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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -4.3671561050226844 \cdot 10^{+101}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 5.6646816643665726 \cdot 10^{-285}:\\ \;\;\;\;\left(\left(-b\right) + \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}\right) \cdot \frac{1}{a \cdot 2}\\ \mathbf{elif}\;b \le 2.8546456093447043 \cdot 10^{+107}:\\ \;\;\;\;\frac{c \cdot 2}{\left(-b\right) - \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{2 \cdot \left(\frac{c}{b} \cdot a - b\right)}\\ \end{array}\]

double f(double a, double b, double c) {
        double r10668654 = b;
        double r10668655 = -r10668654;
        double r10668656 = r10668654 * r10668654;
        double r10668657 = 4.0;
        double r10668658 = a;
        double r10668659 = r10668657 * r10668658;
        double r10668660 = c;
        double r10668661 = r10668659 * r10668660;
        double r10668662 = r10668656 - r10668661;
        double r10668663 = sqrt(r10668662);
        double r10668664 = r10668655 + r10668663;
        double r10668665 = 2.0;
        double r10668666 = r10668665 * r10668658;
        double r10668667 = r10668664 / r10668666;
        return r10668667;
}

↓

double f(double a, double b, double c) {
        double r10668668 = b;
        double r10668669 = -4.3671561050226844e+101;
        bool r10668670 = r10668668 <= r10668669;
        double r10668671 = c;
        double r10668672 = r10668671 / r10668668;
        double r10668673 = a;
        double r10668674 = r10668668 / r10668673;
        double r10668675 = r10668672 - r10668674;
        double r10668676 = 5.6646816643665726e-285;
        bool r10668677 = r10668668 <= r10668676;
        double r10668678 = -r10668668;
        double r10668679 = r10668668 * r10668668;
        double r10668680 = 4.0;
        double r10668681 = r10668680 * r10668673;
        double r10668682 = r10668671 * r10668681;
        double r10668683 = r10668679 - r10668682;
        double r10668684 = sqrt(r10668683);
        double r10668685 = r10668678 + r10668684;
        double r10668686 = 1.0;
        double r10668687 = 2.0;
        double r10668688 = r10668673 * r10668687;
        double r10668689 = r10668686 / r10668688;
        double r10668690 = r10668685 * r10668689;
        double r10668691 = 2.8546456093447043e+107;
        bool r10668692 = r10668668 <= r10668691;
        double r10668693 = r10668671 * r10668687;
        double r10668694 = r10668678 - r10668684;
        double r10668695 = r10668693 / r10668694;
        double r10668696 = r10668672 * r10668673;
        double r10668697 = r10668696 - r10668668;
        double r10668698 = r10668687 * r10668697;
        double r10668699 = r10668693 / r10668698;
        double r10668700 = r10668692 ? r10668695 : r10668699;
        double r10668701 = r10668677 ? r10668690 : r10668700;
        double r10668702 = r10668670 ? r10668675 : r10668701;
        return r10668702;
}

\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 -4.3671561050226844 \cdot 10^{+101}:\\
\;\;\;\;\frac{c}{b} - \frac{b}{a}\\

\mathbf{elif}\;b \le 5.6646816643665726 \cdot 10^{-285}:\\
\;\;\;\;\left(\left(-b\right) + \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}\right) \cdot \frac{1}{a \cdot 2}\\

\mathbf{elif}\;b \le 2.8546456093447043 \cdot 10^{+107}:\\
\;\;\;\;\frac{c \cdot 2}{\left(-b\right) - \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}\\

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

\end{array}

Original	33.8
Target	21.0
Herbie	6.7

Derivation

Split input into 4 regimes
if b < -4.3671561050226844e+101
1. Initial program 44.7
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Using strategy rm
3. Applied div-inv44.8
  \[\leadsto \color{blue}{\left(\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \frac{1}{2 \cdot a}}\]
4. Taylor expanded around -inf 3.8
  \[\leadsto \color{blue}{\frac{c}{b} - \frac{b}{a}}\]
if -4.3671561050226844e+101 < b < 5.6646816643665726e-285
1. Initial program 9.6
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Using strategy rm
3. Applied div-inv9.7
  \[\leadsto \color{blue}{\left(\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \frac{1}{2 \cdot a}}\]
if 5.6646816643665726e-285 < b < 2.8546456093447043e+107
1. Initial program 33.4
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Using strategy rm
3. Applied div-inv33.5
  \[\leadsto \color{blue}{\left(\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \frac{1}{2 \cdot a}}\]
4. Using strategy rm
5. Applied flip-+33.6
  \[\leadsto \color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}} \cdot \frac{1}{2 \cdot a}\]
6. Applied associate-*l/33.6
  \[\leadsto \color{blue}{\frac{\left(\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \frac{1}{2 \cdot a}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}\]
7. Simplified16.0
  \[\leadsto \frac{\color{blue}{-\frac{\frac{c \cdot a}{\frac{-1}{2}}}{a}}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\]
8. Taylor expanded around -inf 8.7
  \[\leadsto \frac{-\color{blue}{-2 \cdot c}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\]
if 2.8546456093447043e+107 < b
1. Initial program 59.5
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Using strategy rm
3. Applied div-inv59.5
  \[\leadsto \color{blue}{\left(\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \frac{1}{2 \cdot a}}\]
4. Using strategy rm
5. Applied flip-+59.6
  \[\leadsto \color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}} \cdot \frac{1}{2 \cdot a}\]
6. Applied associate-*l/59.6
  \[\leadsto \color{blue}{\frac{\left(\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \frac{1}{2 \cdot a}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}\]
7. Simplified32.0
  \[\leadsto \frac{\color{blue}{-\frac{\frac{c \cdot a}{\frac{-1}{2}}}{a}}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\]
8. Taylor expanded around -inf 31.4
  \[\leadsto \frac{-\color{blue}{-2 \cdot c}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\]
9. Taylor expanded around inf 6.5
  \[\leadsto \frac{--2 \cdot c}{\color{blue}{2 \cdot \frac{a \cdot c}{b} - 2 \cdot b}}\]
10. Simplified2.1
  \[\leadsto \frac{--2 \cdot c}{\color{blue}{\left(\frac{c}{b} \cdot a - b\right) \cdot 2}}\]
Recombined 4 regimes into one program.
Final simplification6.7
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -4.3671561050226844 \cdot 10^{+101}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 5.6646816643665726 \cdot 10^{-285}:\\ \;\;\;\;\left(\left(-b\right) + \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}\right) \cdot \frac{1}{a \cdot 2}\\ \mathbf{elif}\;b \le 2.8546456093447043 \cdot 10^{+107}:\\ \;\;\;\;\frac{c \cdot 2}{\left(-b\right) - \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot 2}{2 \cdot \left(\frac{c}{b} \cdot a - b\right)}\\ \end{array}\]

Error

Target

Derivation

`if b < -4.3671561050226844e+101`

`if -4.3671561050226844e+101 < b < 5.6646816643665726e-285`

`if 5.6646816643665726e-285 < b < 2.8546456093447043e+107`

`if 2.8546456093447043e+107 < b`

Reproduce