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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -9.768773924260542 \cdot 10^{+151}:\\ \;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\ \mathbf{elif}\;b \le 5.9878793504095505 \cdot 10^{-84}:\\ \;\;\;\;\frac{\frac{\sqrt{\mathsf{fma}\left(b, b, -4 \cdot \left(a \cdot c\right)\right)} - b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{c}{b} \cdot -2}{2}\\ \end{array}\]

\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 -9.768773924260542 \cdot 10^{+151}:\\
\;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\

\mathbf{elif}\;b \le 5.9878793504095505 \cdot 10^{-84}:\\
\;\;\;\;\frac{\frac{\sqrt{\mathsf{fma}\left(b, b, -4 \cdot \left(a \cdot c\right)\right)} - b}{a}}{2}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{c}{b} \cdot -2}{2}\\

\end{array}

double f(double a, double b, double c) {
        double r2184092 = b;
        double r2184093 = -r2184092;
        double r2184094 = r2184092 * r2184092;
        double r2184095 = 4.0;
        double r2184096 = a;
        double r2184097 = c;
        double r2184098 = r2184096 * r2184097;
        double r2184099 = r2184095 * r2184098;
        double r2184100 = r2184094 - r2184099;
        double r2184101 = sqrt(r2184100);
        double r2184102 = r2184093 + r2184101;
        double r2184103 = 2.0;
        double r2184104 = r2184103 * r2184096;
        double r2184105 = r2184102 / r2184104;
        return r2184105;
}

↓

double f(double a, double b, double c) {
        double r2184106 = b;
        double r2184107 = -9.768773924260542e+151;
        bool r2184108 = r2184106 <= r2184107;
        double r2184109 = c;
        double r2184110 = r2184109 / r2184106;
        double r2184111 = a;
        double r2184112 = r2184106 / r2184111;
        double r2184113 = r2184110 - r2184112;
        double r2184114 = 2.0;
        double r2184115 = r2184113 * r2184114;
        double r2184116 = r2184115 / r2184114;
        double r2184117 = 5.9878793504095505e-84;
        bool r2184118 = r2184106 <= r2184117;
        double r2184119 = -4.0;
        double r2184120 = r2184111 * r2184109;
        double r2184121 = r2184119 * r2184120;
        double r2184122 = fma(r2184106, r2184106, r2184121);
        double r2184123 = sqrt(r2184122);
        double r2184124 = r2184123 - r2184106;
        double r2184125 = r2184124 / r2184111;
        double r2184126 = r2184125 / r2184114;
        double r2184127 = -2.0;
        double r2184128 = r2184110 * r2184127;
        double r2184129 = r2184128 / r2184114;
        double r2184130 = r2184118 ? r2184126 : r2184129;
        double r2184131 = r2184108 ? r2184116 : r2184130;
        return r2184131;
}

Original	33.6
Target	20.4
Herbie	9.6

Derivation

Split input into 3 regimes
if b < -9.768773924260542e+151
1. Initial program 60.2
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified60.2
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{\mathsf{fma}\left(a \cdot c, -4, b \cdot b\right)} - b}{a}}{2}}\]
3. Taylor expanded around inf 60.2
  \[\leadsto \frac{\frac{\sqrt{\color{blue}{{b}^{2} - 4 \cdot \left(a \cdot c\right)}} - b}{a}}{2}\]
4. Simplified60.2
  \[\leadsto \frac{\frac{\sqrt{\color{blue}{\mathsf{fma}\left(b, b, \left(a \cdot c\right) \cdot -4\right)}} - b}{a}}{2}\]
5. Taylor expanded around -inf 1.7
  \[\leadsto \frac{\color{blue}{2 \cdot \frac{c}{b} - 2 \cdot \frac{b}{a}}}{2}\]
6. Simplified1.7
  \[\leadsto \frac{\color{blue}{2 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}}{2}\]
if -9.768773924260542e+151 < b < 5.9878793504095505e-84
1. Initial program 11.8
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified11.8
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{\mathsf{fma}\left(a \cdot c, -4, b \cdot b\right)} - b}{a}}{2}}\]
3. Taylor expanded around inf 11.8
  \[\leadsto \frac{\frac{\sqrt{\color{blue}{{b}^{2} - 4 \cdot \left(a \cdot c\right)}} - b}{a}}{2}\]
4. Simplified11.8
  \[\leadsto \frac{\frac{\sqrt{\color{blue}{\mathsf{fma}\left(b, b, \left(a \cdot c\right) \cdot -4\right)}} - b}{a}}{2}\]
if 5.9878793504095505e-84 < b
1. Initial program 52.2
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified52.2
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{\mathsf{fma}\left(a \cdot c, -4, b \cdot b\right)} - b}{a}}{2}}\]
3. Taylor expanded around inf 52.2
  \[\leadsto \frac{\frac{\sqrt{\color{blue}{{b}^{2} - 4 \cdot \left(a \cdot c\right)}} - b}{a}}{2}\]
4. Simplified52.2
  \[\leadsto \frac{\frac{\sqrt{\color{blue}{\mathsf{fma}\left(b, b, \left(a \cdot c\right) \cdot -4\right)}} - b}{a}}{2}\]
5. Taylor expanded around inf 9.3
  \[\leadsto \frac{\color{blue}{-2 \cdot \frac{c}{b}}}{2}\]
Recombined 3 regimes into one program.
Final simplification9.6
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -9.768773924260542 \cdot 10^{+151}:\\ \;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\ \mathbf{elif}\;b \le 5.9878793504095505 \cdot 10^{-84}:\\ \;\;\;\;\frac{\frac{\sqrt{\mathsf{fma}\left(b, b, -4 \cdot \left(a \cdot c\right)\right)} - b}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{c}{b} \cdot -2}{2}\\ \end{array}\]

Error

Target

Derivation

`if b < -9.768773924260542e+151`

`if -9.768773924260542e+151 < b < 5.9878793504095505e-84`

`if 5.9878793504095505e-84 < b`

Reproduce