Average Error: 33.2 → 9.9
Time: 18.6s
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 r1817426 = b_2;
        double r1817427 = -r1817426;
        double r1817428 = r1817426 * r1817426;
        double r1817429 = a;
        double r1817430 = c;
        double r1817431 = r1817429 * r1817430;
        double r1817432 = r1817428 - r1817431;
        double r1817433 = sqrt(r1817432);
        double r1817434 = r1817427 - r1817433;
        double r1817435 = r1817434 / r1817429;
        return r1817435;
}
↓
double f(double a, double b_2, double c) {
        double r1817436 = b_2;
        double r1817437 = -1.8774910265390396e-73;
        bool r1817438 = r1817436 <= r1817437;
        double r1817439 = -0.5;
        double r1817440 = c;
        double r1817441 = r1817440 / r1817436;
        double r1817442 = r1817439 * r1817441;
        double r1817443 = 2.5703497435733685e+102;
        bool r1817444 = r1817436 <= r1817443;
        double r1817445 = -r1817436;
        double r1817446 = r1817436 * r1817436;
        double r1817447 = a;
        double r1817448 = r1817447 * r1817440;
        double r1817449 = r1817446 - r1817448;
        double r1817450 = sqrt(r1817449);
        double r1817451 = r1817445 - r1817450;
        double r1817452 = 1.0;
        double r1817453 = r1817452 / r1817447;
        double r1817454 = r1817451 * r1817453;
        double r1817455 = 0.5;
        double r1817456 = r1817441 * r1817455;
        double r1817457 = 2.0;
        double r1817458 = r1817436 / r1817447;
        double r1817459 = r1817457 * r1817458;
        double r1817460 = r1817456 - r1817459;
        double r1817461 = r1817444 ? r1817454 : r1817460;
        double r1817462 = r1817438 ? r1817442 : r1817461;
        return r1817462;
}

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 "NMSE problem 3.2.1"
  (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))