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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -8.78453392716348 \cdot 10^{+64}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 7.643168247577731 \cdot 10^{-56}:\\ \;\;\;\;\frac{1}{\frac{a}{\left(\sqrt{(\left(c \cdot -4\right) \cdot a + \left(b \cdot b\right))_*} - b\right) \cdot \frac{1}{2}}}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]

double f(double a, double b, double c) {
        double r5418340 = b;
        double r5418341 = -r5418340;
        double r5418342 = r5418340 * r5418340;
        double r5418343 = 4.0;
        double r5418344 = a;
        double r5418345 = c;
        double r5418346 = r5418344 * r5418345;
        double r5418347 = r5418343 * r5418346;
        double r5418348 = r5418342 - r5418347;
        double r5418349 = sqrt(r5418348);
        double r5418350 = r5418341 + r5418349;
        double r5418351 = 2.0;
        double r5418352 = r5418351 * r5418344;
        double r5418353 = r5418350 / r5418352;
        return r5418353;
}

↓

double f(double a, double b, double c) {
        double r5418354 = b;
        double r5418355 = -8.78453392716348e+64;
        bool r5418356 = r5418354 <= r5418355;
        double r5418357 = c;
        double r5418358 = r5418357 / r5418354;
        double r5418359 = a;
        double r5418360 = r5418354 / r5418359;
        double r5418361 = r5418358 - r5418360;
        double r5418362 = 7.643168247577731e-56;
        bool r5418363 = r5418354 <= r5418362;
        double r5418364 = 1.0;
        double r5418365 = -4.0;
        double r5418366 = r5418357 * r5418365;
        double r5418367 = r5418354 * r5418354;
        double r5418368 = fma(r5418366, r5418359, r5418367);
        double r5418369 = sqrt(r5418368);
        double r5418370 = r5418369 - r5418354;
        double r5418371 = 0.5;
        double r5418372 = r5418370 * r5418371;
        double r5418373 = r5418359 / r5418372;
        double r5418374 = r5418364 / r5418373;
        double r5418375 = -r5418358;
        double r5418376 = r5418363 ? r5418374 : r5418375;
        double r5418377 = r5418356 ? r5418361 : r5418376;
        return r5418377;
}

\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 -8.78453392716348 \cdot 10^{+64}:\\
\;\;\;\;\frac{c}{b} - \frac{b}{a}\\

\mathbf{elif}\;b \le 7.643168247577731 \cdot 10^{-56}:\\
\;\;\;\;\frac{1}{\frac{a}{\left(\sqrt{(\left(c \cdot -4\right) \cdot a + \left(b \cdot b\right))_*} - b\right) \cdot \frac{1}{2}}}\\

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

\end{array}

Original	33.4
Target	20.6
Herbie	10.6

Derivation

Split input into 3 regimes
if b < -8.78453392716348e+64
1. Initial program 37.7
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified37.7
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{(b \cdot b + \left(\left(a \cdot c\right) \cdot -4\right))_*} - b}{2}}{a}}\]
3. Taylor expanded around -inf 5.2
  \[\leadsto \color{blue}{\frac{c}{b} - \frac{b}{a}}\]
if -8.78453392716348e+64 < b < 7.643168247577731e-56
1. Initial program 14.7
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified14.6
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{(b \cdot b + \left(\left(a \cdot c\right) \cdot -4\right))_*} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied *-un-lft-identity14.6
  \[\leadsto \frac{\frac{\sqrt{(b \cdot b + \left(\left(a \cdot c\right) \cdot -4\right))_*} - b}{2}}{\color{blue}{1 \cdot a}}\]
5. Applied div-inv14.6
  \[\leadsto \frac{\color{blue}{\left(\sqrt{(b \cdot b + \left(\left(a \cdot c\right) \cdot -4\right))_*} - b\right) \cdot \frac{1}{2}}}{1 \cdot a}\]
6. Applied times-frac14.7
  \[\leadsto \color{blue}{\frac{\sqrt{(b \cdot b + \left(\left(a \cdot c\right) \cdot -4\right))_*} - b}{1} \cdot \frac{\frac{1}{2}}{a}}\]
7. Simplified14.7
  \[\leadsto \color{blue}{\left(\sqrt{(\left(-4 \cdot c\right) \cdot a + \left(b \cdot b\right))_*} - b\right)} \cdot \frac{\frac{1}{2}}{a}\]
8. Simplified14.7
  \[\leadsto \left(\sqrt{(\left(-4 \cdot c\right) \cdot a + \left(b \cdot b\right))_*} - b\right) \cdot \color{blue}{\frac{\frac{1}{2}}{a}}\]
9. Using strategy rm
10. Applied associate-*r/14.6
  \[\leadsto \color{blue}{\frac{\left(\sqrt{(\left(-4 \cdot c\right) \cdot a + \left(b \cdot b\right))_*} - b\right) \cdot \frac{1}{2}}{a}}\]
11. Using strategy rm
12. Applied clear-num14.7
  \[\leadsto \color{blue}{\frac{1}{\frac{a}{\left(\sqrt{(\left(-4 \cdot c\right) \cdot a + \left(b \cdot b\right))_*} - b\right) \cdot \frac{1}{2}}}}\]
if 7.643168247577731e-56 < b
1. Initial program 53.4
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified53.4
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{(b \cdot b + \left(\left(a \cdot c\right) \cdot -4\right))_*} - b}{2}}{a}}\]
3. Taylor expanded around inf 8.5
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
4. Simplified8.5
  \[\leadsto \color{blue}{-\frac{c}{b}}\]
Recombined 3 regimes into one program.
Final simplification10.6
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -8.78453392716348 \cdot 10^{+64}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 7.643168247577731 \cdot 10^{-56}:\\ \;\;\;\;\frac{1}{\frac{a}{\left(\sqrt{(\left(c \cdot -4\right) \cdot a + \left(b \cdot b\right))_*} - b\right) \cdot \frac{1}{2}}}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]

Error

Target

Derivation

`if b < -8.78453392716348e+64`

`if -8.78453392716348e+64 < b < 7.643168247577731e-56`

`if 7.643168247577731e-56 < b`

Reproduce