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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -8.55528137777049654 \cdot 10^{140}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 5.08374808794434102 \cdot 10^{-70}:\\ \;\;\;\;\sqrt{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}} \cdot \frac{\sqrt{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}}}{a}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

\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 -8.55528137777049654 \cdot 10^{140}:\\
\;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\

\mathbf{elif}\;b \le 5.08374808794434102 \cdot 10^{-70}:\\
\;\;\;\;\sqrt{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}} \cdot \frac{\sqrt{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}}}{a}\\

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

\end{array}

double f(double a, double b, double c) {
        double r68279 = b;
        double r68280 = -r68279;
        double r68281 = r68279 * r68279;
        double r68282 = 4.0;
        double r68283 = a;
        double r68284 = c;
        double r68285 = r68283 * r68284;
        double r68286 = r68282 * r68285;
        double r68287 = r68281 - r68286;
        double r68288 = sqrt(r68287);
        double r68289 = r68280 + r68288;
        double r68290 = 2.0;
        double r68291 = r68290 * r68283;
        double r68292 = r68289 / r68291;
        return r68292;
}

↓

double f(double a, double b, double c) {
        double r68293 = b;
        double r68294 = -8.555281377770497e+140;
        bool r68295 = r68293 <= r68294;
        double r68296 = 1.0;
        double r68297 = c;
        double r68298 = r68297 / r68293;
        double r68299 = a;
        double r68300 = r68293 / r68299;
        double r68301 = r68298 - r68300;
        double r68302 = r68296 * r68301;
        double r68303 = 5.083748087944341e-70;
        bool r68304 = r68293 <= r68303;
        double r68305 = r68293 * r68293;
        double r68306 = 4.0;
        double r68307 = r68299 * r68297;
        double r68308 = r68306 * r68307;
        double r68309 = r68305 - r68308;
        double r68310 = sqrt(r68309);
        double r68311 = r68310 - r68293;
        double r68312 = 2.0;
        double r68313 = r68311 / r68312;
        double r68314 = sqrt(r68313);
        double r68315 = r68314 / r68299;
        double r68316 = r68314 * r68315;
        double r68317 = -1.0;
        double r68318 = r68317 * r68298;
        double r68319 = r68304 ? r68316 : r68318;
        double r68320 = r68295 ? r68302 : r68319;
        return r68320;
}

Original	34.2
Target	21.1
Herbie	10.0

Derivation

Split input into 3 regimes
if b < -8.555281377770497e+140
1. Initial program 58.5
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified58.5
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}}{a}}\]
3. Taylor expanded around -inf 2.4
  \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
4. Simplified2.4
  \[\leadsto \color{blue}{1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}\]
if -8.555281377770497e+140 < b < 5.083748087944341e-70
1. Initial program 12.5
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified12.5
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied *-un-lft-identity12.5
  \[\leadsto \frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}}{\color{blue}{1 \cdot a}}\]
5. Applied add-sqr-sqrt13.0
  \[\leadsto \frac{\color{blue}{\sqrt{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}} \cdot \sqrt{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}}}}{1 \cdot a}\]
6. Applied times-frac13.0
  \[\leadsto \color{blue}{\frac{\sqrt{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}}}{1} \cdot \frac{\sqrt{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}}}{a}}\]
7. Simplified13.0
  \[\leadsto \color{blue}{\sqrt{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}}} \cdot \frac{\sqrt{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}}}{a}\]
if 5.083748087944341e-70 < b
1. Initial program 53.1
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified53.1
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}}{a}}\]
3. Taylor expanded around inf 8.7
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
Recombined 3 regimes into one program.
Final simplification10.0
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -8.55528137777049654 \cdot 10^{140}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 5.08374808794434102 \cdot 10^{-70}:\\ \;\;\;\;\sqrt{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}} \cdot \frac{\sqrt{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}}}{a}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

Falling back on racket egraph because egg-herbie package not installed (more)

Error

Try it out

Target

Derivation

`if b < -8.555281377770497e+140`

`if -8.555281377770497e+140 < b < 5.083748087944341e-70`

`if 5.083748087944341e-70 < b`

Reproduce

In
Out