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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.665963569877209 \cdot 10^{+64}:\\ \;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\ \mathbf{elif}\;b \le 9.831724396970673 \cdot 10^{-110}:\\ \;\;\;\;\frac{\frac{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \end{array}\]

\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 -1.665963569877209 \cdot 10^{+64}:\\
\;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\

\mathbf{elif}\;b \le 9.831724396970673 \cdot 10^{-110}:\\
\;\;\;\;\frac{\frac{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}{a}}{2}\\

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

\end{array}

double f(double a, double b, double c) {
        double r1800630 = b;
        double r1800631 = -r1800630;
        double r1800632 = r1800630 * r1800630;
        double r1800633 = 4.0;
        double r1800634 = a;
        double r1800635 = c;
        double r1800636 = r1800634 * r1800635;
        double r1800637 = r1800633 * r1800636;
        double r1800638 = r1800632 - r1800637;
        double r1800639 = sqrt(r1800638);
        double r1800640 = r1800631 + r1800639;
        double r1800641 = 2.0;
        double r1800642 = r1800641 * r1800634;
        double r1800643 = r1800640 / r1800642;
        return r1800643;
}

↓

double f(double a, double b, double c) {
        double r1800644 = b;
        double r1800645 = -1.665963569877209e+64;
        bool r1800646 = r1800644 <= r1800645;
        double r1800647 = c;
        double r1800648 = r1800647 / r1800644;
        double r1800649 = a;
        double r1800650 = r1800644 / r1800649;
        double r1800651 = r1800648 - r1800650;
        double r1800652 = 2.0;
        double r1800653 = r1800651 * r1800652;
        double r1800654 = r1800653 / r1800652;
        double r1800655 = 9.831724396970673e-110;
        bool r1800656 = r1800644 <= r1800655;
        double r1800657 = r1800644 * r1800644;
        double r1800658 = 4.0;
        double r1800659 = r1800658 * r1800649;
        double r1800660 = r1800647 * r1800659;
        double r1800661 = r1800657 - r1800660;
        double r1800662 = sqrt(r1800661);
        double r1800663 = r1800662 - r1800644;
        double r1800664 = r1800663 / r1800649;
        double r1800665 = r1800664 / r1800652;
        double r1800666 = -2.0;
        double r1800667 = r1800666 * r1800648;
        double r1800668 = r1800667 / r1800652;
        double r1800669 = r1800656 ? r1800665 : r1800668;
        double r1800670 = r1800646 ? r1800654 : r1800669;
        return r1800670;
}

Original	33.1
Target	20.2
Herbie	10.3

Derivation

Split input into 3 regimes
if b < -1.665963569877209e+64
1. Initial program 37.7
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified37.7
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}}{2}}\]
3. Taylor expanded around 0 37.7
  \[\leadsto \frac{\frac{\sqrt{\color{blue}{{b}^{2} - 4 \cdot \left(a \cdot c\right)}} - b}{a}}{2}\]
4. Simplified37.7
  \[\leadsto \frac{\frac{\sqrt{\color{blue}{b \cdot b - \left(4 \cdot a\right) \cdot c}} - b}{a}}{2}\]
5. Using strategy rm
6. Applied div-inv37.8
  \[\leadsto \frac{\color{blue}{\left(\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b\right) \cdot \frac{1}{a}}}{2}\]
7. Taylor expanded around -inf 5.2
  \[\leadsto \frac{\color{blue}{2 \cdot \frac{c}{b} - 2 \cdot \frac{b}{a}}}{2}\]
8. Simplified5.2
  \[\leadsto \frac{\color{blue}{2 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}}{2}\]
if -1.665963569877209e+64 < b < 9.831724396970673e-110
1. Initial program 12.1
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified12.1
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}}{2}}\]
3. Taylor expanded around 0 12.1
  \[\leadsto \frac{\frac{\sqrt{\color{blue}{{b}^{2} - 4 \cdot \left(a \cdot c\right)}} - b}{a}}{2}\]
4. Simplified12.1
  \[\leadsto \frac{\frac{\sqrt{\color{blue}{b \cdot b - \left(4 \cdot a\right) \cdot c}} - b}{a}}{2}\]
if 9.831724396970673e-110 < b
1. Initial program 51.0
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified51.0
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}}{2}}\]
3. Taylor expanded around 0 51.0
  \[\leadsto \frac{\frac{\sqrt{\color{blue}{{b}^{2} - 4 \cdot \left(a \cdot c\right)}} - b}{a}}{2}\]
4. Simplified51.0
  \[\leadsto \frac{\frac{\sqrt{\color{blue}{b \cdot b - \left(4 \cdot a\right) \cdot c}} - b}{a}}{2}\]
5. Taylor expanded around inf 10.8
  \[\leadsto \frac{\color{blue}{-2 \cdot \frac{c}{b}}}{2}\]
Recombined 3 regimes into one program.
Final simplification10.3
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.665963569877209 \cdot 10^{+64}:\\ \;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\ \mathbf{elif}\;b \le 9.831724396970673 \cdot 10^{-110}:\\ \;\;\;\;\frac{\frac{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -1.665963569877209e+64`

`if -1.665963569877209e+64 < b < 9.831724396970673e-110`

`if 9.831724396970673e-110 < b`

Reproduce

In
Out