Average Error: 33.0 → 10.6
Time: 18.0s
Precision: 64
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -3.794505329565205 \cdot 10^{+146}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 1.6194276288860963:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]
\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}
↓
\begin{array}{l}
\mathbf{if}\;b \le -3.794505329565205 \cdot 10^{+146}:\\
\;\;\;\;\frac{c}{b} - \frac{b}{a}\\

\mathbf{elif}\;b \le 1.6194276288860963:\\
\;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}{a \cdot 2}\\

\mathbf{else}:\\
\;\;\;\;-\frac{c}{b}\\

\end{array}
double f(double a, double b, double c) {
        double r1699288 = b;
        double r1699289 = -r1699288;
        double r1699290 = r1699288 * r1699288;
        double r1699291 = 4.0;
        double r1699292 = a;
        double r1699293 = r1699291 * r1699292;
        double r1699294 = c;
        double r1699295 = r1699293 * r1699294;
        double r1699296 = r1699290 - r1699295;
        double r1699297 = sqrt(r1699296);
        double r1699298 = r1699289 + r1699297;
        double r1699299 = 2.0;
        double r1699300 = r1699299 * r1699292;
        double r1699301 = r1699298 / r1699300;
        return r1699301;
}
↓
double f(double a, double b, double c) {
        double r1699302 = b;
        double r1699303 = -3.794505329565205e+146;
        bool r1699304 = r1699302 <= r1699303;
        double r1699305 = c;
        double r1699306 = r1699305 / r1699302;
        double r1699307 = a;
        double r1699308 = r1699302 / r1699307;
        double r1699309 = r1699306 - r1699308;
        double r1699310 = 1.6194276288860963;
        bool r1699311 = r1699302 <= r1699310;
        double r1699312 = -r1699302;
        double r1699313 = r1699302 * r1699302;
        double r1699314 = 4.0;
        double r1699315 = r1699314 * r1699307;
        double r1699316 = r1699305 * r1699315;
        double r1699317 = r1699313 - r1699316;
        double r1699318 = sqrt(r1699317);
        double r1699319 = r1699312 + r1699318;
        double r1699320 = 2.0;
        double r1699321 = r1699307 * r1699320;
        double r1699322 = r1699319 / r1699321;
        double r1699323 = -r1699306;
        double r1699324 = r1699311 ? r1699322 : r1699323;
        double r1699325 = r1699304 ? r1699309 : r1699324;
        return r1699325;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if b < -3.794505329565205e+146

    1. Initial program 58.0

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
    2. Using strategy rm

    3. Applied div-inv58.0

      \[\leadsto \color{blue}{\left(\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \frac{1}{2 \cdot a}}\]

    4. Simplified58.0

      \[\leadsto \left(\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \color{blue}{\frac{\frac{1}{2}}{a}}\]

    5. Taylor expanded around -inf 3.1

      \[\leadsto \color{blue}{\frac{c}{b} - \frac{b}{a}}\]

    if -3.794505329565205e+146 < b < 1.6194276288860963

    1. Initial program 15.0

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]

    if 1.6194276288860963 < b

    1. Initial program 54.4

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]

    2. Taylor expanded around inf 5.9

      \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]

    3. Simplified5.9

      \[\leadsto \color{blue}{-\frac{c}{b}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification10.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -3.794505329565205 \cdot 10^{+146}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 1.6194276288860963:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]

Reproduce

herbie shell --seed 2019129 
(FPCore (a b c)
  :name "Quadratic roots, full range"
  (/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)))