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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.2303558036345968 \cdot 10^{-110}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le 5.869467752933353 \cdot 10^{+121}:\\ \;\;\;\;\frac{\frac{\left(-b\right) - \sqrt{(\left(c \cdot a\right) \cdot -4 + \left(b \cdot b\right))_*}}{2}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\]

\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 -1.2303558036345968 \cdot 10^{-110}:\\
\;\;\;\;-\frac{c}{b}\\

\mathbf{elif}\;b \le 5.869467752933353 \cdot 10^{+121}:\\
\;\;\;\;\frac{\frac{\left(-b\right) - \sqrt{(\left(c \cdot a\right) \cdot -4 + \left(b \cdot b\right))_*}}{2}}{a}\\

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

\end{array}

double f(double a, double b, double c) {
        double r4172127 = b;
        double r4172128 = -r4172127;
        double r4172129 = r4172127 * r4172127;
        double r4172130 = 4.0;
        double r4172131 = a;
        double r4172132 = c;
        double r4172133 = r4172131 * r4172132;
        double r4172134 = r4172130 * r4172133;
        double r4172135 = r4172129 - r4172134;
        double r4172136 = sqrt(r4172135);
        double r4172137 = r4172128 - r4172136;
        double r4172138 = 2.0;
        double r4172139 = r4172138 * r4172131;
        double r4172140 = r4172137 / r4172139;
        return r4172140;
}

↓

double f(double a, double b, double c) {
        double r4172141 = b;
        double r4172142 = -1.2303558036345968e-110;
        bool r4172143 = r4172141 <= r4172142;
        double r4172144 = c;
        double r4172145 = r4172144 / r4172141;
        double r4172146 = -r4172145;
        double r4172147 = 5.869467752933353e+121;
        bool r4172148 = r4172141 <= r4172147;
        double r4172149 = -r4172141;
        double r4172150 = a;
        double r4172151 = r4172144 * r4172150;
        double r4172152 = -4.0;
        double r4172153 = r4172141 * r4172141;
        double r4172154 = fma(r4172151, r4172152, r4172153);
        double r4172155 = sqrt(r4172154);
        double r4172156 = r4172149 - r4172155;
        double r4172157 = 2.0;
        double r4172158 = r4172156 / r4172157;
        double r4172159 = r4172158 / r4172150;
        double r4172160 = r4172141 / r4172150;
        double r4172161 = r4172145 - r4172160;
        double r4172162 = r4172148 ? r4172159 : r4172161;
        double r4172163 = r4172143 ? r4172146 : r4172162;
        return r4172163;
}

Original	33.3
Target	20.2
Herbie	9.6

Derivation

Split input into 3 regimes
if b < -1.2303558036345968e-110
1. Initial program 50.8
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified50.8
  \[\leadsto \color{blue}{\frac{\frac{\left(-b\right) - \sqrt{(\left(a \cdot c\right) \cdot -4 + \left(b \cdot b\right))_*}}{2}}{a}}\]
3. Taylor expanded around 0 50.8
  \[\leadsto \frac{\frac{\left(-b\right) - \sqrt{\color{blue}{{b}^{2} - 4 \cdot \left(a \cdot c\right)}}}{2}}{a}\]
4. Simplified50.8
  \[\leadsto \frac{\frac{\left(-b\right) - \sqrt{\color{blue}{(\left(a \cdot c\right) \cdot -4 + \left(b \cdot b\right))_*}}}{2}}{a}\]
5. Using strategy rm
6. Applied *-un-lft-identity50.8
  \[\leadsto \frac{\frac{\left(-b\right) - \sqrt{(\left(a \cdot c\right) \cdot -4 + \left(b \cdot b\right))_*}}{2}}{\color{blue}{1 \cdot a}}\]
7. Applied div-inv50.8
  \[\leadsto \frac{\color{blue}{\left(\left(-b\right) - \sqrt{(\left(a \cdot c\right) \cdot -4 + \left(b \cdot b\right))_*}\right) \cdot \frac{1}{2}}}{1 \cdot a}\]
8. Applied times-frac50.8
  \[\leadsto \color{blue}{\frac{\left(-b\right) - \sqrt{(\left(a \cdot c\right) \cdot -4 + \left(b \cdot b\right))_*}}{1} \cdot \frac{\frac{1}{2}}{a}}\]
9. Simplified50.8
  \[\leadsto \color{blue}{\left(-\left(b + \sqrt{(a \cdot \left(c \cdot -4\right) + \left(b \cdot b\right))_*}\right)\right)} \cdot \frac{\frac{1}{2}}{a}\]
10. Simplified50.8
  \[\leadsto \left(-\left(b + \sqrt{(a \cdot \left(c \cdot -4\right) + \left(b \cdot b\right))_*}\right)\right) \cdot \color{blue}{\frac{\frac{1}{2}}{a}}\]
11. Taylor expanded around -inf 10.2
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
12. Simplified10.2
  \[\leadsto \color{blue}{-\frac{c}{b}}\]
if -1.2303558036345968e-110 < b < 5.869467752933353e+121
1. Initial program 11.0
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified11.0
  \[\leadsto \color{blue}{\frac{\frac{\left(-b\right) - \sqrt{(\left(a \cdot c\right) \cdot -4 + \left(b \cdot b\right))_*}}{2}}{a}}\]
3. Taylor expanded around 0 11.0
  \[\leadsto \frac{\frac{\left(-b\right) - \sqrt{\color{blue}{{b}^{2} - 4 \cdot \left(a \cdot c\right)}}}{2}}{a}\]
4. Simplified11.0
  \[\leadsto \frac{\frac{\left(-b\right) - \sqrt{\color{blue}{(\left(a \cdot c\right) \cdot -4 + \left(b \cdot b\right))_*}}}{2}}{a}\]
if 5.869467752933353e+121 < b
1. Initial program 51.7
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified51.7
  \[\leadsto \color{blue}{\frac{\frac{\left(-b\right) - \sqrt{(\left(a \cdot c\right) \cdot -4 + \left(b \cdot b\right))_*}}{2}}{a}}\]
3. Taylor expanded around inf 3.4
  \[\leadsto \color{blue}{\frac{c}{b} - \frac{b}{a}}\]
Recombined 3 regimes into one program.
Final simplification9.6
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.2303558036345968 \cdot 10^{-110}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le 5.869467752933353 \cdot 10^{+121}:\\ \;\;\;\;\frac{\frac{\left(-b\right) - \sqrt{(\left(c \cdot a\right) \cdot -4 + \left(b \cdot b\right))_*}}{2}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\]

Error

Target

Derivation

`if b < -1.2303558036345968e-110`

`if -1.2303558036345968e-110 < b < 5.869467752933353e+121`

`if 5.869467752933353e+121 < b`

Reproduce