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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.390658213785421360285622940547871300736 \cdot 10^{101}:\\ \;\;\;\;\frac{\left(\frac{c}{\frac{b}{a}} - b\right) \cdot 1}{a}\\ \mathbf{elif}\;b \le 4.330541687749954965862284767620099540245 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{1}{\frac{2}{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{1}{b} - \frac{1 \cdot b}{c \cdot a}}}{a}\\ \end{array}\]

\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 -1.390658213785421360285622940547871300736 \cdot 10^{101}:\\
\;\;\;\;\frac{\left(\frac{c}{\frac{b}{a}} - b\right) \cdot 1}{a}\\

\mathbf{elif}\;b \le 4.330541687749954965862284767620099540245 \cdot 10^{-17}:\\
\;\;\;\;\frac{\frac{1}{\frac{2}{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}}}{a}\\

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

\end{array}

double f(double a, double b, double c) {
        double r4981349 = b;
        double r4981350 = -r4981349;
        double r4981351 = r4981349 * r4981349;
        double r4981352 = 4.0;
        double r4981353 = a;
        double r4981354 = r4981352 * r4981353;
        double r4981355 = c;
        double r4981356 = r4981354 * r4981355;
        double r4981357 = r4981351 - r4981356;
        double r4981358 = sqrt(r4981357);
        double r4981359 = r4981350 + r4981358;
        double r4981360 = 2.0;
        double r4981361 = r4981360 * r4981353;
        double r4981362 = r4981359 / r4981361;
        return r4981362;
}

↓

double f(double a, double b, double c) {
        double r4981363 = b;
        double r4981364 = -1.3906582137854214e+101;
        bool r4981365 = r4981363 <= r4981364;
        double r4981366 = c;
        double r4981367 = a;
        double r4981368 = r4981363 / r4981367;
        double r4981369 = r4981366 / r4981368;
        double r4981370 = r4981369 - r4981363;
        double r4981371 = 1.0;
        double r4981372 = r4981370 * r4981371;
        double r4981373 = r4981372 / r4981367;
        double r4981374 = 4.330541687749955e-17;
        bool r4981375 = r4981363 <= r4981374;
        double r4981376 = 1.0;
        double r4981377 = 2.0;
        double r4981378 = r4981363 * r4981363;
        double r4981379 = r4981366 * r4981367;
        double r4981380 = 4.0;
        double r4981381 = r4981379 * r4981380;
        double r4981382 = r4981378 - r4981381;
        double r4981383 = sqrt(r4981382);
        double r4981384 = r4981383 - r4981363;
        double r4981385 = r4981377 / r4981384;
        double r4981386 = r4981376 / r4981385;
        double r4981387 = r4981386 / r4981367;
        double r4981388 = r4981371 / r4981363;
        double r4981389 = r4981371 * r4981363;
        double r4981390 = r4981389 / r4981379;
        double r4981391 = r4981388 - r4981390;
        double r4981392 = r4981376 / r4981391;
        double r4981393 = r4981392 / r4981367;
        double r4981394 = r4981375 ? r4981387 : r4981393;
        double r4981395 = r4981365 ? r4981373 : r4981394;
        return r4981395;
}

Original	34.4
Target	21.3
Herbie	14.1

Derivation

Split input into 3 regimes
if b < -1.3906582137854214e+101
1. Initial program 48.2
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified48.2
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{2}}{a}}\]
3. Taylor expanded around -inf 10.3
  \[\leadsto \frac{\color{blue}{1 \cdot \frac{a \cdot c}{b} - 1 \cdot b}}{a}\]
4. Simplified3.5
  \[\leadsto \frac{\color{blue}{1 \cdot \left(\frac{c}{\frac{b}{a}} - b\right)}}{a}\]
if -1.3906582137854214e+101 < b < 4.330541687749955e-17
1. Initial program 15.2
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified15.2
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied clear-num15.3
  \[\leadsto \frac{\color{blue}{\frac{1}{\frac{2}{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}}}}{a}\]
if 4.330541687749955e-17 < b
1. Initial program 55.6
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified55.6
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied clear-num55.6
  \[\leadsto \frac{\color{blue}{\frac{1}{\frac{2}{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}}}}{a}\]
5. Taylor expanded around inf 17.3
  \[\leadsto \frac{\frac{1}{\color{blue}{1 \cdot \frac{1}{b} - 1 \cdot \frac{b}{a \cdot c}}}}{a}\]
6. Simplified17.3
  \[\leadsto \frac{\frac{1}{\color{blue}{\frac{1}{b} - \frac{b \cdot 1}{c \cdot a}}}}{a}\]
Recombined 3 regimes into one program.
Final simplification14.1
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.390658213785421360285622940547871300736 \cdot 10^{101}:\\ \;\;\;\;\frac{\left(\frac{c}{\frac{b}{a}} - b\right) \cdot 1}{a}\\ \mathbf{elif}\;b \le 4.330541687749954965862284767620099540245 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{1}{\frac{2}{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{1}{b} - \frac{1 \cdot b}{c \cdot a}}}{a}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -1.3906582137854214e+101`

`if -1.3906582137854214e+101 < b < 4.330541687749955e-17`

`if 4.330541687749955e-17 < b`

Reproduce

In
Out