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

↓

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

\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 r4468804 = b;
        double r4468805 = -r4468804;
        double r4468806 = r4468804 * r4468804;
        double r4468807 = 4.0;
        double r4468808 = a;
        double r4468809 = c;
        double r4468810 = r4468808 * r4468809;
        double r4468811 = r4468807 * r4468810;
        double r4468812 = r4468806 - r4468811;
        double r4468813 = sqrt(r4468812);
        double r4468814 = r4468805 + r4468813;
        double r4468815 = 2.0;
        double r4468816 = r4468815 * r4468808;
        double r4468817 = r4468814 / r4468816;
        return r4468817;
}

↓

double f(double a, double b, double c) {
        double r4468818 = b;
        double r4468819 = -1.7633154797394035e+89;
        bool r4468820 = r4468818 <= r4468819;
        double r4468821 = -2.0;
        double r4468822 = a;
        double r4468823 = r4468818 / r4468822;
        double r4468824 = c;
        double r4468825 = 2.0;
        double r4468826 = r4468824 * r4468825;
        double r4468827 = r4468826 / r4468818;
        double r4468828 = fma(r4468821, r4468823, r4468827);
        double r4468829 = r4468828 / r4468825;
        double r4468830 = 9.136492990928292e-23;
        bool r4468831 = r4468818 <= r4468830;
        double r4468832 = 1.0;
        double r4468833 = r4468832 / r4468822;
        double r4468834 = r4468818 * r4468818;
        double r4468835 = 4.0;
        double r4468836 = r4468822 * r4468835;
        double r4468837 = r4468824 * r4468836;
        double r4468838 = r4468834 - r4468837;
        double r4468839 = sqrt(r4468838);
        double r4468840 = r4468839 - r4468818;
        double r4468841 = r4468833 * r4468840;
        double r4468842 = r4468841 / r4468825;
        double r4468843 = -2.0;
        double r4468844 = r4468824 / r4468818;
        double r4468845 = r4468843 * r4468844;
        double r4468846 = r4468845 / r4468825;
        double r4468847 = r4468831 ? r4468842 : r4468846;
        double r4468848 = r4468820 ? r4468829 : r4468847;
        return r4468848;
}

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