Average Error: 37.3 → 25.5
Time: 5.0s
Precision: 64
\[\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.472200864118953065071901202153872070472 \cdot 10^{97}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \le 9.739776979507705930755011088832346945497 \cdot 10^{134}:\\ \;\;\;\;\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.472200864118953065071901202153872070472 \cdot 10^{97}:\\
\;\;\;\;-x\\

\mathbf{elif}\;x \le 9.739776979507705930755011088832346945497 \cdot 10^{134}:\\
\;\;\;\;\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r469536 = x;
        double r469537 = r469536 * r469536;
        double r469538 = y;
        double r469539 = r469538 * r469538;
        double r469540 = r469537 + r469539;
        double r469541 = z;
        double r469542 = r469541 * r469541;
        double r469543 = r469540 + r469542;
        double r469544 = sqrt(r469543);
        return r469544;
}
↓
double f(double x, double y, double z) {
        double r469545 = x;
        double r469546 = -1.472200864118953e+97;
        bool r469547 = r469545 <= r469546;
        double r469548 = -r469545;
        double r469549 = 9.739776979507706e+134;
        bool r469550 = r469545 <= r469549;
        double r469551 = r469545 * r469545;
        double r469552 = y;
        double r469553 = r469552 * r469552;
        double r469554 = r469551 + r469553;
        double r469555 = z;
        double r469556 = r469555 * r469555;
        double r469557 = r469554 + r469556;
        double r469558 = sqrt(r469557);
        double r469559 = r469550 ? r469558 : r469545;
        double r469560 = r469547 ? r469548 : r469559;
        return r469560;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original37.3
Target24.7
Herbie25.5
\[\begin{array}{l} \mathbf{if}\;z \lt -6.396479394109775845820908799933348003545 \cdot 10^{136}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \lt 7.320293694404182125923160810847974073098 \cdot 10^{117}:\\ \;\;\;\;\sqrt{\left(z \cdot z + x \cdot x\right) + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -1.472200864118953e+97

    1. Initial program 55.7

      \[\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}\]

    2. Taylor expanded around -inf 19.7

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

    3. Simplified19.7

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

    if -1.472200864118953e+97 < x < 9.739776979507706e+134

    1. Initial program 28.8

      \[\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}\]

    if 9.739776979507706e+134 < x

    1. Initial program 59.9

      \[\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}\]

    2. Taylor expanded around inf 15.2

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

  4. Final simplification25.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.472200864118953065071901202153872070472 \cdot 10^{97}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \le 9.739776979507705930755011088832346945497 \cdot 10^{134}:\\ \;\;\;\;\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z)
  :name "FRP.Yampa.Vector3:vector3Rho from Yampa-0.10.2"
  :precision binary64

  :herbie-target
  (if (< z -6.3964793941097758e136) (- z) (if (< z 7.3202936944041821e117) (sqrt (+ (+ (* z z) (* x x)) (* y y))) z))

  (sqrt (+ (+ (* x x) (* y y)) (* z z))))