Average Error: 33.2 → 9.9
Time: 18.3s
Precision: 64
\[\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b_2 \le -1.8774910265390396 \cdot 10^{-73}:\\ \;\;\;\;\frac{-1}{2} \cdot \frac{c}{b_2}\\ \mathbf{elif}\;b_2 \le 2.5703497435733685 \cdot 10^{+102}:\\ \;\;\;\;\left(\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}\right) \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b_2} \cdot \frac{1}{2} - 2 \cdot \frac{b_2}{a}\\ \end{array}\]
\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}
↓
\begin{array}{l}
\mathbf{if}\;b_2 \le -1.8774910265390396 \cdot 10^{-73}:\\
\;\;\;\;\frac{-1}{2} \cdot \frac{c}{b_2}\\

\mathbf{elif}\;b_2 \le 2.5703497435733685 \cdot 10^{+102}:\\
\;\;\;\;\left(\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}\right) \cdot \frac{1}{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 r524585 = b_2;
        double r524586 = -r524585;
        double r524587 = r524585 * r524585;
        double r524588 = a;
        double r524589 = c;
        double r524590 = r524588 * r524589;
        double r524591 = r524587 - r524590;
        double r524592 = sqrt(r524591);
        double r524593 = r524586 - r524592;
        double r524594 = r524593 / r524588;
        return r524594;
}
↓
double f(double a, double b_2, double c) {
        double r524595 = b_2;
        double r524596 = -1.8774910265390396e-73;
        bool r524597 = r524595 <= r524596;
        double r524598 = -0.5;
        double r524599 = c;
        double r524600 = r524599 / r524595;
        double r524601 = r524598 * r524600;
        double r524602 = 2.5703497435733685e+102;
        bool r524603 = r524595 <= r524602;
        double r524604 = -r524595;
        double r524605 = r524595 * r524595;
        double r524606 = a;
        double r524607 = r524606 * r524599;
        double r524608 = r524605 - r524607;
        double r524609 = sqrt(r524608);
        double r524610 = r524604 - r524609;
        double r524611 = 1.0;
        double r524612 = r524611 / r524606;
        double r524613 = r524610 * r524612;
        double r524614 = 0.5;
        double r524615 = r524600 * r524614;
        double r524616 = 2.0;
        double r524617 = r524595 / r524606;
        double r524618 = r524616 * r524617;
        double r524619 = r524615 - r524618;
        double r524620 = r524603 ? r524613 : r524619;
        double r524621 = r524597 ? r524601 : r524620;
        return r524621;
}

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 < -1.8774910265390396e-73

    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 8.6

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

    if -1.8774910265390396e-73 < b_2 < 2.5703497435733685e+102

    1. Initial program 13.1

      \[\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]
    2. Using strategy rm

    3. Applied div-inv13.2

      \[\leadsto \color{blue}{\left(\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}\right) \cdot \frac{1}{a}}\]

    if 2.5703497435733685e+102 < b_2

    1. Initial program 43.9

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

    2. Taylor expanded around inf 2.9

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

  4. Final simplification9.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;b_2 \le -1.8774910265390396 \cdot 10^{-73}:\\ \;\;\;\;\frac{-1}{2} \cdot \frac{c}{b_2}\\ \mathbf{elif}\;b_2 \le 2.5703497435733685 \cdot 10^{+102}:\\ \;\;\;\;\left(\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}\right) \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b_2} \cdot \frac{1}{2} - 2 \cdot \frac{b_2}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019153 
(FPCore (a b_2 c)
  :name "quad2m (problem 3.2.1, negative)"
  (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))