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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.762479091812706 \cdot 10^{+65}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le -2.436990347475487 \cdot 10^{-257}:\\ \;\;\;\;\frac{4}{\sqrt{c \cdot \left(-4 \cdot a\right) + b \cdot b} - b} \cdot \left(\frac{1}{2} \cdot c\right)\\ \mathbf{elif}\;b \le 2.598286182153128 \cdot 10^{+84}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b + \left(c \cdot -4\right) \cdot a}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;-\frac{b}{a}\\ \end{array}\]

double f(double a, double b, double c) {
        double r5369297 = b;
        double r5369298 = -r5369297;
        double r5369299 = r5369297 * r5369297;
        double r5369300 = 4.0;
        double r5369301 = a;
        double r5369302 = c;
        double r5369303 = r5369301 * r5369302;
        double r5369304 = r5369300 * r5369303;
        double r5369305 = r5369299 - r5369304;
        double r5369306 = sqrt(r5369305);
        double r5369307 = r5369298 - r5369306;
        double r5369308 = 2.0;
        double r5369309 = r5369308 * r5369301;
        double r5369310 = r5369307 / r5369309;
        return r5369310;
}

↓

double f(double a, double b, double c) {
        double r5369311 = b;
        double r5369312 = -1.762479091812706e+65;
        bool r5369313 = r5369311 <= r5369312;
        double r5369314 = c;
        double r5369315 = r5369314 / r5369311;
        double r5369316 = -r5369315;
        double r5369317 = -2.436990347475487e-257;
        bool r5369318 = r5369311 <= r5369317;
        double r5369319 = 4.0;
        double r5369320 = -4.0;
        double r5369321 = a;
        double r5369322 = r5369320 * r5369321;
        double r5369323 = r5369314 * r5369322;
        double r5369324 = r5369311 * r5369311;
        double r5369325 = r5369323 + r5369324;
        double r5369326 = sqrt(r5369325);
        double r5369327 = r5369326 - r5369311;
        double r5369328 = r5369319 / r5369327;
        double r5369329 = 0.5;
        double r5369330 = r5369329 * r5369314;
        double r5369331 = r5369328 * r5369330;
        double r5369332 = 2.598286182153128e+84;
        bool r5369333 = r5369311 <= r5369332;
        double r5369334 = -r5369311;
        double r5369335 = r5369314 * r5369320;
        double r5369336 = r5369335 * r5369321;
        double r5369337 = r5369324 + r5369336;
        double r5369338 = sqrt(r5369337);
        double r5369339 = r5369334 - r5369338;
        double r5369340 = 2.0;
        double r5369341 = r5369340 * r5369321;
        double r5369342 = r5369339 / r5369341;
        double r5369343 = r5369311 / r5369321;
        double r5369344 = -r5369343;
        double r5369345 = r5369333 ? r5369342 : r5369344;
        double r5369346 = r5369318 ? r5369331 : r5369345;
        double r5369347 = r5369313 ? r5369316 : r5369346;
        return r5369347;
}

\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 -1.762479091812706 \cdot 10^{+65}:\\
\;\;\;\;-\frac{c}{b}\\

\mathbf{elif}\;b \le -2.436990347475487 \cdot 10^{-257}:\\
\;\;\;\;\frac{4}{\sqrt{c \cdot \left(-4 \cdot a\right) + b \cdot b} - b} \cdot \left(\frac{1}{2} \cdot c\right)\\

\mathbf{elif}\;b \le 2.598286182153128 \cdot 10^{+84}:\\
\;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b + \left(c \cdot -4\right) \cdot a}}{2 \cdot a}\\

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

\end{array}

Original	33.2
Target	20.1
Herbie	7.0

Derivation

Split input into 4 regimes
if b < -1.762479091812706e+65
1. Initial program 57.3
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Taylor expanded around -inf 3.8
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
3. Simplified3.8
  \[\leadsto \color{blue}{-\frac{c}{b}}\]
if -1.762479091812706e+65 < b < -2.436990347475487e-257
1. Initial program 31.7
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Using strategy rm
3. Applied flip--31.8
  \[\leadsto \frac{\color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} \cdot \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a}\]
4. Applied associate-/l/36.6
  \[\leadsto \color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} \cdot \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{\left(2 \cdot a\right) \cdot \left(\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}\]
5. Simplified21.3
  \[\leadsto \frac{\color{blue}{\left(a \cdot c\right) \cdot 4}}{\left(2 \cdot a\right) \cdot \left(\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}\]
6. Using strategy rm
7. Applied times-frac15.9
  \[\leadsto \color{blue}{\frac{a \cdot c}{2 \cdot a} \cdot \frac{4}{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}\]
8. Simplified8.3
  \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot c\right)} \cdot \frac{4}{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}\]
9. Simplified8.3
  \[\leadsto \left(\frac{1}{2} \cdot c\right) \cdot \color{blue}{\frac{4}{\sqrt{c \cdot \left(-4 \cdot a\right) + b \cdot b} - b}}\]
if -2.436990347475487e-257 < b < 2.598286182153128e+84
1. Initial program 10.0
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Taylor expanded around -inf 10.0
  \[\leadsto \frac{\left(-b\right) - \sqrt{\color{blue}{{b}^{2} - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\]
3. Simplified10.0
  \[\leadsto \frac{\left(-b\right) - \sqrt{\color{blue}{b \cdot b + \left(c \cdot -4\right) \cdot a}}}{2 \cdot a}\]
if 2.598286182153128e+84 < b
1. Initial program 40.7
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Using strategy rm
3. Applied flip--60.9
  \[\leadsto \frac{\color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} \cdot \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a}\]
4. Applied associate-/l/61.2
  \[\leadsto \color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} \cdot \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{\left(2 \cdot a\right) \cdot \left(\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}\]
5. Simplified61.4
  \[\leadsto \frac{\color{blue}{\left(a \cdot c\right) \cdot 4}}{\left(2 \cdot a\right) \cdot \left(\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}\]
6. Using strategy rm
7. Applied times-frac61.2
  \[\leadsto \color{blue}{\frac{a \cdot c}{2 \cdot a} \cdot \frac{4}{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}\]
8. Simplified61.1
  \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot c\right)} \cdot \frac{4}{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}\]
9. Simplified61.1
  \[\leadsto \left(\frac{1}{2} \cdot c\right) \cdot \color{blue}{\frac{4}{\sqrt{c \cdot \left(-4 \cdot a\right) + b \cdot b} - b}}\]
10. Taylor expanded around 0 4.5
  \[\leadsto \color{blue}{-1 \cdot \frac{b}{a}}\]
11. Simplified4.5
  \[\leadsto \color{blue}{-\frac{b}{a}}\]
Recombined 4 regimes into one program.
Final simplification7.0
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.762479091812706 \cdot 10^{+65}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le -2.436990347475487 \cdot 10^{-257}:\\ \;\;\;\;\frac{4}{\sqrt{c \cdot \left(-4 \cdot a\right) + b \cdot b} - b} \cdot \left(\frac{1}{2} \cdot c\right)\\ \mathbf{elif}\;b \le 2.598286182153128 \cdot 10^{+84}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b + \left(c \cdot -4\right) \cdot a}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;-\frac{b}{a}\\ \end{array}\]

Error

Target

Derivation

`if b < -1.762479091812706e+65`

`if -1.762479091812706e+65 < b < -2.436990347475487e-257`

`if -2.436990347475487e-257 < b < 2.598286182153128e+84`

`if 2.598286182153128e+84 < b`

Reproduce