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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -4.356959927988237168348139414849710212524 \cdot 10^{-56}:\\ \;\;\;\;\frac{-1 \cdot c}{b}\\ \mathbf{elif}\;b \le 3.087668654677018032633364446323411964642 \cdot 10^{130}:\\ \;\;\;\;\frac{\frac{-\left(\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4} + b\right)}{2}}{a}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \end{array}\]

\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 -4.356959927988237168348139414849710212524 \cdot 10^{-56}:\\
\;\;\;\;\frac{-1 \cdot c}{b}\\

\mathbf{elif}\;b \le 3.087668654677018032633364446323411964642 \cdot 10^{130}:\\
\;\;\;\;\frac{\frac{-\left(\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4} + b\right)}{2}}{a}\\

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

\end{array}

double f(double a, double b, double c) {
        double r62828 = b;
        double r62829 = -r62828;
        double r62830 = r62828 * r62828;
        double r62831 = 4.0;
        double r62832 = a;
        double r62833 = c;
        double r62834 = r62832 * r62833;
        double r62835 = r62831 * r62834;
        double r62836 = r62830 - r62835;
        double r62837 = sqrt(r62836);
        double r62838 = r62829 - r62837;
        double r62839 = 2.0;
        double r62840 = r62839 * r62832;
        double r62841 = r62838 / r62840;
        return r62841;
}

↓

double f(double a, double b, double c) {
        double r62842 = b;
        double r62843 = -4.356959927988237e-56;
        bool r62844 = r62842 <= r62843;
        double r62845 = -1.0;
        double r62846 = c;
        double r62847 = r62845 * r62846;
        double r62848 = r62847 / r62842;
        double r62849 = 3.087668654677018e+130;
        bool r62850 = r62842 <= r62849;
        double r62851 = r62842 * r62842;
        double r62852 = a;
        double r62853 = r62852 * r62846;
        double r62854 = 4.0;
        double r62855 = r62853 * r62854;
        double r62856 = r62851 - r62855;
        double r62857 = sqrt(r62856);
        double r62858 = r62857 + r62842;
        double r62859 = -r62858;
        double r62860 = 2.0;
        double r62861 = r62859 / r62860;
        double r62862 = r62861 / r62852;
        double r62863 = 1.0;
        double r62864 = r62846 / r62842;
        double r62865 = r62842 / r62852;
        double r62866 = r62864 - r62865;
        double r62867 = r62863 * r62866;
        double r62868 = r62850 ? r62862 : r62867;
        double r62869 = r62844 ? r62848 : r62868;
        return r62869;
}

Original	34.1
Target	21.1
Herbie	9.4

Derivation

Split input into 3 regimes
if b < -4.356959927988237e-56
1. Initial program 54.0
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified54.0
  \[\leadsto \color{blue}{\frac{\left(-b\right) - \sqrt{b \cdot b - a \cdot \left(4 \cdot c\right)}}{2 \cdot a}}\]
3. Taylor expanded around -inf 7.7
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
4. Simplified7.7
  \[\leadsto \color{blue}{\frac{-1 \cdot c}{b}}\]
if -4.356959927988237e-56 < b < 3.087668654677018e+130
1. Initial program 12.6
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified12.6
  \[\leadsto \color{blue}{\frac{\left(-b\right) - \sqrt{b \cdot b - a \cdot \left(4 \cdot c\right)}}{2 \cdot a}}\]
3. Using strategy rm
4. Applied div-inv12.8
  \[\leadsto \color{blue}{\left(\left(-b\right) - \sqrt{b \cdot b - a \cdot \left(4 \cdot c\right)}\right) \cdot \frac{1}{2 \cdot a}}\]
5. Simplified12.7
  \[\leadsto \left(\left(-b\right) - \sqrt{b \cdot b - a \cdot \left(4 \cdot c\right)}\right) \cdot \color{blue}{\frac{\frac{1}{2}}{a}}\]
6. Using strategy rm
7. Applied associate-*r/12.6
  \[\leadsto \color{blue}{\frac{\left(\left(-b\right) - \sqrt{b \cdot b - a \cdot \left(4 \cdot c\right)}\right) \cdot \frac{1}{2}}{a}}\]
8. Simplified12.6
  \[\leadsto \frac{\color{blue}{\frac{-\left(b + \sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)}\right)}{2}}}{a}\]
if 3.087668654677018e+130 < b
1. Initial program 56.2
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified56.2
  \[\leadsto \color{blue}{\frac{\left(-b\right) - \sqrt{b \cdot b - a \cdot \left(4 \cdot c\right)}}{2 \cdot a}}\]
3. Using strategy rm
4. Applied div-inv56.2
  \[\leadsto \color{blue}{\left(\left(-b\right) - \sqrt{b \cdot b - a \cdot \left(4 \cdot c\right)}\right) \cdot \frac{1}{2 \cdot a}}\]
5. Simplified56.2
  \[\leadsto \left(\left(-b\right) - \sqrt{b \cdot b - a \cdot \left(4 \cdot c\right)}\right) \cdot \color{blue}{\frac{\frac{1}{2}}{a}}\]
6. Using strategy rm
7. Applied associate-*r/56.2
  \[\leadsto \color{blue}{\frac{\left(\left(-b\right) - \sqrt{b \cdot b - a \cdot \left(4 \cdot c\right)}\right) \cdot \frac{1}{2}}{a}}\]
8. Simplified56.2
  \[\leadsto \frac{\color{blue}{\frac{-\left(b + \sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)}\right)}{2}}}{a}\]
9. Taylor expanded around inf 2.4
  \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
10. Simplified2.4
  \[\leadsto \color{blue}{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 1}\]
Recombined 3 regimes into one program.
Final simplification9.4
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -4.356959927988237168348139414849710212524 \cdot 10^{-56}:\\ \;\;\;\;\frac{-1 \cdot c}{b}\\ \mathbf{elif}\;b \le 3.087668654677018032633364446323411964642 \cdot 10^{130}:\\ \;\;\;\;\frac{\frac{-\left(\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4} + b\right)}{2}}{a}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -4.356959927988237e-56`

`if -4.356959927988237e-56 < b < 3.087668654677018e+130`

`if 3.087668654677018e+130 < b`

Reproduce

In
Out