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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.933466258714373398674404571719044836719 \cdot 10^{-151}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \mathbf{elif}\;b \le 7.97473148708154202610743994820925403473 \cdot 10^{107}:\\ \;\;\;\;\frac{-\left(b + \sqrt{\mathsf{fma}\left(c \cdot a, 4 - 4, \mathsf{fma}\left(4 \cdot a, -c, b \cdot b\right)\right)}\right)}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \end{array}\]

\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 -1.933466258714373398674404571719044836719 \cdot 10^{-151}:\\
\;\;\;\;-1 \cdot \frac{c}{b}\\

\mathbf{elif}\;b \le 7.97473148708154202610743994820925403473 \cdot 10^{107}:\\
\;\;\;\;\frac{-\left(b + \sqrt{\mathsf{fma}\left(c \cdot a, 4 - 4, \mathsf{fma}\left(4 \cdot a, -c, b \cdot b\right)\right)}\right)}{2 \cdot a}\\

\mathbf{else}:\\
\;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\

\end{array}

double f(double a, double b, double c) {
        double r80211 = b;
        double r80212 = -r80211;
        double r80213 = r80211 * r80211;
        double r80214 = 4.0;
        double r80215 = a;
        double r80216 = c;
        double r80217 = r80215 * r80216;
        double r80218 = r80214 * r80217;
        double r80219 = r80213 - r80218;
        double r80220 = sqrt(r80219);
        double r80221 = r80212 - r80220;
        double r80222 = 2.0;
        double r80223 = r80222 * r80215;
        double r80224 = r80221 / r80223;
        return r80224;
}

↓

double f(double a, double b, double c) {
        double r80225 = b;
        double r80226 = -1.9334662587143734e-151;
        bool r80227 = r80225 <= r80226;
        double r80228 = -1.0;
        double r80229 = c;
        double r80230 = r80229 / r80225;
        double r80231 = r80228 * r80230;
        double r80232 = 7.974731487081542e+107;
        bool r80233 = r80225 <= r80232;
        double r80234 = a;
        double r80235 = r80229 * r80234;
        double r80236 = 4.0;
        double r80237 = r80236 - r80236;
        double r80238 = r80236 * r80234;
        double r80239 = -r80229;
        double r80240 = r80225 * r80225;
        double r80241 = fma(r80238, r80239, r80240);
        double r80242 = fma(r80235, r80237, r80241);
        double r80243 = sqrt(r80242);
        double r80244 = r80225 + r80243;
        double r80245 = -r80244;
        double r80246 = 2.0;
        double r80247 = r80246 * r80234;
        double r80248 = r80245 / r80247;
        double r80249 = 1.0;
        double r80250 = r80225 / r80234;
        double r80251 = r80230 - r80250;
        double r80252 = r80249 * r80251;
        double r80253 = r80233 ? r80248 : r80252;
        double r80254 = r80227 ? r80231 : r80253;
        return r80254;
}

Original	34.9
Target	21.4
Herbie	10.9

Derivation

Split input into 3 regimes
if b < -1.9334662587143734e-151
1. Initial program 50.5
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Taylor expanded around -inf 13.2
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
if -1.9334662587143734e-151 < b < 7.974731487081542e+107
1. Initial program 11.4
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Using strategy rm
3. Applied div-inv11.5
  \[\leadsto \color{blue}{\left(\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{1}{2 \cdot a}}\]
4. Using strategy rm
5. Applied prod-diff11.5
  \[\leadsto \left(\left(-b\right) - \sqrt{\color{blue}{\mathsf{fma}\left(b, b, -\left(a \cdot c\right) \cdot 4\right) + \mathsf{fma}\left(-a \cdot c, 4, \left(a \cdot c\right) \cdot 4\right)}}\right) \cdot \frac{1}{2 \cdot a}\]
6. Simplified11.5
  \[\leadsto \left(\left(-b\right) - \sqrt{\color{blue}{\mathsf{fma}\left(4 \cdot a, -c, b \cdot b\right)} + \mathsf{fma}\left(-a \cdot c, 4, \left(a \cdot c\right) \cdot 4\right)}\right) \cdot \frac{1}{2 \cdot a}\]
7. Simplified11.5
  \[\leadsto \left(\left(-b\right) - \sqrt{\mathsf{fma}\left(4 \cdot a, -c, b \cdot b\right) + \color{blue}{\left(a \cdot c\right) \cdot \left(\left(-4\right) + 4\right)}}\right) \cdot \frac{1}{2 \cdot a}\]
8. Using strategy rm
9. Applied associate-*r/11.4
  \[\leadsto \color{blue}{\frac{\left(\left(-b\right) - \sqrt{\mathsf{fma}\left(4 \cdot a, -c, b \cdot b\right) + \left(a \cdot c\right) \cdot \left(\left(-4\right) + 4\right)}\right) \cdot 1}{2 \cdot a}}\]
10. Simplified11.4
  \[\leadsto \frac{\color{blue}{-\left(b + \sqrt{\mathsf{fma}\left(c \cdot a, 4 - 4, \mathsf{fma}\left(4 \cdot a, -c, b \cdot b\right)\right)}\right)}}{2 \cdot a}\]
if 7.974731487081542e+107 < b
1. Initial program 49.6
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Taylor expanded around inf 3.0
  \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
3. Simplified3.0
  \[\leadsto \color{blue}{1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}\]
Recombined 3 regimes into one program.
Final simplification10.9
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.933466258714373398674404571719044836719 \cdot 10^{-151}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \mathbf{elif}\;b \le 7.97473148708154202610743994820925403473 \cdot 10^{107}:\\ \;\;\;\;\frac{-\left(b + \sqrt{\mathsf{fma}\left(c \cdot a, 4 - 4, \mathsf{fma}\left(4 \cdot a, -c, b \cdot b\right)\right)}\right)}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \end{array}\]

Error

Target

Derivation

`if b < -1.9334662587143734e-151`

`if -1.9334662587143734e-151 < b < 7.974731487081542e+107`

`if 7.974731487081542e+107 < b`

Reproduce