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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -2.615257373542238721197930661559276546696 \cdot 10^{153}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 1.388070047225937856958905133202240499626 \cdot 10^{-143}:\\ \;\;\;\;\frac{1}{2} \cdot \frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{a}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

\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 -2.615257373542238721197930661559276546696 \cdot 10^{153}:\\
\;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\

\mathbf{elif}\;b \le 1.388070047225937856958905133202240499626 \cdot 10^{-143}:\\
\;\;\;\;\frac{1}{2} \cdot \frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{a}\\

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

\end{array}

double f(double a, double b, double c) {
        double r80088 = b;
        double r80089 = -r80088;
        double r80090 = r80088 * r80088;
        double r80091 = 4.0;
        double r80092 = a;
        double r80093 = c;
        double r80094 = r80092 * r80093;
        double r80095 = r80091 * r80094;
        double r80096 = r80090 - r80095;
        double r80097 = sqrt(r80096);
        double r80098 = r80089 + r80097;
        double r80099 = 2.0;
        double r80100 = r80099 * r80092;
        double r80101 = r80098 / r80100;
        return r80101;
}

↓

double f(double a, double b, double c) {
        double r80102 = b;
        double r80103 = -2.6152573735422387e+153;
        bool r80104 = r80102 <= r80103;
        double r80105 = 1.0;
        double r80106 = c;
        double r80107 = r80106 / r80102;
        double r80108 = a;
        double r80109 = r80102 / r80108;
        double r80110 = r80107 - r80109;
        double r80111 = r80105 * r80110;
        double r80112 = 1.3880700472259379e-143;
        bool r80113 = r80102 <= r80112;
        double r80114 = 1.0;
        double r80115 = 2.0;
        double r80116 = r80114 / r80115;
        double r80117 = r80102 * r80102;
        double r80118 = 4.0;
        double r80119 = r80108 * r80106;
        double r80120 = r80118 * r80119;
        double r80121 = r80117 - r80120;
        double r80122 = sqrt(r80121);
        double r80123 = r80122 - r80102;
        double r80124 = r80123 / r80108;
        double r80125 = r80116 * r80124;
        double r80126 = -1.0;
        double r80127 = r80126 * r80107;
        double r80128 = r80113 ? r80125 : r80127;
        double r80129 = r80104 ? r80111 : r80128;
        return r80129;
}

Original	34.5
Target	21.5
Herbie	10.9

Derivation

Split input into 3 regimes
if b < -2.6152573735422387e+153
1. Initial program 63.8
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified63.8
  \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2 \cdot a}}\]
3. Taylor expanded around -inf 2.1
  \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
4. Simplified2.1
  \[\leadsto \color{blue}{1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}\]
if -2.6152573735422387e+153 < b < 1.3880700472259379e-143
1. Initial program 11.5
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified11.5
  \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2 \cdot a}}\]
3. Using strategy rm
4. Applied clear-num11.6
  \[\leadsto \color{blue}{\frac{1}{\frac{2 \cdot a}{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}}}\]
5. Using strategy rm
6. Applied *-un-lft-identity11.6
  \[\leadsto \frac{1}{\frac{2 \cdot a}{\color{blue}{1 \cdot \left(\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b\right)}}}\]
7. Applied times-frac11.6
  \[\leadsto \frac{1}{\color{blue}{\frac{2}{1} \cdot \frac{a}{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}}}\]
8. Applied add-cube-cbrt11.6
  \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{2}{1} \cdot \frac{a}{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}}\]
9. Applied times-frac11.6
  \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{2}{1}} \cdot \frac{\sqrt[3]{1}}{\frac{a}{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}}}\]
10. Simplified11.6
  \[\leadsto \color{blue}{\frac{1}{2}} \cdot \frac{\sqrt[3]{1}}{\frac{a}{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}}\]
11. Simplified11.5
  \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{a}}\]
if 1.3880700472259379e-143 < b
1. Initial program 50.3
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified50.3
  \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2 \cdot a}}\]
3. Taylor expanded around inf 12.6
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
Recombined 3 regimes into one program.
Final simplification10.9
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -2.615257373542238721197930661559276546696 \cdot 10^{153}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 1.388070047225937856958905133202240499626 \cdot 10^{-143}:\\ \;\;\;\;\frac{1}{2} \cdot \frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{a}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

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

Error

Try it out

Target

Derivation

`if b < -2.6152573735422387e+153`

`if -2.6152573735422387e+153 < b < 1.3880700472259379e-143`

`if 1.3880700472259379e-143 < b`

Reproduce

In
Out