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

↓

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

\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(-4 \cdot c\right) \cdot a\right)} - b}}}{2}\\

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

\end{array}

double f(double a, double b, double c) {
        double r3298396 = b;
        double r3298397 = -r3298396;
        double r3298398 = r3298396 * r3298396;
        double r3298399 = 4.0;
        double r3298400 = a;
        double r3298401 = r3298399 * r3298400;
        double r3298402 = c;
        double r3298403 = r3298401 * r3298402;
        double r3298404 = r3298398 - r3298403;
        double r3298405 = sqrt(r3298404);
        double r3298406 = r3298397 + r3298405;
        double r3298407 = 2.0;
        double r3298408 = r3298407 * r3298400;
        double r3298409 = r3298406 / r3298408;
        return r3298409;
}

↓

double f(double a, double b, double c) {
        double r3298410 = b;
        double r3298411 = -7.397994825724217e+150;
        bool r3298412 = r3298410 <= r3298411;
        double r3298413 = c;
        double r3298414 = r3298413 / r3298410;
        double r3298415 = a;
        double r3298416 = r3298410 / r3298415;
        double r3298417 = r3298414 - r3298416;
        double r3298418 = 2.0;
        double r3298419 = r3298417 * r3298418;
        double r3298420 = r3298419 / r3298418;
        double r3298421 = 1.2158870426682226e-82;
        bool r3298422 = r3298410 <= r3298421;
        double r3298423 = 1.0;
        double r3298424 = -4.0;
        double r3298425 = r3298424 * r3298413;
        double r3298426 = r3298425 * r3298415;
        double r3298427 = fma(r3298410, r3298410, r3298426);
        double r3298428 = sqrt(r3298427);
        double r3298429 = r3298428 - r3298410;
        double r3298430 = r3298415 / r3298429;
        double r3298431 = r3298423 / r3298430;
        double r3298432 = r3298431 / r3298418;
        double r3298433 = -2.0;
        double r3298434 = r3298433 * r3298414;
        double r3298435 = r3298434 / r3298418;
        double r3298436 = r3298422 ? r3298432 : r3298435;
        double r3298437 = r3298412 ? r3298420 : r3298436;
        return r3298437;
}

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. Using strategy rm
4. Applied associate-*l*59.1
  \[\leadsto \frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \color{blue}{a \cdot \left(-4 \cdot c\right)}\right)} - b}{a}}{2}\]
5. Taylor expanded around -inf 2.2
  \[\leadsto \frac{\color{blue}{2 \cdot \frac{c}{b} - 2 \cdot \frac{b}{a}}}{2}\]
6. Simplified2.2
  \[\leadsto \frac{\color{blue}{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}}{2}\]
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. Using strategy rm
4. Applied associate-*l*11.7
  \[\leadsto \frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \color{blue}{a \cdot \left(-4 \cdot c\right)}\right)} - b}{a}}{2}\]
5. Using strategy rm
6. Applied clear-num11.9
  \[\leadsto \frac{\color{blue}{\frac{1}{\frac{a}{\sqrt{\mathsf{fma}\left(b, b, a \cdot \left(-4 \cdot c\right)\right)} - b}}}}{2}\]
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. Using strategy rm
4. Applied associate-*l*52.3
  \[\leadsto \frac{\frac{\sqrt{\mathsf{fma}\left(b, b, \color{blue}{a \cdot \left(-4 \cdot c\right)}\right)} - b}{a}}{2}\]
5. 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
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -7.397994825724217 \cdot 10^{+150}:\\ \;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\ \mathbf{elif}\;b \le 1.2158870426682226 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{1}{\frac{a}{\sqrt{\mathsf{fma}\left(b, b, \left(-4 \cdot c\right) \cdot a\right)} - b}}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \end{array}\]

Error

Target

Derivation

`if b < -7.397994825724217e+150`

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

`if 1.2158870426682226e-82 < b`

Reproduce