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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.763315479739403460017265344144602342789 \cdot 10^{89}:\\ \;\;\;\;\frac{\frac{1}{\frac{-1}{b}}}{a}\\ \mathbf{elif}\;b \le 5.860223638943180333955717619400031865396 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{1}{\frac{2}{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{1}{b} - \frac{b}{c \cdot a} \cdot 1}}{a}\\ \end{array}\]

\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 -1.763315479739403460017265344144602342789 \cdot 10^{89}:\\
\;\;\;\;\frac{\frac{1}{\frac{-1}{b}}}{a}\\

\mathbf{elif}\;b \le 5.860223638943180333955717619400031865396 \cdot 10^{-17}:\\
\;\;\;\;\frac{\frac{1}{\frac{2}{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}}}{a}\\

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

\end{array}

double f(double a, double b, double c) {
        double r4259197 = b;
        double r4259198 = -r4259197;
        double r4259199 = r4259197 * r4259197;
        double r4259200 = 4.0;
        double r4259201 = a;
        double r4259202 = r4259200 * r4259201;
        double r4259203 = c;
        double r4259204 = r4259202 * r4259203;
        double r4259205 = r4259199 - r4259204;
        double r4259206 = sqrt(r4259205);
        double r4259207 = r4259198 + r4259206;
        double r4259208 = 2.0;
        double r4259209 = r4259208 * r4259201;
        double r4259210 = r4259207 / r4259209;
        return r4259210;
}

↓

double f(double a, double b, double c) {
        double r4259211 = b;
        double r4259212 = -1.7633154797394035e+89;
        bool r4259213 = r4259211 <= r4259212;
        double r4259214 = 1.0;
        double r4259215 = -1.0;
        double r4259216 = r4259215 / r4259211;
        double r4259217 = r4259214 / r4259216;
        double r4259218 = a;
        double r4259219 = r4259217 / r4259218;
        double r4259220 = 5.86022363894318e-17;
        bool r4259221 = r4259211 <= r4259220;
        double r4259222 = 2.0;
        double r4259223 = r4259211 * r4259211;
        double r4259224 = 4.0;
        double r4259225 = c;
        double r4259226 = r4259225 * r4259218;
        double r4259227 = r4259224 * r4259226;
        double r4259228 = r4259223 - r4259227;
        double r4259229 = sqrt(r4259228);
        double r4259230 = r4259229 - r4259211;
        double r4259231 = r4259222 / r4259230;
        double r4259232 = r4259214 / r4259231;
        double r4259233 = r4259232 / r4259218;
        double r4259234 = 1.0;
        double r4259235 = r4259234 / r4259211;
        double r4259236 = r4259211 / r4259226;
        double r4259237 = r4259236 * r4259234;
        double r4259238 = r4259235 - r4259237;
        double r4259239 = r4259214 / r4259238;
        double r4259240 = r4259239 / r4259218;
        double r4259241 = r4259221 ? r4259233 : r4259240;
        double r4259242 = r4259213 ? r4259219 : r4259241;
        return r4259242;
}

Original	34.4
Target	21.3
Herbie	14.2

Derivation

Split input into 3 regimes
if b < -1.7633154797394035e+89
1. Initial program 45.7
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified45.7
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied clear-num45.8
  \[\leadsto \frac{\color{blue}{\frac{1}{\frac{2}{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}}}}{a}\]
5. Taylor expanded around -inf 4.2
  \[\leadsto \frac{\frac{1}{\color{blue}{\frac{-1}{b}}}}{a}\]
if -1.7633154797394035e+89 < b < 5.86022363894318e-17
1. Initial program 15.4
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified15.4
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied clear-num15.4
  \[\leadsto \frac{\color{blue}{\frac{1}{\frac{2}{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}}}}{a}\]
if 5.86022363894318e-17 < b
1. Initial program 55.6
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified55.6
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied clear-num55.6
  \[\leadsto \frac{\color{blue}{\frac{1}{\frac{2}{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}}}}{a}\]
5. Taylor expanded around inf 17.3
  \[\leadsto \frac{\frac{1}{\color{blue}{1 \cdot \frac{1}{b} - 1 \cdot \frac{b}{a \cdot c}}}}{a}\]
6. Simplified17.3
  \[\leadsto \frac{\frac{1}{\color{blue}{\frac{1}{b} - 1 \cdot \frac{b}{c \cdot a}}}}{a}\]
Recombined 3 regimes into one program.
Final simplification14.2
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.763315479739403460017265344144602342789 \cdot 10^{89}:\\ \;\;\;\;\frac{\frac{1}{\frac{-1}{b}}}{a}\\ \mathbf{elif}\;b \le 5.860223638943180333955717619400031865396 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{1}{\frac{2}{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{1}{b} - \frac{b}{c \cdot a} \cdot 1}}{a}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -1.7633154797394035e+89`

`if -1.7633154797394035e+89 < b < 5.86022363894318e-17`

`if 5.86022363894318e-17 < b`

Reproduce

In
Out