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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -4.12310353364421125 \cdot 10^{95}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 3.446447862996811 \cdot 10^{-75}:\\ \;\;\;\;\left(\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b\right) \cdot \frac{1}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

\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 -4.12310353364421125 \cdot 10^{95}:\\
\;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\

\mathbf{elif}\;b \le 3.446447862996811 \cdot 10^{-75}:\\
\;\;\;\;\left(\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b\right) \cdot \frac{1}{2 \cdot a}\\

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

\end{array}

double f(double a, double b, double c) {
        double r79795 = b;
        double r79796 = -r79795;
        double r79797 = r79795 * r79795;
        double r79798 = 4.0;
        double r79799 = a;
        double r79800 = c;
        double r79801 = r79799 * r79800;
        double r79802 = r79798 * r79801;
        double r79803 = r79797 - r79802;
        double r79804 = sqrt(r79803);
        double r79805 = r79796 + r79804;
        double r79806 = 2.0;
        double r79807 = r79806 * r79799;
        double r79808 = r79805 / r79807;
        return r79808;
}

↓

double f(double a, double b, double c) {
        double r79809 = b;
        double r79810 = -4.123103533644211e+95;
        bool r79811 = r79809 <= r79810;
        double r79812 = 1.0;
        double r79813 = c;
        double r79814 = r79813 / r79809;
        double r79815 = a;
        double r79816 = r79809 / r79815;
        double r79817 = r79814 - r79816;
        double r79818 = r79812 * r79817;
        double r79819 = 3.446447862996811e-75;
        bool r79820 = r79809 <= r79819;
        double r79821 = r79809 * r79809;
        double r79822 = 4.0;
        double r79823 = r79815 * r79813;
        double r79824 = r79822 * r79823;
        double r79825 = r79821 - r79824;
        double r79826 = sqrt(r79825);
        double r79827 = r79826 - r79809;
        double r79828 = 1.0;
        double r79829 = 2.0;
        double r79830 = r79829 * r79815;
        double r79831 = r79828 / r79830;
        double r79832 = r79827 * r79831;
        double r79833 = -1.0;
        double r79834 = r79833 * r79814;
        double r79835 = r79820 ? r79832 : r79834;
        double r79836 = r79811 ? r79818 : r79835;
        return r79836;
}

Original	34.2
Target	21.1
Herbie	10.4

Derivation

Split input into 3 regimes
if b < -4.123103533644211e+95
1. Initial program 47.3
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified47.3
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}}{a}}\]
3. Taylor expanded around -inf 3.8
  \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
4. Simplified3.8
  \[\leadsto \color{blue}{1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}\]
if -4.123103533644211e+95 < b < 3.446447862996811e-75
1. Initial program 13.3
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified13.3
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied clear-num13.4
  \[\leadsto \color{blue}{\frac{1}{\frac{a}{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}}}}\]
5. Using strategy rm
6. Applied div-inv13.4
  \[\leadsto \frac{1}{\frac{a}{\color{blue}{\left(\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b\right) \cdot \frac{1}{2}}}}\]
7. Applied *-un-lft-identity13.4
  \[\leadsto \frac{1}{\frac{\color{blue}{1 \cdot a}}{\left(\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b\right) \cdot \frac{1}{2}}}\]
8. Applied times-frac13.5
  \[\leadsto \frac{1}{\color{blue}{\frac{1}{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b} \cdot \frac{a}{\frac{1}{2}}}}\]
9. Applied add-cube-cbrt13.5
  \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{1}{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b} \cdot \frac{a}{\frac{1}{2}}}\]
10. Applied times-frac13.5
  \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{1}{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}} \cdot \frac{\sqrt[3]{1}}{\frac{a}{\frac{1}{2}}}}\]
11. Simplified13.4
  \[\leadsto \color{blue}{\left(\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b\right)} \cdot \frac{\sqrt[3]{1}}{\frac{a}{\frac{1}{2}}}\]
12. Simplified13.4
  \[\leadsto \left(\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b\right) \cdot \color{blue}{\frac{1}{2 \cdot a}}\]
if 3.446447862996811e-75 < b
1. Initial program 52.5
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified52.5
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}}{a}}\]
3. Taylor expanded around inf 9.7
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
Recombined 3 regimes into one program.
Final simplification10.4
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -4.12310353364421125 \cdot 10^{95}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 3.446447862996811 \cdot 10^{-75}:\\ \;\;\;\;\left(\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b\right) \cdot \frac{1}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

Falling back on racket egraph because egg-herbie package not installed (more)

Error

Try it out

Target

Derivation

`if b < -4.123103533644211e+95`

`if -4.123103533644211e+95 < b < 3.446447862996811e-75`

`if 3.446447862996811e-75 < b`

Reproduce

In
Out