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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -2.541338025369698 \cdot 10^{+80}:\\ \;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\ \mathbf{elif}\;b \le 1.1094847447691107 \cdot 10^{-113}:\\ \;\;\;\;\frac{\frac{1}{\frac{a}{\sqrt{\mathsf{fma}\left(b, b, \left(-4 \cdot a\right) \cdot c\right)} - b}}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \end{array}\]

\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 -2.541338025369698 \cdot 10^{+80}:\\
\;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\

\mathbf{elif}\;b \le 1.1094847447691107 \cdot 10^{-113}:\\
\;\;\;\;\frac{\frac{1}{\frac{a}{\sqrt{\mathsf{fma}\left(b, b, \left(-4 \cdot a\right) \cdot c\right)} - b}}}{2}\\

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

\end{array}

double f(double a, double b, double c) {
        double r4191611 = b;
        double r4191612 = -r4191611;
        double r4191613 = r4191611 * r4191611;
        double r4191614 = 4.0;
        double r4191615 = a;
        double r4191616 = r4191614 * r4191615;
        double r4191617 = c;
        double r4191618 = r4191616 * r4191617;
        double r4191619 = r4191613 - r4191618;
        double r4191620 = sqrt(r4191619);
        double r4191621 = r4191612 + r4191620;
        double r4191622 = 2.0;
        double r4191623 = r4191622 * r4191615;
        double r4191624 = r4191621 / r4191623;
        return r4191624;
}

↓

double f(double a, double b, double c) {
        double r4191625 = b;
        double r4191626 = -2.541338025369698e+80;
        bool r4191627 = r4191625 <= r4191626;
        double r4191628 = c;
        double r4191629 = r4191628 / r4191625;
        double r4191630 = a;
        double r4191631 = r4191625 / r4191630;
        double r4191632 = r4191629 - r4191631;
        double r4191633 = 2.0;
        double r4191634 = r4191632 * r4191633;
        double r4191635 = r4191634 / r4191633;
        double r4191636 = 1.1094847447691107e-113;
        bool r4191637 = r4191625 <= r4191636;
        double r4191638 = 1.0;
        double r4191639 = -4.0;
        double r4191640 = r4191639 * r4191630;
        double r4191641 = r4191640 * r4191628;
        double r4191642 = fma(r4191625, r4191625, r4191641);
        double r4191643 = sqrt(r4191642);
        double r4191644 = r4191643 - r4191625;
        double r4191645 = r4191630 / r4191644;
        double r4191646 = r4191638 / r4191645;
        double r4191647 = r4191646 / r4191633;
        double r4191648 = -2.0;
        double r4191649 = r4191648 * r4191629;
        double r4191650 = r4191649 / r4191633;
        double r4191651 = r4191637 ? r4191647 : r4191650;
        double r4191652 = r4191627 ? r4191635 : r4191651;
        return r4191652;
}

Original	34.0
Target	20.9
Herbie	10.4

Derivation

Split input into 3 regimes
if b < -2.541338025369698e+80
1. Initial program 41.0
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified41.0
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot -4\right) \cdot c\right)} - b}{a}}{2}}\]
3. Taylor expanded around -inf 4.2
  \[\leadsto \frac{\color{blue}{2 \cdot \frac{c}{b} - 2 \cdot \frac{b}{a}}}{2}\]
4. Simplified4.2
  \[\leadsto \frac{\color{blue}{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}}{2}\]
if -2.541338025369698e+80 < b < 1.1094847447691107e-113
1. Initial program 12.5
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified12.5
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot -4\right) \cdot c\right)} - b}{a}}{2}}\]
3. Using strategy rm
4. Applied *-un-lft-identity12.5
  \[\leadsto \frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot -4\right) \cdot c\right)} - \color{blue}{1 \cdot b}}{a}}{2}\]
5. Applied *-un-lft-identity12.5
  \[\leadsto \frac{\frac{\color{blue}{1 \cdot \sqrt{\mathsf{fma}\left(b, b, \left(a \cdot -4\right) \cdot c\right)}} - 1 \cdot b}{a}}{2}\]
6. Applied distribute-lft-out--12.5
  \[\leadsto \frac{\frac{\color{blue}{1 \cdot \left(\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot -4\right) \cdot c\right)} - b\right)}}{a}}{2}\]
7. Applied associate-/l*12.7
  \[\leadsto \frac{\color{blue}{\frac{1}{\frac{a}{\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot -4\right) \cdot c\right)} - b}}}}{2}\]
if 1.1094847447691107e-113 < b
1. Initial program 51.6
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified51.6
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot -4\right) \cdot c\right)} - b}{a}}{2}}\]
3. Taylor expanded around inf 10.8
  \[\leadsto \frac{\color{blue}{-2 \cdot \frac{c}{b}}}{2}\]
Recombined 3 regimes into one program.
Final simplification10.4
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -2.541338025369698 \cdot 10^{+80}:\\ \;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\ \mathbf{elif}\;b \le 1.1094847447691107 \cdot 10^{-113}:\\ \;\;\;\;\frac{\frac{1}{\frac{a}{\sqrt{\mathsf{fma}\left(b, b, \left(-4 \cdot a\right) \cdot c\right)} - b}}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \end{array}\]

Error

Target

Derivation

`if b < -2.541338025369698e+80`

`if -2.541338025369698e+80 < b < 1.1094847447691107e-113`

`if 1.1094847447691107e-113 < b`

Reproduce