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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.2957079292059776 \cdot 10^{+154}:\\ \;\;\;\;\frac{\frac{-2 \cdot b}{a}}{2}\\ \mathbf{elif}\;b \le 1.502588793204478 \cdot 10^{-55}:\\ \;\;\;\;\frac{\frac{\sqrt{\mathsf{fma}\left(b, b, c \cdot \left(-4 \cdot a\right)\right)} - b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{a \cdot c}{b} \cdot -2}{a}}{2}\\ \end{array}\]

\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 -1.2957079292059776 \cdot 10^{+154}:\\
\;\;\;\;\frac{\frac{-2 \cdot b}{a}}{2}\\

\mathbf{elif}\;b \le 1.502588793204478 \cdot 10^{-55}:\\
\;\;\;\;\frac{\frac{\sqrt{\mathsf{fma}\left(b, b, c \cdot \left(-4 \cdot a\right)\right)} - b}{a}}{2}\\

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

\end{array}

double f(double a, double b, double c) {
        double r1160995 = b;
        double r1160996 = -r1160995;
        double r1160997 = r1160995 * r1160995;
        double r1160998 = 4.0;
        double r1160999 = a;
        double r1161000 = r1160998 * r1160999;
        double r1161001 = c;
        double r1161002 = r1161000 * r1161001;
        double r1161003 = r1160997 - r1161002;
        double r1161004 = sqrt(r1161003);
        double r1161005 = r1160996 + r1161004;
        double r1161006 = 2.0;
        double r1161007 = r1161006 * r1160999;
        double r1161008 = r1161005 / r1161007;
        return r1161008;
}

↓

double f(double a, double b, double c) {
        double r1161009 = b;
        double r1161010 = -1.2957079292059776e+154;
        bool r1161011 = r1161009 <= r1161010;
        double r1161012 = -2.0;
        double r1161013 = r1161012 * r1161009;
        double r1161014 = a;
        double r1161015 = r1161013 / r1161014;
        double r1161016 = 2.0;
        double r1161017 = r1161015 / r1161016;
        double r1161018 = 1.502588793204478e-55;
        bool r1161019 = r1161009 <= r1161018;
        double r1161020 = c;
        double r1161021 = -4.0;
        double r1161022 = r1161021 * r1161014;
        double r1161023 = r1161020 * r1161022;
        double r1161024 = fma(r1161009, r1161009, r1161023);
        double r1161025 = sqrt(r1161024);
        double r1161026 = r1161025 - r1161009;
        double r1161027 = r1161026 / r1161014;
        double r1161028 = r1161027 / r1161016;
        double r1161029 = r1161014 * r1161020;
        double r1161030 = r1161029 / r1161009;
        double r1161031 = r1161030 * r1161012;
        double r1161032 = r1161031 / r1161014;
        double r1161033 = r1161032 / r1161016;
        double r1161034 = r1161019 ? r1161028 : r1161033;
        double r1161035 = r1161011 ? r1161017 : r1161034;
        return r1161035;
}

Original	33.3
Target	20.5
Herbie	13.8

Derivation

Split input into 3 regimes
if b < -1.2957079292059776e+154
1. Initial program 60.9
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified60.9
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot -4\right) \cdot c\right)} - b}{a}}{2}}\]
3. Using strategy rm
4. Applied add-sqr-sqrt60.9
  \[\leadsto \frac{\frac{\sqrt{\color{blue}{\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot -4\right) \cdot c\right)} \cdot \sqrt{\mathsf{fma}\left(b, b, \left(a \cdot -4\right) \cdot c\right)}}} - b}{a}}{2}\]
5. Applied sqrt-prod60.9
  \[\leadsto \frac{\frac{\color{blue}{\sqrt{\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot -4\right) \cdot c\right)}} \cdot \sqrt{\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot -4\right) \cdot c\right)}}} - b}{a}}{2}\]
6. Applied fma-neg60.9
  \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(\sqrt{\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot -4\right) \cdot c\right)}}, \sqrt{\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot -4\right) \cdot c\right)}}, -b\right)}}{a}}{2}\]
7. Taylor expanded around -inf 2.0
  \[\leadsto \frac{\frac{\color{blue}{-2 \cdot b}}{a}}{2}\]
8. Simplified2.0
  \[\leadsto \frac{\frac{\color{blue}{b \cdot -2}}{a}}{2}\]
if -1.2957079292059776e+154 < b < 1.502588793204478e-55
1. Initial program 12.7
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified12.7
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot -4\right) \cdot c\right)} - b}{a}}{2}}\]
3. Using strategy rm
4. Applied *-commutative12.7
  \[\leadsto \frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \color{blue}{c \cdot \left(a \cdot -4\right)}\right)} - b}{a}}{2}\]
if 1.502588793204478e-55 < b
1. Initial program 52.9
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified52.9
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot -4\right) \cdot c\right)} - b}{a}}{2}}\]
3. Taylor expanded around inf 18.8
  \[\leadsto \frac{\frac{\color{blue}{-2 \cdot \frac{a \cdot c}{b}}}{a}}{2}\]
Recombined 3 regimes into one program.
Final simplification13.8
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.2957079292059776 \cdot 10^{+154}:\\ \;\;\;\;\frac{\frac{-2 \cdot b}{a}}{2}\\ \mathbf{elif}\;b \le 1.502588793204478 \cdot 10^{-55}:\\ \;\;\;\;\frac{\frac{\sqrt{\mathsf{fma}\left(b, b, c \cdot \left(-4 \cdot a\right)\right)} - b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{a \cdot c}{b} \cdot -2}{a}}{2}\\ \end{array}\]

Error

Target

Derivation

`if b < -1.2957079292059776e+154`

`if -1.2957079292059776e+154 < b < 1.502588793204478e-55`

`if 1.502588793204478e-55 < b`

Reproduce