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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -2.766818940874854722177248139872145176232 \cdot 10^{100}:\\ \;\;\;\;\frac{2 \cdot \frac{c}{b} - 2 \cdot \frac{b}{a}}{2}\\ \mathbf{elif}\;b \le 7.923524897992036987166355557663274472861 \cdot 10^{-153}:\\ \;\;\;\;\frac{\frac{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4} - b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \end{array}\]

\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 -2.766818940874854722177248139872145176232 \cdot 10^{100}:\\
\;\;\;\;\frac{2 \cdot \frac{c}{b} - 2 \cdot \frac{b}{a}}{2}\\

\mathbf{elif}\;b \le 7.923524897992036987166355557663274472861 \cdot 10^{-153}:\\
\;\;\;\;\frac{\frac{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4} - b}{a}}{2}\\

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

\end{array}

double f(double a, double b, double c) {
        double r4100907 = b;
        double r4100908 = -r4100907;
        double r4100909 = r4100907 * r4100907;
        double r4100910 = 4.0;
        double r4100911 = a;
        double r4100912 = c;
        double r4100913 = r4100911 * r4100912;
        double r4100914 = r4100910 * r4100913;
        double r4100915 = r4100909 - r4100914;
        double r4100916 = sqrt(r4100915);
        double r4100917 = r4100908 + r4100916;
        double r4100918 = 2.0;
        double r4100919 = r4100918 * r4100911;
        double r4100920 = r4100917 / r4100919;
        return r4100920;
}

↓

double f(double a, double b, double c) {
        double r4100921 = b;
        double r4100922 = -2.7668189408748547e+100;
        bool r4100923 = r4100921 <= r4100922;
        double r4100924 = 2.0;
        double r4100925 = c;
        double r4100926 = r4100925 / r4100921;
        double r4100927 = r4100924 * r4100926;
        double r4100928 = 2.0;
        double r4100929 = a;
        double r4100930 = r4100921 / r4100929;
        double r4100931 = r4100928 * r4100930;
        double r4100932 = r4100927 - r4100931;
        double r4100933 = r4100932 / r4100924;
        double r4100934 = 7.923524897992037e-153;
        bool r4100935 = r4100921 <= r4100934;
        double r4100936 = r4100921 * r4100921;
        double r4100937 = r4100929 * r4100925;
        double r4100938 = 4.0;
        double r4100939 = r4100937 * r4100938;
        double r4100940 = r4100936 - r4100939;
        double r4100941 = sqrt(r4100940);
        double r4100942 = r4100941 - r4100921;
        double r4100943 = r4100942 / r4100929;
        double r4100944 = r4100943 / r4100924;
        double r4100945 = -2.0;
        double r4100946 = r4100945 * r4100926;
        double r4100947 = r4100946 / r4100924;
        double r4100948 = r4100935 ? r4100944 : r4100947;
        double r4100949 = r4100923 ? r4100933 : r4100948;
        return r4100949;
}

Original	34.6
Target	21.1
Herbie	10.6

Derivation

Split input into 3 regimes
if b < -2.7668189408748547e+100
1. Initial program 47.2
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified47.2
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(a \cdot 4\right) \cdot c} - b}{a}}{2}}\]
3. Taylor expanded around -inf 4.1
  \[\leadsto \frac{\color{blue}{2 \cdot \frac{c}{b} - 2 \cdot \frac{b}{a}}}{2}\]
if -2.7668189408748547e+100 < b < 7.923524897992037e-153
1. Initial program 10.9
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified10.9
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(a \cdot 4\right) \cdot c} - b}{a}}{2}}\]
3. Using strategy rm
4. Applied clear-num11.0
  \[\leadsto \frac{\color{blue}{\frac{1}{\frac{a}{\sqrt{b \cdot b - \left(a \cdot 4\right) \cdot c} - b}}}}{2}\]
5. Using strategy rm
6. Applied *-un-lft-identity11.0
  \[\leadsto \frac{\frac{1}{\frac{a}{\color{blue}{1 \cdot \left(\sqrt{b \cdot b - \left(a \cdot 4\right) \cdot c} - b\right)}}}}{2}\]
7. Applied *-un-lft-identity11.0
  \[\leadsto \frac{\frac{1}{\frac{\color{blue}{1 \cdot a}}{1 \cdot \left(\sqrt{b \cdot b - \left(a \cdot 4\right) \cdot c} - b\right)}}}{2}\]
8. Applied times-frac11.0
  \[\leadsto \frac{\frac{1}{\color{blue}{\frac{1}{1} \cdot \frac{a}{\sqrt{b \cdot b - \left(a \cdot 4\right) \cdot c} - b}}}}{2}\]
9. Applied add-cube-cbrt11.0
  \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{1}{1} \cdot \frac{a}{\sqrt{b \cdot b - \left(a \cdot 4\right) \cdot c} - b}}}{2}\]
10. Applied times-frac11.0
  \[\leadsto \frac{\color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{1}{1}} \cdot \frac{\sqrt[3]{1}}{\frac{a}{\sqrt{b \cdot b - \left(a \cdot 4\right) \cdot c} - b}}}}{2}\]
11. Simplified11.0
  \[\leadsto \frac{\color{blue}{1} \cdot \frac{\sqrt[3]{1}}{\frac{a}{\sqrt{b \cdot b - \left(a \cdot 4\right) \cdot c} - b}}}{2}\]
12. Simplified10.9
  \[\leadsto \frac{1 \cdot \color{blue}{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{a}}}{2}\]
if 7.923524897992037e-153 < b
1. Initial program 50.5
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified50.5
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(a \cdot 4\right) \cdot c} - b}{a}}{2}}\]
3. Taylor expanded around inf 12.7
  \[\leadsto \frac{\color{blue}{-2 \cdot \frac{c}{b}}}{2}\]
Recombined 3 regimes into one program.
Final simplification10.6
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -2.766818940874854722177248139872145176232 \cdot 10^{100}:\\ \;\;\;\;\frac{2 \cdot \frac{c}{b} - 2 \cdot \frac{b}{a}}{2}\\ \mathbf{elif}\;b \le 7.923524897992036987166355557663274472861 \cdot 10^{-153}:\\ \;\;\;\;\frac{\frac{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4} - b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -2.7668189408748547e+100`

`if -2.7668189408748547e+100 < b < 7.923524897992037e-153`

`if 7.923524897992037e-153 < b`

Reproduce

In
Out