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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -2.3165289123951838 \cdot 10^{-123}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \mathbf{elif}\;b \le 6.7711658147871089 \cdot 10^{125}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \mathsf{fma}\left(\frac{1}{\sqrt[3]{b} \cdot \sqrt[3]{b}}, \frac{c}{\sqrt[3]{b}}, -\frac{b}{a}\right)\\ \end{array}\]

\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 -2.3165289123951838 \cdot 10^{-123}:\\
\;\;\;\;-1 \cdot \frac{c}{b}\\

\mathbf{elif}\;b \le 6.7711658147871089 \cdot 10^{125}:\\
\;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\

\mathbf{else}:\\
\;\;\;\;1 \cdot \mathsf{fma}\left(\frac{1}{\sqrt[3]{b} \cdot \sqrt[3]{b}}, \frac{c}{\sqrt[3]{b}}, -\frac{b}{a}\right)\\

\end{array}

double f(double a, double b, double c) {
        double r79098 = b;
        double r79099 = -r79098;
        double r79100 = r79098 * r79098;
        double r79101 = 4.0;
        double r79102 = a;
        double r79103 = c;
        double r79104 = r79102 * r79103;
        double r79105 = r79101 * r79104;
        double r79106 = r79100 - r79105;
        double r79107 = sqrt(r79106);
        double r79108 = r79099 - r79107;
        double r79109 = 2.0;
        double r79110 = r79109 * r79102;
        double r79111 = r79108 / r79110;
        return r79111;
}

↓

double f(double a, double b, double c) {
        double r79112 = b;
        double r79113 = -2.3165289123951838e-123;
        bool r79114 = r79112 <= r79113;
        double r79115 = -1.0;
        double r79116 = c;
        double r79117 = r79116 / r79112;
        double r79118 = r79115 * r79117;
        double r79119 = 6.771165814787109e+125;
        bool r79120 = r79112 <= r79119;
        double r79121 = -r79112;
        double r79122 = r79112 * r79112;
        double r79123 = 4.0;
        double r79124 = a;
        double r79125 = r79124 * r79116;
        double r79126 = r79123 * r79125;
        double r79127 = r79122 - r79126;
        double r79128 = sqrt(r79127);
        double r79129 = r79121 - r79128;
        double r79130 = 2.0;
        double r79131 = r79130 * r79124;
        double r79132 = r79129 / r79131;
        double r79133 = 1.0;
        double r79134 = 1.0;
        double r79135 = cbrt(r79112);
        double r79136 = r79135 * r79135;
        double r79137 = r79134 / r79136;
        double r79138 = r79116 / r79135;
        double r79139 = r79112 / r79124;
        double r79140 = -r79139;
        double r79141 = fma(r79137, r79138, r79140);
        double r79142 = r79133 * r79141;
        double r79143 = r79120 ? r79132 : r79142;
        double r79144 = r79114 ? r79118 : r79143;
        return r79144;
}

Original	34.1
Target	21.2
Herbie	10.3

Derivation

Split input into 3 regimes
if b < -2.3165289123951838e-123
1. Initial program 51.0
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Taylor expanded around -inf 11.7
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
if -2.3165289123951838e-123 < b < 6.771165814787109e+125
1. Initial program 11.4
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Using strategy rm
3. Applied div-inv11.5
  \[\leadsto \color{blue}{\left(\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{1}{2 \cdot a}}\]
4. Using strategy rm
5. Applied un-div-inv11.4
  \[\leadsto \color{blue}{\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\]
if 6.771165814787109e+125 < b
1. Initial program 53.5
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Taylor expanded around inf 2.5
  \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
3. Simplified2.5
  \[\leadsto \color{blue}{1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}\]
4. Using strategy rm
5. Applied add-cube-cbrt2.5
  \[\leadsto 1 \cdot \left(\frac{c}{\color{blue}{\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \sqrt[3]{b}}} - \frac{b}{a}\right)\]
6. Applied *-un-lft-identity2.5
  \[\leadsto 1 \cdot \left(\frac{\color{blue}{1 \cdot c}}{\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \sqrt[3]{b}} - \frac{b}{a}\right)\]
7. Applied times-frac2.5
  \[\leadsto 1 \cdot \left(\color{blue}{\frac{1}{\sqrt[3]{b} \cdot \sqrt[3]{b}} \cdot \frac{c}{\sqrt[3]{b}}} - \frac{b}{a}\right)\]
8. Applied fma-neg2.5
  \[\leadsto 1 \cdot \color{blue}{\mathsf{fma}\left(\frac{1}{\sqrt[3]{b} \cdot \sqrt[3]{b}}, \frac{c}{\sqrt[3]{b}}, -\frac{b}{a}\right)}\]
Recombined 3 regimes into one program.
Final simplification10.3
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -2.3165289123951838 \cdot 10^{-123}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \mathbf{elif}\;b \le 6.7711658147871089 \cdot 10^{125}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \mathsf{fma}\left(\frac{1}{\sqrt[3]{b} \cdot \sqrt[3]{b}}, \frac{c}{\sqrt[3]{b}}, -\frac{b}{a}\right)\\ \end{array}\]

Error

Target

Derivation

`if b < -2.3165289123951838e-123`

`if -2.3165289123951838e-123 < b < 6.771165814787109e+125`

`if 6.771165814787109e+125 < b`

Reproduce