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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.762479091812706 \cdot 10^{+65}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le -2.436990347475487 \cdot 10^{-257}:\\ \;\;\;\;\frac{4}{\sqrt{c \cdot \left(-4 \cdot a\right) + b \cdot b} - b} \cdot \left(\frac{1}{2} \cdot c\right)\\ \mathbf{elif}\;b \le 2.598286182153128 \cdot 10^{+84}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b + \left(c \cdot -4\right) \cdot a}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;-\frac{b}{a}\\ \end{array}\]

double f(double a, double b, double c) {
        double r7022737 = b;
        double r7022738 = -r7022737;
        double r7022739 = r7022737 * r7022737;
        double r7022740 = 4.0;
        double r7022741 = a;
        double r7022742 = c;
        double r7022743 = r7022741 * r7022742;
        double r7022744 = r7022740 * r7022743;
        double r7022745 = r7022739 - r7022744;
        double r7022746 = sqrt(r7022745);
        double r7022747 = r7022738 - r7022746;
        double r7022748 = 2.0;
        double r7022749 = r7022748 * r7022741;
        double r7022750 = r7022747 / r7022749;
        return r7022750;
}

↓

double f(double a, double b, double c) {
        double r7022751 = b;
        double r7022752 = -1.762479091812706e+65;
        bool r7022753 = r7022751 <= r7022752;
        double r7022754 = c;
        double r7022755 = r7022754 / r7022751;
        double r7022756 = -r7022755;
        double r7022757 = -2.436990347475487e-257;
        bool r7022758 = r7022751 <= r7022757;
        double r7022759 = 4.0;
        double r7022760 = -4.0;
        double r7022761 = a;
        double r7022762 = r7022760 * r7022761;
        double r7022763 = r7022754 * r7022762;
        double r7022764 = r7022751 * r7022751;
        double r7022765 = r7022763 + r7022764;
        double r7022766 = sqrt(r7022765);
        double r7022767 = r7022766 - r7022751;
        double r7022768 = r7022759 / r7022767;
        double r7022769 = 0.5;
        double r7022770 = r7022769 * r7022754;
        double r7022771 = r7022768 * r7022770;
        double r7022772 = 2.598286182153128e+84;
        bool r7022773 = r7022751 <= r7022772;
        double r7022774 = -r7022751;
        double r7022775 = r7022754 * r7022760;
        double r7022776 = r7022775 * r7022761;
        double r7022777 = r7022764 + r7022776;
        double r7022778 = sqrt(r7022777);
        double r7022779 = r7022774 - r7022778;
        double r7022780 = 2.0;
        double r7022781 = r7022780 * r7022761;
        double r7022782 = r7022779 / r7022781;
        double r7022783 = r7022751 / r7022761;
        double r7022784 = -r7022783;
        double r7022785 = r7022773 ? r7022782 : r7022784;
        double r7022786 = r7022758 ? r7022771 : r7022785;
        double r7022787 = r7022753 ? r7022756 : r7022786;
        return r7022787;
}

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

↓

\begin{array}{l}
\mathbf{if}\;b \le -1.762479091812706 \cdot 10^{+65}:\\
\;\;\;\;-\frac{c}{b}\\

\mathbf{elif}\;b \le -2.436990347475487 \cdot 10^{-257}:\\
\;\;\;\;\frac{4}{\sqrt{c \cdot \left(-4 \cdot a\right) + b \cdot b} - b} \cdot \left(\frac{1}{2} \cdot c\right)\\

\mathbf{elif}\;b \le 2.598286182153128 \cdot 10^{+84}:\\
\;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b + \left(c \cdot -4\right) \cdot a}}{2 \cdot a}\\

\mathbf{else}:\\
\;\;\;\;-\frac{b}{a}\\

\end{array}

Original	33.2
Target	20.1
Herbie	7.0

Derivation

Split input into 4 regimes
if b < -1.762479091812706e+65
1. Initial program 57.3
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Taylor expanded around -inf 3.8
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
3. Simplified3.8
  \[\leadsto \color{blue}{-\frac{c}{b}}\]
if -1.762479091812706e+65 < b < -2.436990347475487e-257
1. Initial program 31.7
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Using strategy rm
3. Applied flip--31.8
  \[\leadsto \frac{\color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} \cdot \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a}\]
4. Applied associate-/l/36.6
  \[\leadsto \color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} \cdot \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{\left(2 \cdot a\right) \cdot \left(\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}\]
5. Simplified21.3
  \[\leadsto \frac{\color{blue}{\left(a \cdot c\right) \cdot 4}}{\left(2 \cdot a\right) \cdot \left(\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}\]
6. Using strategy rm
7. Applied times-frac15.9
  \[\leadsto \color{blue}{\frac{a \cdot c}{2 \cdot a} \cdot \frac{4}{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}\]
8. Simplified8.3
  \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot c\right)} \cdot \frac{4}{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}\]
9. Simplified8.3
  \[\leadsto \left(\frac{1}{2} \cdot c\right) \cdot \color{blue}{\frac{4}{\sqrt{c \cdot \left(-4 \cdot a\right) + b \cdot b} - b}}\]
if -2.436990347475487e-257 < b < 2.598286182153128e+84
1. Initial program 10.0
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Taylor expanded around 0 10.0
  \[\leadsto \frac{\left(-b\right) - \sqrt{\color{blue}{{b}^{2} - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\]
3. Simplified10.0
  \[\leadsto \frac{\left(-b\right) - \sqrt{\color{blue}{b \cdot b + \left(c \cdot -4\right) \cdot a}}}{2 \cdot a}\]
if 2.598286182153128e+84 < b
1. Initial program 40.7
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Using strategy rm
3. Applied flip--60.9
  \[\leadsto \frac{\color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} \cdot \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a}\]
4. Applied associate-/l/61.2
  \[\leadsto \color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} \cdot \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{\left(2 \cdot a\right) \cdot \left(\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}\]
5. Simplified61.4
  \[\leadsto \frac{\color{blue}{\left(a \cdot c\right) \cdot 4}}{\left(2 \cdot a\right) \cdot \left(\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}\]
6. Taylor expanded around 0 4.5
  \[\leadsto \color{blue}{-1 \cdot \frac{b}{a}}\]
7. Simplified4.5
  \[\leadsto \color{blue}{-\frac{b}{a}}\]
Recombined 4 regimes into one program.
Final simplification7.0
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.762479091812706 \cdot 10^{+65}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le -2.436990347475487 \cdot 10^{-257}:\\ \;\;\;\;\frac{4}{\sqrt{c \cdot \left(-4 \cdot a\right) + b \cdot b} - b} \cdot \left(\frac{1}{2} \cdot c\right)\\ \mathbf{elif}\;b \le 2.598286182153128 \cdot 10^{+84}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b + \left(c \cdot -4\right) \cdot a}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;-\frac{b}{a}\\ \end{array}\]

Error

Target

Derivation

`if b < -1.762479091812706e+65`

`if -1.762479091812706e+65 < b < -2.436990347475487e-257`

`if -2.436990347475487e-257 < b < 2.598286182153128e+84`

`if 2.598286182153128e+84 < b`

Reproduce