Average Error: 32.5 → 10.2
Time: 28.3s
Precision: 64
\[\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b_2 \le -1.2963906698702263 \cdot 10^{-56}:\\ \;\;\;\;\frac{-1}{2} \cdot \frac{c}{b_2}\\ \mathbf{elif}\;b_2 \le 9.735084379330809 \cdot 10^{+35}:\\ \;\;\;\;\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b_2} \cdot \frac{1}{2} - 2 \cdot \frac{b_2}{a}\\ \end{array}\]
\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}
↓
\begin{array}{l}
\mathbf{if}\;b_2 \le -1.2963906698702263 \cdot 10^{-56}:\\
\;\;\;\;\frac{-1}{2} \cdot \frac{c}{b_2}\\

\mathbf{elif}\;b_2 \le 9.735084379330809 \cdot 10^{+35}:\\
\;\;\;\;\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\\

\mathbf{else}:\\
\;\;\;\;\frac{c}{b_2} \cdot \frac{1}{2} - 2 \cdot \frac{b_2}{a}\\

\end{array}
double f(double a, double b_2, double c) {
        double r996378 = b_2;
        double r996379 = -r996378;
        double r996380 = r996378 * r996378;
        double r996381 = a;
        double r996382 = c;
        double r996383 = r996381 * r996382;
        double r996384 = r996380 - r996383;
        double r996385 = sqrt(r996384);
        double r996386 = r996379 - r996385;
        double r996387 = r996386 / r996381;
        return r996387;
}
↓
double f(double a, double b_2, double c) {
        double r996388 = b_2;
        double r996389 = -1.2963906698702263e-56;
        bool r996390 = r996388 <= r996389;
        double r996391 = -0.5;
        double r996392 = c;
        double r996393 = r996392 / r996388;
        double r996394 = r996391 * r996393;
        double r996395 = 9.735084379330809e+35;
        bool r996396 = r996388 <= r996395;
        double r996397 = -r996388;
        double r996398 = r996388 * r996388;
        double r996399 = a;
        double r996400 = r996399 * r996392;
        double r996401 = r996398 - r996400;
        double r996402 = sqrt(r996401);
        double r996403 = r996397 - r996402;
        double r996404 = r996403 / r996399;
        double r996405 = 0.5;
        double r996406 = r996393 * r996405;
        double r996407 = 2.0;
        double r996408 = r996388 / r996399;
        double r996409 = r996407 * r996408;
        double r996410 = r996406 - r996409;
        double r996411 = r996396 ? r996404 : r996410;
        double r996412 = r996390 ? r996394 : r996411;
        return r996412;
}

Error

Bits error versus a

Bits error versus b_2

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_2 < -1.2963906698702263e-56

    1. Initial program 52.5

      \[\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]

    2. Taylor expanded around -inf 8.3

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{c}{b_2}}\]

    if -1.2963906698702263e-56 < b_2 < 9.735084379330809e+35

    1. Initial program 13.8

      \[\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]

    if 9.735084379330809e+35 < b_2

    1. Initial program 33.0

      \[\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]

    2. Taylor expanded around inf 6.6

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{c}{b_2} - 2 \cdot \frac{b_2}{a}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification10.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;b_2 \le -1.2963906698702263 \cdot 10^{-56}:\\ \;\;\;\;\frac{-1}{2} \cdot \frac{c}{b_2}\\ \mathbf{elif}\;b_2 \le 9.735084379330809 \cdot 10^{+35}:\\ \;\;\;\;\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b_2} \cdot \frac{1}{2} - 2 \cdot \frac{b_2}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019149 
(FPCore (a b_2 c)
  :name "quad2m (problem 3.2.1, negative)"
  (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))