Average Error: 31.8 → 18.8
Time: 994.0ms
Precision: 64
\[\sqrt{x \cdot x + y \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -8789989068572990460:\\ \;\;\;\;-1 \cdot x\\ \mathbf{elif}\;x \le -4.2015690056388073 \cdot 10^{-231}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le 1.33367121357677706 \cdot 10^{-291}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 8.0509896767148372 \cdot 10^{-74}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le 1.3202809311828264 \cdot 10^{-48}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 3.9171532397504441 \cdot 10^{68}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
\sqrt{x \cdot x + y \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -8789989068572990460:\\
\;\;\;\;-1 \cdot x\\

\mathbf{elif}\;x \le -4.2015690056388073 \cdot 10^{-231}:\\
\;\;\;\;\sqrt{x \cdot x + y \cdot y}\\

\mathbf{elif}\;x \le 1.33367121357677706 \cdot 10^{-291}:\\
\;\;\;\;y\\

\mathbf{elif}\;x \le 8.0509896767148372 \cdot 10^{-74}:\\
\;\;\;\;\sqrt{x \cdot x + y \cdot y}\\

\mathbf{elif}\;x \le 1.3202809311828264 \cdot 10^{-48}:\\
\;\;\;\;y\\

\mathbf{elif}\;x \le 3.9171532397504441 \cdot 10^{68}:\\
\;\;\;\;\sqrt{x \cdot x + y \cdot y}\\

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

\end{array}
double f(double x, double y) {
        double r701974 = x;
        double r701975 = r701974 * r701974;
        double r701976 = y;
        double r701977 = r701976 * r701976;
        double r701978 = r701975 + r701977;
        double r701979 = sqrt(r701978);
        return r701979;
}
↓
double f(double x, double y) {
        double r701980 = x;
        double r701981 = -8.78998906857299e+18;
        bool r701982 = r701980 <= r701981;
        double r701983 = -1.0;
        double r701984 = r701983 * r701980;
        double r701985 = -4.2015690056388073e-231;
        bool r701986 = r701980 <= r701985;
        double r701987 = r701980 * r701980;
        double r701988 = y;
        double r701989 = r701988 * r701988;
        double r701990 = r701987 + r701989;
        double r701991 = sqrt(r701990);
        double r701992 = 1.333671213576777e-291;
        bool r701993 = r701980 <= r701992;
        double r701994 = 8.050989676714837e-74;
        bool r701995 = r701980 <= r701994;
        double r701996 = 1.3202809311828264e-48;
        bool r701997 = r701980 <= r701996;
        double r701998 = 3.917153239750444e+68;
        bool r701999 = r701980 <= r701998;
        double r702000 = r701999 ? r701991 : r701980;
        double r702001 = r701997 ? r701988 : r702000;
        double r702002 = r701995 ? r701991 : r702001;
        double r702003 = r701993 ? r701988 : r702002;
        double r702004 = r701986 ? r701991 : r702003;
        double r702005 = r701982 ? r701984 : r702004;
        return r702005;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original31.8
Target17.3
Herbie18.8
\[\begin{array}{l} \mathbf{if}\;x \lt -1.123695082659983 \cdot 10^{145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \lt 1.11655762118336204 \cdot 10^{93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if x < -8.78998906857299e+18

    1. Initial program 42.6

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

    2. Taylor expanded around -inf 13.9

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

    if -8.78998906857299e+18 < x < -4.2015690056388073e-231 or 1.333671213576777e-291 < x < 8.050989676714837e-74 or 1.3202809311828264e-48 < x < 3.917153239750444e+68

    1. Initial program 20.2

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

    if -4.2015690056388073e-231 < x < 1.333671213576777e-291 or 8.050989676714837e-74 < x < 1.3202809311828264e-48

    1. Initial program 28.0

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

    2. Taylor expanded around 0 36.9

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

    if 3.917153239750444e+68 < x

    1. Initial program 48.1

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

    2. Taylor expanded around inf 12.1

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

  4. Final simplification18.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -8789989068572990460:\\ \;\;\;\;-1 \cdot x\\ \mathbf{elif}\;x \le -4.2015690056388073 \cdot 10^{-231}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le 1.33367121357677706 \cdot 10^{-291}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 8.0509896767148372 \cdot 10^{-74}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le 1.3202809311828264 \cdot 10^{-48}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 3.9171532397504441 \cdot 10^{68}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 
(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))))