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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -7.397994825724217 \cdot 10^{+150}:\\ \;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\ \mathbf{elif}\;b \le 1.2158870426682226 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{1}{\frac{a}{\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot c\right) \cdot -4\right)} - b}}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \end{array}\]

\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 -7.397994825724217 \cdot 10^{+150}:\\
\;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\

\mathbf{elif}\;b \le 1.2158870426682226 \cdot 10^{-82}:\\
\;\;\;\;\frac{\frac{1}{\frac{a}{\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot c\right) \cdot -4\right)} - b}}}{2}\\

\mathbf{else}:\\
\;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\

\end{array}

double f(double a, double b, double c) {
        double r6207382 = b;
        double r6207383 = -r6207382;
        double r6207384 = r6207382 * r6207382;
        double r6207385 = 4.0;
        double r6207386 = a;
        double r6207387 = r6207385 * r6207386;
        double r6207388 = c;
        double r6207389 = r6207387 * r6207388;
        double r6207390 = r6207384 - r6207389;
        double r6207391 = sqrt(r6207390);
        double r6207392 = r6207383 + r6207391;
        double r6207393 = 2.0;
        double r6207394 = r6207393 * r6207386;
        double r6207395 = r6207392 / r6207394;
        return r6207395;
}

↓

double f(double a, double b, double c) {
        double r6207396 = b;
        double r6207397 = -7.397994825724217e+150;
        bool r6207398 = r6207396 <= r6207397;
        double r6207399 = c;
        double r6207400 = r6207399 / r6207396;
        double r6207401 = a;
        double r6207402 = r6207396 / r6207401;
        double r6207403 = r6207400 - r6207402;
        double r6207404 = 2.0;
        double r6207405 = r6207403 * r6207404;
        double r6207406 = r6207405 / r6207404;
        double r6207407 = 1.2158870426682226e-82;
        bool r6207408 = r6207396 <= r6207407;
        double r6207409 = 1.0;
        double r6207410 = r6207401 * r6207399;
        double r6207411 = -4.0;
        double r6207412 = r6207410 * r6207411;
        double r6207413 = fma(r6207396, r6207396, r6207412);
        double r6207414 = sqrt(r6207413);
        double r6207415 = r6207414 - r6207396;
        double r6207416 = r6207401 / r6207415;
        double r6207417 = r6207409 / r6207416;
        double r6207418 = r6207417 / r6207404;
        double r6207419 = -2.0;
        double r6207420 = r6207419 * r6207400;
        double r6207421 = r6207420 / r6207404;
        double r6207422 = r6207408 ? r6207418 : r6207421;
        double r6207423 = r6207398 ? r6207406 : r6207422;
        return r6207423;
}

Original	33.2
Target	20.6
Herbie	10.0

Derivation

Split input into 3 regimes
if b < -7.397994825724217e+150
1. Initial program 59.1
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified59.1
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot -4\right) \cdot c\right)} - b}{a}}{2}}\]
3. Taylor expanded around 0 59.1
  \[\leadsto \frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \color{blue}{-4 \cdot \left(a \cdot c\right)}\right)} - b}{a}}{2}\]
4. Taylor expanded around -inf 2.2
  \[\leadsto \frac{\color{blue}{2 \cdot \frac{c}{b} - 2 \cdot \frac{b}{a}}}{2}\]
5. Simplified2.2
  \[\leadsto \frac{\color{blue}{2 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}}{2}\]
if -7.397994825724217e+150 < b < 1.2158870426682226e-82
1. Initial program 11.8
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified11.8
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot -4\right) \cdot c\right)} - b}{a}}{2}}\]
3. Taylor expanded around 0 11.7
  \[\leadsto \frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \color{blue}{-4 \cdot \left(a \cdot c\right)}\right)} - b}{a}}{2}\]
4. Using strategy rm
5. Applied clear-num11.9
  \[\leadsto \frac{\color{blue}{\frac{1}{\frac{a}{\sqrt{\mathsf{fma}\left(b, b, -4 \cdot \left(a \cdot c\right)\right)} - b}}}}{2}\]
if 1.2158870426682226e-82 < b
1. Initial program 52.3
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified52.3
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot -4\right) \cdot c\right)} - b}{a}}{2}}\]
3. Taylor expanded around 0 52.3
  \[\leadsto \frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \color{blue}{-4 \cdot \left(a \cdot c\right)}\right)} - b}{a}}{2}\]
4. Taylor expanded around inf 9.9
  \[\leadsto \frac{\color{blue}{-2 \cdot \frac{c}{b}}}{2}\]
Recombined 3 regimes into one program.
Final simplification10.0
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -7.397994825724217 \cdot 10^{+150}:\\ \;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\ \mathbf{elif}\;b \le 1.2158870426682226 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{1}{\frac{a}{\sqrt{\mathsf{fma}\left(b, b, \left(a \cdot c\right) \cdot -4\right)} - b}}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \end{array}\]

Error

Target

Derivation

`if b < -7.397994825724217e+150`

`if -7.397994825724217e+150 < b < 1.2158870426682226e-82`

`if 1.2158870426682226e-82 < b`

Reproduce