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

↓

\[\begin{array}{l} \mathbf{if}\;b_2 \le -6.316763554346385 \cdot 10^{+26}:\\ \;\;\;\;\frac{(\frac{1}{2} \cdot \left(\frac{a}{\frac{b_2}{c}}\right) + \left(b_2 \cdot -2\right))_*}{a}\\ \mathbf{elif}\;b_2 \le 7.643168247577731 \cdot 10^{-56}:\\ \;\;\;\;\frac{1}{\frac{a}{\sqrt{b_2 \cdot b_2 - a \cdot c} - b_2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b_2} \cdot \frac{-1}{2}\\ \end{array}\]

double f(double a, double b_2, double c) {
        double r1707395 = b_2;
        double r1707396 = -r1707395;
        double r1707397 = r1707395 * r1707395;
        double r1707398 = a;
        double r1707399 = c;
        double r1707400 = r1707398 * r1707399;
        double r1707401 = r1707397 - r1707400;
        double r1707402 = sqrt(r1707401);
        double r1707403 = r1707396 + r1707402;
        double r1707404 = r1707403 / r1707398;
        return r1707404;
}

↓

double f(double a, double b_2, double c) {
        double r1707405 = b_2;
        double r1707406 = -6.316763554346385e+26;
        bool r1707407 = r1707405 <= r1707406;
        double r1707408 = 0.5;
        double r1707409 = a;
        double r1707410 = c;
        double r1707411 = r1707405 / r1707410;
        double r1707412 = r1707409 / r1707411;
        double r1707413 = -2.0;
        double r1707414 = r1707405 * r1707413;
        double r1707415 = fma(r1707408, r1707412, r1707414);
        double r1707416 = r1707415 / r1707409;
        double r1707417 = 7.643168247577731e-56;
        bool r1707418 = r1707405 <= r1707417;
        double r1707419 = 1.0;
        double r1707420 = r1707405 * r1707405;
        double r1707421 = r1707409 * r1707410;
        double r1707422 = r1707420 - r1707421;
        double r1707423 = sqrt(r1707422);
        double r1707424 = r1707423 - r1707405;
        double r1707425 = r1707409 / r1707424;
        double r1707426 = r1707419 / r1707425;
        double r1707427 = r1707410 / r1707405;
        double r1707428 = -0.5;
        double r1707429 = r1707427 * r1707428;
        double r1707430 = r1707418 ? r1707426 : r1707429;
        double r1707431 = r1707407 ? r1707416 : r1707430;
        return r1707431;
}

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

↓

\begin{array}{l}
\mathbf{if}\;b_2 \le -6.316763554346385 \cdot 10^{+26}:\\
\;\;\;\;\frac{(\frac{1}{2} \cdot \left(\frac{a}{\frac{b_2}{c}}\right) + \left(b_2 \cdot -2\right))_*}{a}\\

\mathbf{elif}\;b_2 \le 7.643168247577731 \cdot 10^{-56}:\\
\;\;\;\;\frac{1}{\frac{a}{\sqrt{b_2 \cdot b_2 - a \cdot c} - b_2}}\\

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

\end{array}

Derivation

Split input into 3 regimes
if b_2 < -6.316763554346385e+26
1. Initial program 32.7
  \[\frac{\left(-b_2\right) + \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]
2. Simplified32.7
  \[\leadsto \color{blue}{\frac{\sqrt{b_2 \cdot b_2 - a \cdot c} - b_2}{a}}\]
3. Taylor expanded around -inf 10.5
  \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot \frac{a \cdot c}{b_2} - 2 \cdot b_2}}{a}\]
4. Simplified6.5
  \[\leadsto \frac{\color{blue}{(\frac{1}{2} \cdot \left(\frac{a}{\frac{b_2}{c}}\right) + \left(-2 \cdot b_2\right))_*}}{a}\]
if -6.316763554346385e+26 < b_2 < 7.643168247577731e-56
1. Initial program 15.5
  \[\frac{\left(-b_2\right) + \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]
2. Simplified15.5
  \[\leadsto \color{blue}{\frac{\sqrt{b_2 \cdot b_2 - a \cdot c} - b_2}{a}}\]
3. Using strategy rm
4. Applied *-un-lft-identity15.5
  \[\leadsto \frac{\sqrt{b_2 \cdot b_2 - a \cdot c} - \color{blue}{1 \cdot b_2}}{a}\]
5. Applied *-un-lft-identity15.5
  \[\leadsto \frac{\color{blue}{1 \cdot \sqrt{b_2 \cdot b_2 - a \cdot c}} - 1 \cdot b_2}{a}\]
6. Applied distribute-lft-out--15.5
  \[\leadsto \frac{\color{blue}{1 \cdot \left(\sqrt{b_2 \cdot b_2 - a \cdot c} - b_2\right)}}{a}\]
7. Applied associate-/l*15.6
  \[\leadsto \color{blue}{\frac{1}{\frac{a}{\sqrt{b_2 \cdot b_2 - a \cdot c} - b_2}}}\]
if 7.643168247577731e-56 < b_2
1. Initial program 53.3
  \[\frac{\left(-b_2\right) + \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]
2. Simplified53.3
  \[\leadsto \color{blue}{\frac{\sqrt{b_2 \cdot b_2 - a \cdot c} - b_2}{a}}\]
3. Taylor expanded around inf 8.5
  \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{c}{b_2}}\]
Recombined 3 regimes into one program.
Final simplification10.9
\[\leadsto \begin{array}{l} \mathbf{if}\;b_2 \le -6.316763554346385 \cdot 10^{+26}:\\ \;\;\;\;\frac{(\frac{1}{2} \cdot \left(\frac{a}{\frac{b_2}{c}}\right) + \left(b_2 \cdot -2\right))_*}{a}\\ \mathbf{elif}\;b_2 \le 7.643168247577731 \cdot 10^{-56}:\\ \;\;\;\;\frac{1}{\frac{a}{\sqrt{b_2 \cdot b_2 - a \cdot c} - b_2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b_2} \cdot \frac{-1}{2}\\ \end{array}\]

Error

Derivation

`if b_2 < -6.316763554346385e+26`

`if -6.316763554346385e+26 < b_2 < 7.643168247577731e-56`

`if 7.643168247577731e-56 < b_2`

Reproduce