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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -2.6737765706499252 \cdot 10^{47}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 9.39036747108992214 \cdot 10^{-69}:\\ \;\;\;\;\frac{1}{2} \cdot \left(\left(\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \frac{1}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{2} \cdot \left(-2 \cdot \frac{c}{b}\right)\\ \end{array}\]

\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 -2.6737765706499252 \cdot 10^{47}:\\
\;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\

\mathbf{elif}\;b \le 9.39036747108992214 \cdot 10^{-69}:\\
\;\;\;\;\frac{1}{2} \cdot \left(\left(\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \frac{1}{a}\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{2} \cdot \left(-2 \cdot \frac{c}{b}\right)\\

\end{array}

double f(double a, double b, double c) {
        double r141592 = b;
        double r141593 = -r141592;
        double r141594 = r141592 * r141592;
        double r141595 = 4.0;
        double r141596 = a;
        double r141597 = r141595 * r141596;
        double r141598 = c;
        double r141599 = r141597 * r141598;
        double r141600 = r141594 - r141599;
        double r141601 = sqrt(r141600);
        double r141602 = r141593 + r141601;
        double r141603 = 2.0;
        double r141604 = r141603 * r141596;
        double r141605 = r141602 / r141604;
        return r141605;
}

↓

double f(double a, double b, double c) {
        double r141606 = b;
        double r141607 = -2.6737765706499252e+47;
        bool r141608 = r141606 <= r141607;
        double r141609 = 1.0;
        double r141610 = c;
        double r141611 = r141610 / r141606;
        double r141612 = a;
        double r141613 = r141606 / r141612;
        double r141614 = r141611 - r141613;
        double r141615 = r141609 * r141614;
        double r141616 = 9.390367471089922e-69;
        bool r141617 = r141606 <= r141616;
        double r141618 = 1.0;
        double r141619 = 2.0;
        double r141620 = r141618 / r141619;
        double r141621 = -r141606;
        double r141622 = r141606 * r141606;
        double r141623 = 4.0;
        double r141624 = r141623 * r141612;
        double r141625 = r141624 * r141610;
        double r141626 = r141622 - r141625;
        double r141627 = sqrt(r141626);
        double r141628 = r141621 + r141627;
        double r141629 = r141618 / r141612;
        double r141630 = r141628 * r141629;
        double r141631 = r141620 * r141630;
        double r141632 = -2.0;
        double r141633 = r141632 * r141611;
        double r141634 = r141620 * r141633;
        double r141635 = r141617 ? r141631 : r141634;
        double r141636 = r141608 ? r141615 : r141635;
        return r141636;
}

Original	34.6
Target	21.2
Herbie	10.2

Derivation

Split input into 3 regimes
if b < -2.6737765706499252e+47
1. Initial program 37.5
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Taylor expanded around -inf 5.3
  \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
3. Simplified5.3
  \[\leadsto \color{blue}{1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}\]
if -2.6737765706499252e+47 < b < 9.390367471089922e-69
1. Initial program 14.0
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Using strategy rm
3. Applied *-un-lft-identity14.0
  \[\leadsto \frac{\color{blue}{1 \cdot \left(\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right)}}{2 \cdot a}\]
4. Applied times-frac14.0
  \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{a}}\]
5. Using strategy rm
6. Applied div-inv14.1
  \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(\left(\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \frac{1}{a}\right)}\]
if 9.390367471089922e-69 < b
1. Initial program 53.5
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Using strategy rm
3. Applied *-un-lft-identity53.5
  \[\leadsto \frac{\color{blue}{1 \cdot \left(\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right)}}{2 \cdot a}\]
4. Applied times-frac53.5
  \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{a}}\]
5. Using strategy rm
6. Applied div-inv53.5
  \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(\left(\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \frac{1}{a}\right)}\]
7. Taylor expanded around inf 8.7
  \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(-2 \cdot \frac{c}{b}\right)}\]
Recombined 3 regimes into one program.
Final simplification10.2
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -2.6737765706499252 \cdot 10^{47}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 9.39036747108992214 \cdot 10^{-69}:\\ \;\;\;\;\frac{1}{2} \cdot \left(\left(\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \frac{1}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{2} \cdot \left(-2 \cdot \frac{c}{b}\right)\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -2.6737765706499252e+47`

`if -2.6737765706499252e+47 < b < 9.390367471089922e-69`

`if 9.390367471089922e-69 < b`

Reproduce

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