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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.006124725233072906597672755451758607334 \cdot 10^{153}:\\ \;\;\;\;\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 1\\ \mathbf{elif}\;b \le 5.668416736491797065158030167390678793472 \cdot 10^{-35}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{a \cdot 2} - \frac{b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} \cdot -1\\ \end{array}\]

\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 -1.006124725233072906597672755451758607334 \cdot 10^{153}:\\
\;\;\;\;\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 1\\

\mathbf{elif}\;b \le 5.668416736491797065158030167390678793472 \cdot 10^{-35}:\\
\;\;\;\;\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{a \cdot 2} - \frac{b}{a \cdot 2}\\

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

\end{array}

double f(double a, double b, double c) {
        double r4777838 = b;
        double r4777839 = -r4777838;
        double r4777840 = r4777838 * r4777838;
        double r4777841 = 4.0;
        double r4777842 = a;
        double r4777843 = r4777841 * r4777842;
        double r4777844 = c;
        double r4777845 = r4777843 * r4777844;
        double r4777846 = r4777840 - r4777845;
        double r4777847 = sqrt(r4777846);
        double r4777848 = r4777839 + r4777847;
        double r4777849 = 2.0;
        double r4777850 = r4777849 * r4777842;
        double r4777851 = r4777848 / r4777850;
        return r4777851;
}

↓

double f(double a, double b, double c) {
        double r4777852 = b;
        double r4777853 = -1.0061247252330729e+153;
        bool r4777854 = r4777852 <= r4777853;
        double r4777855 = c;
        double r4777856 = r4777855 / r4777852;
        double r4777857 = a;
        double r4777858 = r4777852 / r4777857;
        double r4777859 = r4777856 - r4777858;
        double r4777860 = 1.0;
        double r4777861 = r4777859 * r4777860;
        double r4777862 = 5.668416736491797e-35;
        bool r4777863 = r4777852 <= r4777862;
        double r4777864 = r4777852 * r4777852;
        double r4777865 = 4.0;
        double r4777866 = r4777857 * r4777855;
        double r4777867 = r4777865 * r4777866;
        double r4777868 = r4777864 - r4777867;
        double r4777869 = sqrt(r4777868);
        double r4777870 = 2.0;
        double r4777871 = r4777857 * r4777870;
        double r4777872 = r4777869 / r4777871;
        double r4777873 = r4777852 / r4777871;
        double r4777874 = r4777872 - r4777873;
        double r4777875 = -1.0;
        double r4777876 = r4777856 * r4777875;
        double r4777877 = r4777863 ? r4777874 : r4777876;
        double r4777878 = r4777854 ? r4777861 : r4777877;
        return r4777878;
}

Original	34.0
Target	21.1
Herbie	10.2

Derivation

Split input into 3 regimes
if b < -1.0061247252330729e+153
1. Initial program 63.7
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Using strategy rm
3. Applied div-inv63.7
  \[\leadsto \color{blue}{\left(\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \frac{1}{2 \cdot a}}\]
4. Taylor expanded around -inf 2.0
  \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
5. Simplified2.0
  \[\leadsto \color{blue}{1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}\]
if -1.0061247252330729e+153 < b < 5.668416736491797e-35
1. Initial program 13.9
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Using strategy rm
3. Applied clear-num14.1
  \[\leadsto \color{blue}{\frac{1}{\frac{2 \cdot a}{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}}\]
4. Simplified14.1
  \[\leadsto \frac{1}{\color{blue}{\frac{a \cdot 2}{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4} - b}}}\]
5. Using strategy rm
6. Applied *-un-lft-identity14.1
  \[\leadsto \frac{1}{\color{blue}{1 \cdot \frac{a \cdot 2}{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4} - b}}}\]
7. Applied add-cube-cbrt14.1
  \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{1 \cdot \frac{a \cdot 2}{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4} - b}}\]
8. Applied times-frac14.1
  \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1} \cdot \frac{\sqrt[3]{1}}{\frac{a \cdot 2}{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4} - b}}}\]
9. Simplified14.1
  \[\leadsto \color{blue}{1} \cdot \frac{\sqrt[3]{1}}{\frac{a \cdot 2}{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4} - b}}\]
10. Simplified13.9
  \[\leadsto 1 \cdot \color{blue}{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{a \cdot 2}}\]
11. Using strategy rm
12. Applied div-sub14.0
  \[\leadsto 1 \cdot \color{blue}{\left(\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a \cdot 2} - \frac{b}{a \cdot 2}\right)}\]
if 5.668416736491797e-35 < b
1. Initial program 54.6
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Taylor expanded around inf 7.2
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
Recombined 3 regimes into one program.
Final simplification10.2
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.006124725233072906597672755451758607334 \cdot 10^{153}:\\ \;\;\;\;\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 1\\ \mathbf{elif}\;b \le 5.668416736491797065158030167390678793472 \cdot 10^{-35}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{a \cdot 2} - \frac{b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} \cdot -1\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -1.0061247252330729e+153`

`if -1.0061247252330729e+153 < b < 5.668416736491797e-35`

`if 5.668416736491797e-35 < b`

Reproduce

In
Out