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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -3.4350120867177856 \cdot 10^{+86}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 9.022485597500134 \cdot 10^{-56}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}{a} \cdot \frac{1}{2}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]

double f(double a, double b, double c) {
        double r10855162 = b;
        double r10855163 = -r10855162;
        double r10855164 = r10855162 * r10855162;
        double r10855165 = 4.0;
        double r10855166 = a;
        double r10855167 = r10855165 * r10855166;
        double r10855168 = c;
        double r10855169 = r10855167 * r10855168;
        double r10855170 = r10855164 - r10855169;
        double r10855171 = sqrt(r10855170);
        double r10855172 = r10855163 + r10855171;
        double r10855173 = 2.0;
        double r10855174 = r10855173 * r10855166;
        double r10855175 = r10855172 / r10855174;
        return r10855175;
}

↓

double f(double a, double b, double c) {
        double r10855176 = b;
        double r10855177 = -3.4350120867177856e+86;
        bool r10855178 = r10855176 <= r10855177;
        double r10855179 = c;
        double r10855180 = r10855179 / r10855176;
        double r10855181 = a;
        double r10855182 = r10855176 / r10855181;
        double r10855183 = r10855180 - r10855182;
        double r10855184 = 9.022485597500134e-56;
        bool r10855185 = r10855176 <= r10855184;
        double r10855186 = r10855176 * r10855176;
        double r10855187 = 4.0;
        double r10855188 = r10855187 * r10855181;
        double r10855189 = r10855179 * r10855188;
        double r10855190 = r10855186 - r10855189;
        double r10855191 = sqrt(r10855190);
        double r10855192 = r10855191 - r10855176;
        double r10855193 = r10855192 / r10855181;
        double r10855194 = 0.5;
        double r10855195 = r10855193 * r10855194;
        double r10855196 = -r10855180;
        double r10855197 = r10855185 ? r10855195 : r10855196;
        double r10855198 = r10855178 ? r10855183 : r10855197;
        return r10855198;
}

\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 -3.4350120867177856 \cdot 10^{+86}:\\
\;\;\;\;\frac{c}{b} - \frac{b}{a}\\

\mathbf{elif}\;b \le 9.022485597500134 \cdot 10^{-56}:\\
\;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}{a} \cdot \frac{1}{2}\\

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

\end{array}

Original	33.4
Target	20.6
Herbie	10.5

Derivation

Split input into 3 regimes
if b < -3.4350120867177856e+86
1. Initial program 41.4
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Taylor expanded around -inf 4.4
  \[\leadsto \color{blue}{\frac{c}{b} - \frac{b}{a}}\]
if -3.4350120867177856e+86 < b < 9.022485597500134e-56
1. Initial program 14.3
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Using strategy rm
3. Applied *-un-lft-identity14.3
  \[\leadsto \frac{\color{blue}{1 \cdot \left(\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right)}}{2 \cdot a}\]
4. Applied associate-/l*14.4
  \[\leadsto \color{blue}{\frac{1}{\frac{2 \cdot a}{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}}\]
5. Using strategy rm
6. Applied *-un-lft-identity14.4
  \[\leadsto \frac{1}{\frac{2 \cdot a}{\color{blue}{1 \cdot \left(\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right)}}}\]
7. Applied times-frac14.4
  \[\leadsto \frac{1}{\color{blue}{\frac{2}{1} \cdot \frac{a}{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}}\]
8. Applied add-sqr-sqrt14.4
  \[\leadsto \frac{\color{blue}{\sqrt{1} \cdot \sqrt{1}}}{\frac{2}{1} \cdot \frac{a}{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}\]
9. Applied times-frac14.4
  \[\leadsto \color{blue}{\frac{\sqrt{1}}{\frac{2}{1}} \cdot \frac{\sqrt{1}}{\frac{a}{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}}\]
10. Simplified14.4
  \[\leadsto \color{blue}{\frac{1}{2}} \cdot \frac{\sqrt{1}}{\frac{a}{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}\]
11. Simplified14.3
  \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}}\]
if 9.022485597500134e-56 < b
1. Initial program 53.4
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Taylor expanded around inf 8.5
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
3. Simplified8.5
  \[\leadsto \color{blue}{-\frac{c}{b}}\]
Recombined 3 regimes into one program.
Final simplification10.5
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -3.4350120867177856 \cdot 10^{+86}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 9.022485597500134 \cdot 10^{-56}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}{a} \cdot \frac{1}{2}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]

Error

Target

Derivation

`if b < -3.4350120867177856e+86`

`if -3.4350120867177856e+86 < b < 9.022485597500134e-56`

`if 9.022485597500134e-56 < b`

Reproduce