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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -4.829903230896134050158793286773621805382 \cdot 10^{148}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 1.058331905530479345989188577279018272684 \cdot 10^{-144}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \mathbf{elif}\;b \le 400482480739649191422756162656796672:\\ \;\;\;\;\frac{\frac{0 + 4 \cdot \left(a \cdot c\right)}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

\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 -4.829903230896134050158793286773621805382 \cdot 10^{148}:\\
\;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\

\mathbf{elif}\;b \le 1.058331905530479345989188577279018272684 \cdot 10^{-144}:\\
\;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\

\mathbf{elif}\;b \le 400482480739649191422756162656796672:\\
\;\;\;\;\frac{\frac{0 + 4 \cdot \left(a \cdot c\right)}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\\

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

\end{array}

double f(double a, double b, double c) {
        double r83124 = b;
        double r83125 = -r83124;
        double r83126 = r83124 * r83124;
        double r83127 = 4.0;
        double r83128 = a;
        double r83129 = r83127 * r83128;
        double r83130 = c;
        double r83131 = r83129 * r83130;
        double r83132 = r83126 - r83131;
        double r83133 = sqrt(r83132);
        double r83134 = r83125 + r83133;
        double r83135 = 2.0;
        double r83136 = r83135 * r83128;
        double r83137 = r83134 / r83136;
        return r83137;
}

↓

double f(double a, double b, double c) {
        double r83138 = b;
        double r83139 = -4.829903230896134e+148;
        bool r83140 = r83138 <= r83139;
        double r83141 = 1.0;
        double r83142 = c;
        double r83143 = r83142 / r83138;
        double r83144 = a;
        double r83145 = r83138 / r83144;
        double r83146 = r83143 - r83145;
        double r83147 = r83141 * r83146;
        double r83148 = 1.0583319055304793e-144;
        bool r83149 = r83138 <= r83148;
        double r83150 = -r83138;
        double r83151 = r83138 * r83138;
        double r83152 = 4.0;
        double r83153 = r83152 * r83144;
        double r83154 = r83153 * r83142;
        double r83155 = r83151 - r83154;
        double r83156 = sqrt(r83155);
        double r83157 = r83150 + r83156;
        double r83158 = 2.0;
        double r83159 = r83158 * r83144;
        double r83160 = r83157 / r83159;
        double r83161 = 4.004824807396492e+35;
        bool r83162 = r83138 <= r83161;
        double r83163 = 0.0;
        double r83164 = r83144 * r83142;
        double r83165 = r83152 * r83164;
        double r83166 = r83163 + r83165;
        double r83167 = r83150 - r83156;
        double r83168 = r83166 / r83167;
        double r83169 = r83168 / r83159;
        double r83170 = -1.0;
        double r83171 = r83170 * r83143;
        double r83172 = r83162 ? r83169 : r83171;
        double r83173 = r83149 ? r83160 : r83172;
        double r83174 = r83140 ? r83147 : r83173;
        return r83174;
}

Original	34.3
Target	20.9
Herbie	8.9

Derivation

Split input into 4 regimes
if b < -4.829903230896134e+148
1. Initial program 61.7
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Taylor expanded around -inf 2.8
  \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
3. Simplified2.8
  \[\leadsto \color{blue}{1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}\]
if -4.829903230896134e+148 < b < 1.0583319055304793e-144
1. Initial program 11.2
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
if 1.0583319055304793e-144 < b < 4.004824807396492e+35
1. Initial program 35.7
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Using strategy rm
3. Applied flip-+35.8
  \[\leadsto \frac{\color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a}\]
4. Simplified16.7
  \[\leadsto \frac{\frac{\color{blue}{0 + 4 \cdot \left(a \cdot c\right)}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\]
if 4.004824807396492e+35 < b
1. Initial program 56.6
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Taylor expanded around inf 4.3
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
Recombined 4 regimes into one program.
Final simplification8.9
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -4.829903230896134050158793286773621805382 \cdot 10^{148}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 1.058331905530479345989188577279018272684 \cdot 10^{-144}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \mathbf{elif}\;b \le 400482480739649191422756162656796672:\\ \;\;\;\;\frac{\frac{0 + 4 \cdot \left(a \cdot c\right)}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -4.829903230896134e+148`

`if -4.829903230896134e+148 < b < 1.0583319055304793e-144`

`if 1.0583319055304793e-144 < b < 4.004824807396492e+35`

`if 4.004824807396492e+35 < b`

Reproduce

In
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