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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -9.238052366259206 \cdot 10^{-38}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le 2.7654658503846575 \cdot 10^{+109}:\\ \;\;\;\;\frac{\frac{-1}{2}}{a} \cdot \left(\sqrt{(a \cdot \left(c \cdot -4\right) + \left(b \cdot b\right))_*} + b\right)\\ \mathbf{else}:\\ \;\;\;\;-\frac{b}{a}\\ \end{array}\]

double f(double a, double b, double c) {
        double r10636008 = b;
        double r10636009 = -r10636008;
        double r10636010 = r10636008 * r10636008;
        double r10636011 = 4.0;
        double r10636012 = a;
        double r10636013 = c;
        double r10636014 = r10636012 * r10636013;
        double r10636015 = r10636011 * r10636014;
        double r10636016 = r10636010 - r10636015;
        double r10636017 = sqrt(r10636016);
        double r10636018 = r10636009 - r10636017;
        double r10636019 = 2.0;
        double r10636020 = r10636019 * r10636012;
        double r10636021 = r10636018 / r10636020;
        return r10636021;
}

↓

double f(double a, double b, double c) {
        double r10636022 = b;
        double r10636023 = -9.238052366259206e-38;
        bool r10636024 = r10636022 <= r10636023;
        double r10636025 = c;
        double r10636026 = r10636025 / r10636022;
        double r10636027 = -r10636026;
        double r10636028 = 2.7654658503846575e+109;
        bool r10636029 = r10636022 <= r10636028;
        double r10636030 = -0.5;
        double r10636031 = a;
        double r10636032 = r10636030 / r10636031;
        double r10636033 = -4.0;
        double r10636034 = r10636025 * r10636033;
        double r10636035 = r10636022 * r10636022;
        double r10636036 = fma(r10636031, r10636034, r10636035);
        double r10636037 = sqrt(r10636036);
        double r10636038 = r10636037 + r10636022;
        double r10636039 = r10636032 * r10636038;
        double r10636040 = r10636022 / r10636031;
        double r10636041 = -r10636040;
        double r10636042 = r10636029 ? r10636039 : r10636041;
        double r10636043 = r10636024 ? r10636027 : r10636042;
        return r10636043;
}

\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 -9.238052366259206 \cdot 10^{-38}:\\
\;\;\;\;-\frac{c}{b}\\

\mathbf{elif}\;b \le 2.7654658503846575 \cdot 10^{+109}:\\
\;\;\;\;\frac{\frac{-1}{2}}{a} \cdot \left(\sqrt{(a \cdot \left(c \cdot -4\right) + \left(b \cdot b\right))_*} + b\right)\\

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

\end{array}

Original	33.5
Target	20.8
Herbie	10.3

Derivation

Split input into 3 regimes
if b < -9.238052366259206e-38
1. Initial program 53.5
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified53.5
  \[\leadsto \color{blue}{\frac{\frac{\left(-b\right) - \sqrt{(\left(a \cdot c\right) \cdot -4 + \left(b \cdot b\right))_*}}{2}}{a}}\]
3. Taylor expanded around -inf 7.8
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
4. Simplified7.8
  \[\leadsto \color{blue}{-\frac{c}{b}}\]
if -9.238052366259206e-38 < b < 2.7654658503846575e+109
1. Initial program 14.2
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified14.2
  \[\leadsto \color{blue}{\frac{\frac{\left(-b\right) - \sqrt{(\left(a \cdot c\right) \cdot -4 + \left(b \cdot b\right))_*}}{2}}{a}}\]
3. Using strategy rm
4. Applied *-un-lft-identity14.2
  \[\leadsto \frac{\frac{\left(-b\right) - \sqrt{(\left(a \cdot c\right) \cdot -4 + \left(b \cdot b\right))_*}}{2}}{\color{blue}{1 \cdot a}}\]
5. Applied div-inv14.2
  \[\leadsto \frac{\color{blue}{\left(\left(-b\right) - \sqrt{(\left(a \cdot c\right) \cdot -4 + \left(b \cdot b\right))_*}\right) \cdot \frac{1}{2}}}{1 \cdot a}\]
6. Applied times-frac14.3
  \[\leadsto \color{blue}{\frac{\left(-b\right) - \sqrt{(\left(a \cdot c\right) \cdot -4 + \left(b \cdot b\right))_*}}{1} \cdot \frac{\frac{1}{2}}{a}}\]
7. Simplified14.4
  \[\leadsto \color{blue}{\left(-\left(b + \sqrt{(a \cdot \left(c \cdot -4\right) + \left(b \cdot b\right))_*}\right)\right)} \cdot \frac{\frac{1}{2}}{a}\]
8. Simplified14.4
  \[\leadsto \left(-\left(b + \sqrt{(a \cdot \left(c \cdot -4\right) + \left(b \cdot b\right))_*}\right)\right) \cdot \color{blue}{\frac{\frac{1}{2}}{a}}\]
if 2.7654658503846575e+109 < b
1. Initial program 47.4
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified47.4
  \[\leadsto \color{blue}{\frac{\frac{\left(-b\right) - \sqrt{(\left(a \cdot c\right) \cdot -4 + \left(b \cdot b\right))_*}}{2}}{a}}\]
3. Using strategy rm
4. Applied clear-num47.5
  \[\leadsto \color{blue}{\frac{1}{\frac{a}{\frac{\left(-b\right) - \sqrt{(\left(a \cdot c\right) \cdot -4 + \left(b \cdot b\right))_*}}{2}}}}\]
5. Taylor expanded around 0 3.4
  \[\leadsto \color{blue}{-1 \cdot \frac{b}{a}}\]
6. Simplified3.4
  \[\leadsto \color{blue}{-\frac{b}{a}}\]
Recombined 3 regimes into one program.
Final simplification10.3
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -9.238052366259206 \cdot 10^{-38}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le 2.7654658503846575 \cdot 10^{+109}:\\ \;\;\;\;\frac{\frac{-1}{2}}{a} \cdot \left(\sqrt{(a \cdot \left(c \cdot -4\right) + \left(b \cdot b\right))_*} + b\right)\\ \mathbf{else}:\\ \;\;\;\;-\frac{b}{a}\\ \end{array}\]

Error

Target

Derivation

`if b < -9.238052366259206e-38`

`if -9.238052366259206e-38 < b < 2.7654658503846575e+109`

`if 2.7654658503846575e+109 < b`

Reproduce