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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -7.397994825724217 \cdot 10^{+150}:\\ \;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\ \mathbf{elif}\;b \le 1.2158870426682226 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{1}{\frac{a}{\sqrt{\mathsf{fma}\left(b, b, \left(-4 \cdot c\right) \cdot a\right)} - b}}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \end{array}\]

\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 -7.397994825724217 \cdot 10^{+150}:\\
\;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\

\mathbf{elif}\;b \le 1.2158870426682226 \cdot 10^{-82}:\\
\;\;\;\;\frac{\frac{1}{\frac{a}{\sqrt{\mathsf{fma}\left(b, b, \left(-4 \cdot c\right) \cdot a\right)} - b}}}{2}\\

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

\end{array}

double f(double a, double b, double c) {
        double r3176808 = b;
        double r3176809 = -r3176808;
        double r3176810 = r3176808 * r3176808;
        double r3176811 = 4.0;
        double r3176812 = a;
        double r3176813 = r3176811 * r3176812;
        double r3176814 = c;
        double r3176815 = r3176813 * r3176814;
        double r3176816 = r3176810 - r3176815;
        double r3176817 = sqrt(r3176816);
        double r3176818 = r3176809 + r3176817;
        double r3176819 = 2.0;
        double r3176820 = r3176819 * r3176812;
        double r3176821 = r3176818 / r3176820;
        return r3176821;
}

↓

double f(double a, double b, double c) {
        double r3176822 = b;
        double r3176823 = -7.397994825724217e+150;
        bool r3176824 = r3176822 <= r3176823;
        double r3176825 = c;
        double r3176826 = r3176825 / r3176822;
        double r3176827 = a;
        double r3176828 = r3176822 / r3176827;
        double r3176829 = r3176826 - r3176828;
        double r3176830 = 2.0;
        double r3176831 = r3176829 * r3176830;
        double r3176832 = r3176831 / r3176830;
        double r3176833 = 1.2158870426682226e-82;
        bool r3176834 = r3176822 <= r3176833;
        double r3176835 = 1.0;
        double r3176836 = -4.0;
        double r3176837 = r3176836 * r3176825;
        double r3176838 = r3176837 * r3176827;
        double r3176839 = fma(r3176822, r3176822, r3176838);
        double r3176840 = sqrt(r3176839);
        double r3176841 = r3176840 - r3176822;
        double r3176842 = r3176827 / r3176841;
        double r3176843 = r3176835 / r3176842;
        double r3176844 = r3176843 / r3176830;
        double r3176845 = -2.0;
        double r3176846 = r3176845 * r3176826;
        double r3176847 = r3176846 / r3176830;
        double r3176848 = r3176834 ? r3176844 : r3176847;
        double r3176849 = r3176824 ? r3176832 : r3176848;
        return r3176849;
}

Original	33.2
Target	20.6
Herbie	10.0

Derivation

Split input into 3 regimes
if b < -7.397994825724217e+150
1. Initial program 59.1
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified59.1
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot -4\right) \cdot c\right)} - b}{a}}{2}}\]
3. Using strategy rm
4. Applied associate-*l*59.1
  \[\leadsto \frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \color{blue}{a \cdot \left(-4 \cdot c\right)}\right)} - b}{a}}{2}\]
5. Taylor expanded around -inf 2.2
  \[\leadsto \frac{\color{blue}{2 \cdot \frac{c}{b} - 2 \cdot \frac{b}{a}}}{2}\]
6. Simplified2.2
  \[\leadsto \frac{\color{blue}{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}}{2}\]
if -7.397994825724217e+150 < b < 1.2158870426682226e-82
1. Initial program 11.8
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified11.8
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot -4\right) \cdot c\right)} - b}{a}}{2}}\]
3. Using strategy rm
4. Applied associate-*l*11.7
  \[\leadsto \frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \color{blue}{a \cdot \left(-4 \cdot c\right)}\right)} - b}{a}}{2}\]
5. Using strategy rm
6. Applied clear-num11.9
  \[\leadsto \frac{\color{blue}{\frac{1}{\frac{a}{\sqrt{\mathsf{fma}\left(b, b, a \cdot \left(-4 \cdot c\right)\right)} - b}}}}{2}\]
if 1.2158870426682226e-82 < b
1. Initial program 52.3
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified52.3
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot -4\right) \cdot c\right)} - b}{a}}{2}}\]
3. Using strategy rm
4. Applied associate-*l*52.3
  \[\leadsto \frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \color{blue}{a \cdot \left(-4 \cdot c\right)}\right)} - b}{a}}{2}\]
5. Taylor expanded around inf 9.9
  \[\leadsto \frac{\color{blue}{-2 \cdot \frac{c}{b}}}{2}\]
Recombined 3 regimes into one program.
Final simplification10.0
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -7.397994825724217 \cdot 10^{+150}:\\ \;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\ \mathbf{elif}\;b \le 1.2158870426682226 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{1}{\frac{a}{\sqrt{\mathsf{fma}\left(b, b, \left(-4 \cdot c\right) \cdot a\right)} - b}}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \end{array}\]

Error

Target

Derivation

`if b < -7.397994825724217e+150`

`if -7.397994825724217e+150 < b < 1.2158870426682226e-82`

`if 1.2158870426682226e-82 < b`

Reproduce