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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -2.221067196710922123169723133116561516447 \cdot 10^{149}:\\ \;\;\;\;\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 1\\ \mathbf{elif}\;b \le 2.898348930695269343280527497904161468201 \cdot 10^{-35}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\sqrt{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4}}, \sqrt{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4}}, -b\right)}{2}}{a}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

\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 -2.221067196710922123169723133116561516447 \cdot 10^{149}:\\
\;\;\;\;\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 1\\

\mathbf{elif}\;b \le 2.898348930695269343280527497904161468201 \cdot 10^{-35}:\\
\;\;\;\;\frac{\frac{\mathsf{fma}\left(\sqrt{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4}}, \sqrt{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4}}, -b\right)}{2}}{a}\\

\mathbf{else}:\\
\;\;\;\;-1 \cdot \frac{c}{b}\\

\end{array}

double f(double a, double b, double c) {
        double r5766635 = b;
        double r5766636 = -r5766635;
        double r5766637 = r5766635 * r5766635;
        double r5766638 = 4.0;
        double r5766639 = a;
        double r5766640 = r5766638 * r5766639;
        double r5766641 = c;
        double r5766642 = r5766640 * r5766641;
        double r5766643 = r5766637 - r5766642;
        double r5766644 = sqrt(r5766643);
        double r5766645 = r5766636 + r5766644;
        double r5766646 = 2.0;
        double r5766647 = r5766646 * r5766639;
        double r5766648 = r5766645 / r5766647;
        return r5766648;
}

↓

double f(double a, double b, double c) {
        double r5766649 = b;
        double r5766650 = -2.221067196710922e+149;
        bool r5766651 = r5766649 <= r5766650;
        double r5766652 = c;
        double r5766653 = r5766652 / r5766649;
        double r5766654 = a;
        double r5766655 = r5766649 / r5766654;
        double r5766656 = r5766653 - r5766655;
        double r5766657 = 1.0;
        double r5766658 = r5766656 * r5766657;
        double r5766659 = 2.8983489306952693e-35;
        bool r5766660 = r5766649 <= r5766659;
        double r5766661 = r5766649 * r5766649;
        double r5766662 = r5766654 * r5766652;
        double r5766663 = 4.0;
        double r5766664 = r5766662 * r5766663;
        double r5766665 = r5766661 - r5766664;
        double r5766666 = sqrt(r5766665);
        double r5766667 = sqrt(r5766666);
        double r5766668 = -r5766649;
        double r5766669 = fma(r5766667, r5766667, r5766668);
        double r5766670 = 2.0;
        double r5766671 = r5766669 / r5766670;
        double r5766672 = r5766671 / r5766654;
        double r5766673 = -1.0;
        double r5766674 = r5766673 * r5766653;
        double r5766675 = r5766660 ? r5766672 : r5766674;
        double r5766676 = r5766651 ? r5766658 : r5766675;
        return r5766676;
}

Original	34.4
Target	21.5
Herbie	10.7

Derivation

Split input into 3 regimes
if b < -2.221067196710922e+149
1. Initial program 62.3
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified62.3
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}{2}}{a}}\]
3. Taylor expanded around -inf 2.7
  \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
4. Simplified2.7
  \[\leadsto \color{blue}{1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}\]
if -2.221067196710922e+149 < b < 2.8983489306952693e-35
1. Initial program 14.6
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified14.6
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied add-sqr-sqrt14.6
  \[\leadsto \frac{\frac{\sqrt{\color{blue}{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} \cdot \sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)}}} - b}{2}}{a}\]
5. Applied sqrt-prod14.8
  \[\leadsto \frac{\frac{\color{blue}{\sqrt{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)}} \cdot \sqrt{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)}}} - b}{2}}{a}\]
6. Applied fma-neg14.8
  \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(\sqrt{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)}}, \sqrt{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)}}, -b\right)}}{2}}{a}\]
if 2.8983489306952693e-35 < b
1. Initial program 54.4
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified54.4
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}{2}}{a}}\]
3. Taylor expanded around inf 7.3
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
Recombined 3 regimes into one program.
Final simplification10.7
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -2.221067196710922123169723133116561516447 \cdot 10^{149}:\\ \;\;\;\;\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 1\\ \mathbf{elif}\;b \le 2.898348930695269343280527497904161468201 \cdot 10^{-35}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\sqrt{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4}}, \sqrt{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4}}, -b\right)}{2}}{a}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

Error

Target

Derivation

`if b < -2.221067196710922e+149`

`if -2.221067196710922e+149 < b < 2.8983489306952693e-35`

`if 2.8983489306952693e-35 < b`

Reproduce