Average Error: 31.6 → 18.7
Time: 1.2s
Precision: 64
\[\sqrt{x \cdot x + y \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -3.8460535119133569 \cdot 10^{74}:\\ \;\;\;\;-1 \cdot x\\ \mathbf{elif}\;x \le -1.3504253849915568 \cdot 10^{-194}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le -2.968956980813959 \cdot 10^{-266}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 1.19099635470288769 \cdot 10^{-228}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le 1.08574889376971239 \cdot 10^{-190}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 3.98422560465703889 \cdot 10^{39}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
\sqrt{x \cdot x + y \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -3.8460535119133569 \cdot 10^{74}:\\
\;\;\;\;-1 \cdot x\\

\mathbf{elif}\;x \le -1.3504253849915568 \cdot 10^{-194}:\\
\;\;\;\;\sqrt{x \cdot x + y \cdot y}\\

\mathbf{elif}\;x \le -2.968956980813959 \cdot 10^{-266}:\\
\;\;\;\;y\\

\mathbf{elif}\;x \le 1.19099635470288769 \cdot 10^{-228}:\\
\;\;\;\;\sqrt{x \cdot x + y \cdot y}\\

\mathbf{elif}\;x \le 1.08574889376971239 \cdot 10^{-190}:\\
\;\;\;\;y\\

\mathbf{elif}\;x \le 3.98422560465703889 \cdot 10^{39}:\\
\;\;\;\;\sqrt{x \cdot x + y \cdot y}\\

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

\end{array}
double f(double x, double y) {
        double r909997 = x;
        double r909998 = r909997 * r909997;
        double r909999 = y;
        double r910000 = r909999 * r909999;
        double r910001 = r909998 + r910000;
        double r910002 = sqrt(r910001);
        return r910002;
}
↓
double f(double x, double y) {
        double r910003 = x;
        double r910004 = -3.846053511913357e+74;
        bool r910005 = r910003 <= r910004;
        double r910006 = -1.0;
        double r910007 = r910006 * r910003;
        double r910008 = -1.3504253849915568e-194;
        bool r910009 = r910003 <= r910008;
        double r910010 = r910003 * r910003;
        double r910011 = y;
        double r910012 = r910011 * r910011;
        double r910013 = r910010 + r910012;
        double r910014 = sqrt(r910013);
        double r910015 = -2.968956980813959e-266;
        bool r910016 = r910003 <= r910015;
        double r910017 = 1.1909963547028877e-228;
        bool r910018 = r910003 <= r910017;
        double r910019 = 1.0857488937697124e-190;
        bool r910020 = r910003 <= r910019;
        double r910021 = 3.984225604657039e+39;
        bool r910022 = r910003 <= r910021;
        double r910023 = r910022 ? r910014 : r910003;
        double r910024 = r910020 ? r910011 : r910023;
        double r910025 = r910018 ? r910014 : r910024;
        double r910026 = r910016 ? r910011 : r910025;
        double r910027 = r910009 ? r910014 : r910026;
        double r910028 = r910005 ? r910007 : r910027;
        return r910028;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original31.6
Target17.8
Herbie18.7
\[\begin{array}{l} \mathbf{if}\;x \lt -1.123695082659983 \cdot 10^{145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \lt 1.11655762118336204 \cdot 10^{93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if x < -3.846053511913357e+74

    1. Initial program 47.2

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

    2. Taylor expanded around -inf 10.7

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

    if -3.846053511913357e+74 < x < -1.3504253849915568e-194 or -2.968956980813959e-266 < x < 1.1909963547028877e-228 or 1.0857488937697124e-190 < x < 3.984225604657039e+39

    1. Initial program 20.9

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

    if -1.3504253849915568e-194 < x < -2.968956980813959e-266 or 1.1909963547028877e-228 < x < 1.0857488937697124e-190

    1. Initial program 31.4

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

    2. Taylor expanded around 0 34.8

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

    if 3.984225604657039e+39 < x

    1. Initial program 43.8

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

    2. Taylor expanded around inf 13.6

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

  4. Final simplification18.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.8460535119133569 \cdot 10^{74}:\\ \;\;\;\;-1 \cdot x\\ \mathbf{elif}\;x \le -1.3504253849915568 \cdot 10^{-194}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le -2.968956980813959 \cdot 10^{-266}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 1.19099635470288769 \cdot 10^{-228}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le 1.08574889376971239 \cdot 10^{-190}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 3.98422560465703889 \cdot 10^{39}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Reproduce

herbie shell --seed 2020057 
(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))))