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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -3.396811349079212 \cdot 10^{+61}:\\ \;\;\;\;\frac{\left(\frac{c}{\frac{b}{a}} - b\right) \cdot 2}{a \cdot 2}\\ \mathbf{elif}\;b \le 1.3659668388152999 \cdot 10^{-67}:\\ \;\;\;\;\frac{\frac{1}{2}}{a} \cdot \left(\sqrt{\mathsf{fma}\left(c, \left(-4 \cdot a\right), \left(b \cdot b\right)\right)} - b\right)\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]

\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 -3.396811349079212 \cdot 10^{+61}:\\
\;\;\;\;\frac{\left(\frac{c}{\frac{b}{a}} - b\right) \cdot 2}{a \cdot 2}\\

\mathbf{elif}\;b \le 1.3659668388152999 \cdot 10^{-67}:\\
\;\;\;\;\frac{\frac{1}{2}}{a} \cdot \left(\sqrt{\mathsf{fma}\left(c, \left(-4 \cdot a\right), \left(b \cdot b\right)\right)} - b\right)\\

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

\end{array}

double f(double a, double b, double c) {
        double r4042206 = b;
        double r4042207 = -r4042206;
        double r4042208 = r4042206 * r4042206;
        double r4042209 = 4.0;
        double r4042210 = a;
        double r4042211 = r4042209 * r4042210;
        double r4042212 = c;
        double r4042213 = r4042211 * r4042212;
        double r4042214 = r4042208 - r4042213;
        double r4042215 = sqrt(r4042214);
        double r4042216 = r4042207 + r4042215;
        double r4042217 = 2.0;
        double r4042218 = r4042217 * r4042210;
        double r4042219 = r4042216 / r4042218;
        return r4042219;
}

↓

double f(double a, double b, double c) {
        double r4042220 = b;
        double r4042221 = -3.396811349079212e+61;
        bool r4042222 = r4042220 <= r4042221;
        double r4042223 = c;
        double r4042224 = a;
        double r4042225 = r4042220 / r4042224;
        double r4042226 = r4042223 / r4042225;
        double r4042227 = r4042226 - r4042220;
        double r4042228 = 2.0;
        double r4042229 = r4042227 * r4042228;
        double r4042230 = r4042224 * r4042228;
        double r4042231 = r4042229 / r4042230;
        double r4042232 = 1.3659668388152999e-67;
        bool r4042233 = r4042220 <= r4042232;
        double r4042234 = 0.5;
        double r4042235 = r4042234 / r4042224;
        double r4042236 = -4.0;
        double r4042237 = r4042236 * r4042224;
        double r4042238 = r4042220 * r4042220;
        double r4042239 = fma(r4042223, r4042237, r4042238);
        double r4042240 = sqrt(r4042239);
        double r4042241 = r4042240 - r4042220;
        double r4042242 = r4042235 * r4042241;
        double r4042243 = r4042223 / r4042220;
        double r4042244 = -r4042243;
        double r4042245 = r4042233 ? r4042242 : r4042244;
        double r4042246 = r4042222 ? r4042231 : r4042245;
        return r4042246;
}

Original	33.6
Target	20.8
Herbie	9.9

Derivation

Split input into 3 regimes
if b < -3.396811349079212e+61
1. Initial program 37.6
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Taylor expanded around -inf 9.6
  \[\leadsto \frac{\color{blue}{2 \cdot \frac{a \cdot c}{b} - 2 \cdot b}}{2 \cdot a}\]
3. Simplified4.4
  \[\leadsto \frac{\color{blue}{\left(\frac{c}{\frac{b}{a}} - b\right) \cdot 2}}{2 \cdot a}\]
if -3.396811349079212e+61 < b < 1.3659668388152999e-67
1. Initial program 13.9
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified13.9
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{\mathsf{fma}\left(c, \left(-4 \cdot a\right), \left(b \cdot b\right)\right)} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied *-un-lft-identity13.9
  \[\leadsto \frac{\frac{\sqrt{\mathsf{fma}\left(c, \left(-4 \cdot a\right), \left(b \cdot b\right)\right)} - b}{2}}{\color{blue}{1 \cdot a}}\]
5. Applied div-inv13.9
  \[\leadsto \frac{\color{blue}{\left(\sqrt{\mathsf{fma}\left(c, \left(-4 \cdot a\right), \left(b \cdot b\right)\right)} - b\right) \cdot \frac{1}{2}}}{1 \cdot a}\]
6. Applied times-frac14.0
  \[\leadsto \color{blue}{\frac{\sqrt{\mathsf{fma}\left(c, \left(-4 \cdot a\right), \left(b \cdot b\right)\right)} - b}{1} \cdot \frac{\frac{1}{2}}{a}}\]
7. Simplified14.0
  \[\leadsto \color{blue}{\left(\sqrt{\mathsf{fma}\left(c, \left(a \cdot -4\right), \left(b \cdot b\right)\right)} - b\right)} \cdot \frac{\frac{1}{2}}{a}\]
8. Simplified14.0
  \[\leadsto \left(\sqrt{\mathsf{fma}\left(c, \left(a \cdot -4\right), \left(b \cdot b\right)\right)} - b\right) \cdot \color{blue}{\frac{\frac{1}{2}}{a}}\]
if 1.3659668388152999e-67 < b
1. Initial program 53.0
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Taylor expanded around inf 8.1
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
3. Simplified8.1
  \[\leadsto \color{blue}{-\frac{c}{b}}\]
Recombined 3 regimes into one program.
Final simplification9.9
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -3.396811349079212 \cdot 10^{+61}:\\ \;\;\;\;\frac{\left(\frac{c}{\frac{b}{a}} - b\right) \cdot 2}{a \cdot 2}\\ \mathbf{elif}\;b \le 1.3659668388152999 \cdot 10^{-67}:\\ \;\;\;\;\frac{\frac{1}{2}}{a} \cdot \left(\sqrt{\mathsf{fma}\left(c, \left(-4 \cdot a\right), \left(b \cdot b\right)\right)} - b\right)\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]

Error

Target

Derivation

`if b < -3.396811349079212e+61`

`if -3.396811349079212e+61 < b < 1.3659668388152999e-67`

`if 1.3659668388152999e-67 < b`

Reproduce