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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.7512236628315378 \cdot 10^{+131}:\\ \;\;\;\;\frac{\frac{\left(\frac{a}{b} \cdot c - b\right) \cdot 2}{a}}{2}\\ \mathbf{elif}\;b \le 1.489031291672483 \cdot 10^{-98}:\\ \;\;\;\;\frac{\frac{\sqrt{b \cdot b + \left(c \cdot a\right) \cdot -4} - b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{c}{b} \cdot -2}{2}\\ \end{array}\]

\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 -1.7512236628315378 \cdot 10^{+131}:\\
\;\;\;\;\frac{\frac{\left(\frac{a}{b} \cdot c - b\right) \cdot 2}{a}}{2}\\

\mathbf{elif}\;b \le 1.489031291672483 \cdot 10^{-98}:\\
\;\;\;\;\frac{\frac{\sqrt{b \cdot b + \left(c \cdot a\right) \cdot -4} - b}{a}}{2}\\

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

\end{array}

double f(double a, double b, double c) {
        double r1545994 = b;
        double r1545995 = -r1545994;
        double r1545996 = r1545994 * r1545994;
        double r1545997 = 4.0;
        double r1545998 = a;
        double r1545999 = c;
        double r1546000 = r1545998 * r1545999;
        double r1546001 = r1545997 * r1546000;
        double r1546002 = r1545996 - r1546001;
        double r1546003 = sqrt(r1546002);
        double r1546004 = r1545995 + r1546003;
        double r1546005 = 2.0;
        double r1546006 = r1546005 * r1545998;
        double r1546007 = r1546004 / r1546006;
        return r1546007;
}

↓

double f(double a, double b, double c) {
        double r1546008 = b;
        double r1546009 = -1.7512236628315378e+131;
        bool r1546010 = r1546008 <= r1546009;
        double r1546011 = a;
        double r1546012 = r1546011 / r1546008;
        double r1546013 = c;
        double r1546014 = r1546012 * r1546013;
        double r1546015 = r1546014 - r1546008;
        double r1546016 = 2.0;
        double r1546017 = r1546015 * r1546016;
        double r1546018 = r1546017 / r1546011;
        double r1546019 = r1546018 / r1546016;
        double r1546020 = 1.489031291672483e-98;
        bool r1546021 = r1546008 <= r1546020;
        double r1546022 = r1546008 * r1546008;
        double r1546023 = r1546013 * r1546011;
        double r1546024 = -4.0;
        double r1546025 = r1546023 * r1546024;
        double r1546026 = r1546022 + r1546025;
        double r1546027 = sqrt(r1546026);
        double r1546028 = r1546027 - r1546008;
        double r1546029 = r1546028 / r1546011;
        double r1546030 = r1546029 / r1546016;
        double r1546031 = r1546013 / r1546008;
        double r1546032 = -2.0;
        double r1546033 = r1546031 * r1546032;
        double r1546034 = r1546033 / r1546016;
        double r1546035 = r1546021 ? r1546030 : r1546034;
        double r1546036 = r1546010 ? r1546019 : r1546035;
        return r1546036;
}

Original	32.9
Target	20.4
Herbie	10.1

Derivation

Split input into 3 regimes
if b < -1.7512236628315378e+131
1. Initial program 51.5
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified51.5
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}}{2}}\]
3. Taylor expanded around -inf 9.8
  \[\leadsto \frac{\frac{\color{blue}{2 \cdot \frac{a \cdot c}{b} - 2 \cdot b}}{a}}{2}\]
4. Simplified3.0
  \[\leadsto \frac{\frac{\color{blue}{2 \cdot \left(\frac{a}{b} \cdot c - b\right)}}{a}}{2}\]
if -1.7512236628315378e+131 < b < 1.489031291672483e-98
1. Initial program 11.6
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified11.6
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}}{2}}\]
3. Using strategy rm
4. Applied sub-neg11.6
  \[\leadsto \frac{\frac{\sqrt{\color{blue}{b \cdot b + \left(-\left(4 \cdot a\right) \cdot c\right)}} - b}{a}}{2}\]
5. Simplified11.6
  \[\leadsto \frac{\frac{\sqrt{b \cdot b + \color{blue}{-4 \cdot \left(a \cdot c\right)}} - b}{a}}{2}\]
6. Using strategy rm
7. Applied *-un-lft-identity11.6
  \[\leadsto \frac{\frac{\sqrt{b \cdot b + -4 \cdot \left(a \cdot c\right)} - b}{\color{blue}{1 \cdot a}}}{2}\]
8. Applied associate-/r*11.6
  \[\leadsto \frac{\color{blue}{\frac{\frac{\sqrt{b \cdot b + -4 \cdot \left(a \cdot c\right)} - b}{1}}{a}}}{2}\]
9. Simplified11.6
  \[\leadsto \frac{\frac{\color{blue}{\sqrt{b \cdot b + \left(a \cdot c\right) \cdot -4} - b}}{a}}{2}\]
if 1.489031291672483e-98 < b
1. Initial program 51.5
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified51.5
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}}{2}}\]
3. Using strategy rm
4. Applied sub-neg51.5
  \[\leadsto \frac{\frac{\sqrt{\color{blue}{b \cdot b + \left(-\left(4 \cdot a\right) \cdot c\right)}} - b}{a}}{2}\]
5. Simplified51.5
  \[\leadsto \frac{\frac{\sqrt{b \cdot b + \color{blue}{-4 \cdot \left(a \cdot c\right)}} - b}{a}}{2}\]
6. Taylor expanded around inf 10.7
  \[\leadsto \frac{\color{blue}{-2 \cdot \frac{c}{b}}}{2}\]
Recombined 3 regimes into one program.
Final simplification10.1
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.7512236628315378 \cdot 10^{+131}:\\ \;\;\;\;\frac{\frac{\left(\frac{a}{b} \cdot c - b\right) \cdot 2}{a}}{2}\\ \mathbf{elif}\;b \le 1.489031291672483 \cdot 10^{-98}:\\ \;\;\;\;\frac{\frac{\sqrt{b \cdot b + \left(c \cdot a\right) \cdot -4} - b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{c}{b} \cdot -2}{2}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -1.7512236628315378e+131`

`if -1.7512236628315378e+131 < b < 1.489031291672483e-98`

`if 1.489031291672483e-98 < b`

Reproduce

In
Out