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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.7512236628315378 \cdot 10^{+131}:\\ \;\;\;\;\frac{\frac{\left(\frac{a}{\frac{b}{c}} - b\right) \cdot 2}{a}}{2}\\ \mathbf{elif}\;b \le 2.2058723073785985 \cdot 10^{-38}:\\ \;\;\;\;\frac{\frac{\sqrt{\mathsf{fma}\left(a, -4 \cdot c, b \cdot b\right)} - b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-2 \cdot \frac{a \cdot c}{b}}{a}}{2}\\ \end{array}\]

\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 -1.7512236628315378 \cdot 10^{+131}:\\
\;\;\;\;\frac{\frac{\left(\frac{a}{\frac{b}{c}} - b\right) \cdot 2}{a}}{2}\\

\mathbf{elif}\;b \le 2.2058723073785985 \cdot 10^{-38}:\\
\;\;\;\;\frac{\frac{\sqrt{\mathsf{fma}\left(a, -4 \cdot c, b \cdot b\right)} - b}{a}}{2}\\

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

\end{array}

double f(double a, double b, double c) {
        double r1187443 = b;
        double r1187444 = -r1187443;
        double r1187445 = r1187443 * r1187443;
        double r1187446 = 4.0;
        double r1187447 = a;
        double r1187448 = r1187446 * r1187447;
        double r1187449 = c;
        double r1187450 = r1187448 * r1187449;
        double r1187451 = r1187445 - r1187450;
        double r1187452 = sqrt(r1187451);
        double r1187453 = r1187444 + r1187452;
        double r1187454 = 2.0;
        double r1187455 = r1187454 * r1187447;
        double r1187456 = r1187453 / r1187455;
        return r1187456;
}

↓

double f(double a, double b, double c) {
        double r1187457 = b;
        double r1187458 = -1.7512236628315378e+131;
        bool r1187459 = r1187457 <= r1187458;
        double r1187460 = a;
        double r1187461 = c;
        double r1187462 = r1187457 / r1187461;
        double r1187463 = r1187460 / r1187462;
        double r1187464 = r1187463 - r1187457;
        double r1187465 = 2.0;
        double r1187466 = r1187464 * r1187465;
        double r1187467 = r1187466 / r1187460;
        double r1187468 = r1187467 / r1187465;
        double r1187469 = 2.2058723073785985e-38;
        bool r1187470 = r1187457 <= r1187469;
        double r1187471 = -4.0;
        double r1187472 = r1187471 * r1187461;
        double r1187473 = r1187457 * r1187457;
        double r1187474 = fma(r1187460, r1187472, r1187473);
        double r1187475 = sqrt(r1187474);
        double r1187476 = r1187475 - r1187457;
        double r1187477 = r1187476 / r1187460;
        double r1187478 = r1187477 / r1187465;
        double r1187479 = -2.0;
        double r1187480 = r1187460 * r1187461;
        double r1187481 = r1187480 / r1187457;
        double r1187482 = r1187479 * r1187481;
        double r1187483 = r1187482 / r1187460;
        double r1187484 = r1187483 / r1187465;
        double r1187485 = r1187470 ? r1187478 : r1187484;
        double r1187486 = r1187459 ? r1187468 : r1187485;
        return r1187486;
}

Original	32.9
Target	20.4
Herbie	14.3

Derivation

Split input into 3 regimes
if b < -1.7512236628315378e+131
1. Initial program 51.5
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified51.5
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot -4\right) \cdot c\right)} - b}{a}}{2}}\]
3. Taylor expanded around -inf 9.8
  \[\leadsto \frac{\frac{\color{blue}{2 \cdot \frac{a \cdot c}{b} - 2 \cdot b}}{a}}{2}\]
4. Simplified3.0
  \[\leadsto \frac{\frac{\color{blue}{2 \cdot \left(\frac{a}{\frac{b}{c}} - b\right)}}{a}}{2}\]
if -1.7512236628315378e+131 < b < 2.2058723073785985e-38
1. Initial program 13.7
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified13.7
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot -4\right) \cdot c\right)} - b}{a}}{2}}\]
3. Taylor expanded around 0 13.7
  \[\leadsto \frac{\frac{\sqrt{\color{blue}{{b}^{2} - 4 \cdot \left(a \cdot c\right)}} - b}{a}}{2}\]
4. Simplified13.7
  \[\leadsto \frac{\frac{\sqrt{\color{blue}{\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)}} - b}{a}}{2}\]
5. Using strategy rm
6. Applied *-un-lft-identity13.7
  \[\leadsto \frac{\frac{\sqrt{\color{blue}{1 \cdot \mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)}} - b}{a}}{2}\]
if 2.2058723073785985e-38 < b
1. Initial program 53.8
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified53.8
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot -4\right) \cdot c\right)} - b}{a}}{2}}\]
3. Taylor expanded around inf 19.0
  \[\leadsto \frac{\frac{\color{blue}{-2 \cdot \frac{a \cdot c}{b}}}{a}}{2}\]
Recombined 3 regimes into one program.
Final simplification14.3
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.7512236628315378 \cdot 10^{+131}:\\ \;\;\;\;\frac{\frac{\left(\frac{a}{\frac{b}{c}} - b\right) \cdot 2}{a}}{2}\\ \mathbf{elif}\;b \le 2.2058723073785985 \cdot 10^{-38}:\\ \;\;\;\;\frac{\frac{\sqrt{\mathsf{fma}\left(a, -4 \cdot c, b \cdot b\right)} - b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-2 \cdot \frac{a \cdot c}{b}}{a}}{2}\\ \end{array}\]

Error

Target

Derivation

`if b < -1.7512236628315378e+131`

`if -1.7512236628315378e+131 < b < 2.2058723073785985e-38`

`if 2.2058723073785985e-38 < b`

Reproduce