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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -2.766818940874854722177248139872145176232 \cdot 10^{100}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 7.923524897992036987166355557663274472861 \cdot 10^{-153}:\\ \;\;\;\;\frac{\frac{1}{2 \cdot a}}{\frac{1}{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} \cdot -1\\ \end{array}\]

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

\mathbf{elif}\;b \le 7.923524897992036987166355557663274472861 \cdot 10^{-153}:\\
\;\;\;\;\frac{\frac{1}{2 \cdot a}}{\frac{1}{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}}\\

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

\end{array}

double f(double a, double b, double c) {
        double r3527902 = b;
        double r3527903 = -r3527902;
        double r3527904 = r3527902 * r3527902;
        double r3527905 = 4.0;
        double r3527906 = a;
        double r3527907 = c;
        double r3527908 = r3527906 * r3527907;
        double r3527909 = r3527905 * r3527908;
        double r3527910 = r3527904 - r3527909;
        double r3527911 = sqrt(r3527910);
        double r3527912 = r3527903 + r3527911;
        double r3527913 = 2.0;
        double r3527914 = r3527913 * r3527906;
        double r3527915 = r3527912 / r3527914;
        return r3527915;
}

↓

double f(double a, double b, double c) {
        double r3527916 = b;
        double r3527917 = -2.7668189408748547e+100;
        bool r3527918 = r3527916 <= r3527917;
        double r3527919 = 1.0;
        double r3527920 = c;
        double r3527921 = r3527920 / r3527916;
        double r3527922 = a;
        double r3527923 = r3527916 / r3527922;
        double r3527924 = r3527921 - r3527923;
        double r3527925 = r3527919 * r3527924;
        double r3527926 = 7.923524897992037e-153;
        bool r3527927 = r3527916 <= r3527926;
        double r3527928 = 1.0;
        double r3527929 = 2.0;
        double r3527930 = r3527929 * r3527922;
        double r3527931 = r3527928 / r3527930;
        double r3527932 = r3527916 * r3527916;
        double r3527933 = 4.0;
        double r3527934 = r3527933 * r3527922;
        double r3527935 = r3527920 * r3527934;
        double r3527936 = r3527932 - r3527935;
        double r3527937 = sqrt(r3527936);
        double r3527938 = r3527937 - r3527916;
        double r3527939 = r3527928 / r3527938;
        double r3527940 = r3527931 / r3527939;
        double r3527941 = -1.0;
        double r3527942 = r3527921 * r3527941;
        double r3527943 = r3527927 ? r3527940 : r3527942;
        double r3527944 = r3527918 ? r3527925 : r3527943;
        return r3527944;
}

Original	34.6
Target	21.1
Herbie	10.7

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
  \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - \left(a \cdot 4\right) \cdot c} - b}{2 \cdot a}}\]
3. Taylor expanded around -inf 4.0
  \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
4. Simplified4.0
  \[\leadsto \color{blue}{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 1}\]
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. Simplified10.8
  \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - \left(a \cdot 4\right) \cdot c} - b}{2 \cdot a}}\]
3. Taylor expanded around 0 10.9
  \[\leadsto \frac{\sqrt{\color{blue}{{b}^{2} - 4 \cdot \left(a \cdot c\right)}} - b}{2 \cdot a}\]
4. Simplified10.8
  \[\leadsto \frac{\sqrt{\color{blue}{b \cdot b - c \cdot \left(a \cdot 4\right)}} - b}{2 \cdot a}\]
5. Taylor expanded around 0 10.9
  \[\leadsto \frac{\sqrt{\color{blue}{{b}^{2} - 4 \cdot \left(a \cdot c\right)}} - b}{2 \cdot a}\]
6. Simplified10.8
  \[\leadsto \frac{\sqrt{\color{blue}{b \cdot b - c \cdot \left(4 \cdot a\right)}} - b}{2 \cdot a}\]
7. Using strategy rm
8. Applied clear-num11.0
  \[\leadsto \color{blue}{\frac{1}{\frac{2 \cdot a}{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}}}\]
9. Using strategy rm
10. Applied div-inv11.0
  \[\leadsto \frac{1}{\color{blue}{\left(2 \cdot a\right) \cdot \frac{1}{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}}}\]
11. Applied associate-/r*11.0
  \[\leadsto \color{blue}{\frac{\frac{1}{2 \cdot a}}{\frac{1}{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}}}\]
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
  \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - \left(a \cdot 4\right) \cdot c} - b}{2 \cdot a}}\]
3. Taylor expanded around inf 12.7
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
Recombined 3 regimes into one program.
Final simplification10.7
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -2.766818940874854722177248139872145176232 \cdot 10^{100}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 7.923524897992036987166355557663274472861 \cdot 10^{-153}:\\ \;\;\;\;\frac{\frac{1}{2 \cdot a}}{\frac{1}{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} \cdot -1\\ \end{array}\]

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