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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.763315479739403460017265344144602342789 \cdot 10^{89}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-2, \frac{b}{a}, \frac{c \cdot 2}{b}\right)}{2}\\ \mathbf{elif}\;b \le 9.136492990928292133394320076175633285536 \cdot 10^{-23}:\\ \;\;\;\;\frac{\frac{1}{a} \cdot \left(\sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)} - b\right)}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;b \le -1.763315479739403460017265344144602342789 \cdot 10^{89}:\\
\;\;\;\;\frac{\mathsf{fma}\left(-2, \frac{b}{a}, \frac{c \cdot 2}{b}\right)}{2}\\

\mathbf{elif}\;b \le 9.136492990928292133394320076175633285536 \cdot 10^{-23}:\\
\;\;\;\;\frac{\frac{1}{a} \cdot \left(\sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)} - b\right)}{2}\\

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

\end{array}

double f(double a, double b, double c) {
        double r3941629 = b;
        double r3941630 = -r3941629;
        double r3941631 = r3941629 * r3941629;
        double r3941632 = 4.0;
        double r3941633 = a;
        double r3941634 = c;
        double r3941635 = r3941633 * r3941634;
        double r3941636 = r3941632 * r3941635;
        double r3941637 = r3941631 - r3941636;
        double r3941638 = sqrt(r3941637);
        double r3941639 = r3941630 + r3941638;
        double r3941640 = 2.0;
        double r3941641 = r3941640 * r3941633;
        double r3941642 = r3941639 / r3941641;
        return r3941642;
}

↓

double f(double a, double b, double c) {
        double r3941643 = b;
        double r3941644 = -1.7633154797394035e+89;
        bool r3941645 = r3941643 <= r3941644;
        double r3941646 = -2.0;
        double r3941647 = a;
        double r3941648 = r3941643 / r3941647;
        double r3941649 = c;
        double r3941650 = 2.0;
        double r3941651 = r3941649 * r3941650;
        double r3941652 = r3941651 / r3941643;
        double r3941653 = fma(r3941646, r3941648, r3941652);
        double r3941654 = r3941653 / r3941650;
        double r3941655 = 9.136492990928292e-23;
        bool r3941656 = r3941643 <= r3941655;
        double r3941657 = 1.0;
        double r3941658 = r3941657 / r3941647;
        double r3941659 = r3941643 * r3941643;
        double r3941660 = 4.0;
        double r3941661 = r3941647 * r3941660;
        double r3941662 = r3941649 * r3941661;
        double r3941663 = r3941659 - r3941662;
        double r3941664 = sqrt(r3941663);
        double r3941665 = r3941664 - r3941643;
        double r3941666 = r3941658 * r3941665;
        double r3941667 = r3941666 / r3941650;
        double r3941668 = -2.0;
        double r3941669 = r3941649 / r3941643;
        double r3941670 = r3941668 * r3941669;
        double r3941671 = r3941670 / r3941650;
        double r3941672 = r3941656 ? r3941667 : r3941671;
        double r3941673 = r3941645 ? r3941654 : r3941672;
        return r3941673;
}

Original	34.4
Target	21.3
Herbie	10.3

Derivation

Split input into 3 regimes
if b < -1.7633154797394035e+89
1. Initial program 45.7
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified45.7
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}}{2}}\]
3. Using strategy rm
4. Applied div-inv45.8
  \[\leadsto \frac{\color{blue}{\left(\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b\right) \cdot \frac{1}{a}}}{2}\]
5. Taylor expanded around -inf 3.9
  \[\leadsto \frac{\color{blue}{2 \cdot \frac{c}{b} - 2 \cdot \frac{b}{a}}}{2}\]
6. Simplified4.0
  \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-2, \frac{b}{a}, \frac{2 \cdot c}{b}\right)}}{2}\]
if -1.7633154797394035e+89 < b < 9.136492990928292e-23
1. Initial program 15.0
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified15.0
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}}{2}}\]
3. Using strategy rm
4. Applied div-inv15.2
  \[\leadsto \frac{\color{blue}{\left(\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b\right) \cdot \frac{1}{a}}}{2}\]
if 9.136492990928292e-23 < b
1. Initial program 55.4
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified55.5
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}}{2}}\]
3. Taylor expanded around inf 6.7
  \[\leadsto \frac{\color{blue}{-2 \cdot \frac{c}{b}}}{2}\]
Recombined 3 regimes into one program.
Final simplification10.3
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.763315479739403460017265344144602342789 \cdot 10^{89}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-2, \frac{b}{a}, \frac{c \cdot 2}{b}\right)}{2}\\ \mathbf{elif}\;b \le 9.136492990928292133394320076175633285536 \cdot 10^{-23}:\\ \;\;\;\;\frac{\frac{1}{a} \cdot \left(\sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)} - b\right)}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \end{array}\]

Error

Target

Derivation

`if b < -1.7633154797394035e+89`

`if -1.7633154797394035e+89 < b < 9.136492990928292e-23`

`if 9.136492990928292e-23 < b`

Reproduce