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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.569310777886352095486911207889814773134 \cdot 10^{111}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 5.202443222624254327680309207854310362882 \cdot 10^{-45}:\\ \;\;\;\;\frac{1}{2} \cdot \frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

\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 -1.569310777886352095486911207889814773134 \cdot 10^{111}:\\
\;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\

\mathbf{elif}\;b \le 5.202443222624254327680309207854310362882 \cdot 10^{-45}:\\
\;\;\;\;\frac{1}{2} \cdot \frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}\\

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

\end{array}

double f(double a, double b, double c) {
        double r93205 = b;
        double r93206 = -r93205;
        double r93207 = r93205 * r93205;
        double r93208 = 4.0;
        double r93209 = a;
        double r93210 = r93208 * r93209;
        double r93211 = c;
        double r93212 = r93210 * r93211;
        double r93213 = r93207 - r93212;
        double r93214 = sqrt(r93213);
        double r93215 = r93206 + r93214;
        double r93216 = 2.0;
        double r93217 = r93216 * r93209;
        double r93218 = r93215 / r93217;
        return r93218;
}

↓

double f(double a, double b, double c) {
        double r93219 = b;
        double r93220 = -1.569310777886352e+111;
        bool r93221 = r93219 <= r93220;
        double r93222 = 1.0;
        double r93223 = c;
        double r93224 = r93223 / r93219;
        double r93225 = a;
        double r93226 = r93219 / r93225;
        double r93227 = r93224 - r93226;
        double r93228 = r93222 * r93227;
        double r93229 = 5.2024432226242543e-45;
        bool r93230 = r93219 <= r93229;
        double r93231 = 1.0;
        double r93232 = 2.0;
        double r93233 = r93231 / r93232;
        double r93234 = r93219 * r93219;
        double r93235 = 4.0;
        double r93236 = r93235 * r93225;
        double r93237 = r93236 * r93223;
        double r93238 = r93234 - r93237;
        double r93239 = sqrt(r93238);
        double r93240 = r93239 - r93219;
        double r93241 = r93240 / r93225;
        double r93242 = r93233 * r93241;
        double r93243 = -1.0;
        double r93244 = r93243 * r93224;
        double r93245 = r93230 ? r93242 : r93244;
        double r93246 = r93221 ? r93228 : r93245;
        return r93246;
}

Original	34.3
Target	21.1
Herbie	10.1

Derivation

Split input into 3 regimes
if b < -1.569310777886352e+111
1. Initial program 50.4
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified50.4
  \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{2 \cdot a}}\]
3. Taylor expanded around -inf 3.9
  \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
4. Simplified3.9
  \[\leadsto \color{blue}{1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}\]
if -1.569310777886352e+111 < b < 5.2024432226242543e-45
1. Initial program 14.0
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified14.0
  \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{2 \cdot a}}\]
3. Using strategy rm
4. Applied clear-num14.1
  \[\leadsto \color{blue}{\frac{1}{\frac{2 \cdot a}{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}}}\]
5. Using strategy rm
6. Applied *-un-lft-identity14.1
  \[\leadsto \frac{1}{\frac{2 \cdot a}{\color{blue}{1 \cdot \left(\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b\right)}}}\]
7. Applied times-frac14.1
  \[\leadsto \frac{1}{\color{blue}{\frac{2}{1} \cdot \frac{a}{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}}}\]
8. Applied add-cube-cbrt14.1
  \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{2}{1} \cdot \frac{a}{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}}\]
9. Applied times-frac14.1
  \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{2}{1}} \cdot \frac{\sqrt[3]{1}}{\frac{a}{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}}}\]
10. Simplified14.1
  \[\leadsto \color{blue}{\frac{1}{2}} \cdot \frac{\sqrt[3]{1}}{\frac{a}{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}}\]
11. Simplified14.0
  \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}}\]
if 5.2024432226242543e-45 < b
1. Initial program 54.5
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified54.5
  \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{2 \cdot a}}\]
3. Taylor expanded around inf 7.4
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
Recombined 3 regimes into one program.
Final simplification10.1
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.569310777886352095486911207889814773134 \cdot 10^{111}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 5.202443222624254327680309207854310362882 \cdot 10^{-45}:\\ \;\;\;\;\frac{1}{2} \cdot \frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -1.569310777886352e+111`

`if -1.569310777886352e+111 < b < 5.2024432226242543e-45`

`if 5.2024432226242543e-45 < b`

Reproduce

In
Out