024475259888e+153

    1. Initial program 63.9

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

    2. Taylor expanded around -inf 7.8

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

    3. Simplified7.8

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

    if -8.15024475259888e+153 < x < -9.528172448826491e-265 or 1.047455535241276e-281 < x < 2.70835173311075e+105

    1. Initial program 21.0

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

    if -9.528172448826491e-265 < x < 1.047455535241276e-281

    1. Initial program 30.8

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

    2. Taylor expanded around 0 32.9

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

    if 2.70835173311075e+105 < x

    1. Initial program 52.5

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

    2. Taylor expanded around inf 8.8

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

  4. Final simplification18.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -8.15024475259887937 \cdot 10^{153}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \le -9.52817244882649108 \cdot 10^{-265}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le 1.04745553524127593 \cdot 10^{-281}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 2.70835173311075 \cdot 10^{105}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(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))))