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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -7.93152454634661985 \cdot 10^{153}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 2.0569776426586135 \cdot 10^{-106}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{\frac{a}{\frac{1}{2}}}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

\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 -7.93152454634661985 \cdot 10^{153}:\\
\;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\

\mathbf{elif}\;b \le 2.0569776426586135 \cdot 10^{-106}:\\
\;\;\;\;\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{\frac{a}{\frac{1}{2}}}\\

\mathbf{else}:\\
\;\;\;\;-1 \cdot \frac{c}{b}\\

\end{array}

double f(double a, double b, double c) {
        double r77058 = b;
        double r77059 = -r77058;
        double r77060 = r77058 * r77058;
        double r77061 = 4.0;
        double r77062 = a;
        double r77063 = c;
        double r77064 = r77062 * r77063;
        double r77065 = r77061 * r77064;
        double r77066 = r77060 - r77065;
        double r77067 = sqrt(r77066);
        double r77068 = r77059 + r77067;
        double r77069 = 2.0;
        double r77070 = r77069 * r77062;
        double r77071 = r77068 / r77070;
        return r77071;
}

↓

double f(double a, double b, double c) {
        double r77072 = b;
        double r77073 = -7.93152454634662e+153;
        bool r77074 = r77072 <= r77073;
        double r77075 = 1.0;
        double r77076 = c;
        double r77077 = r77076 / r77072;
        double r77078 = a;
        double r77079 = r77072 / r77078;
        double r77080 = r77077 - r77079;
        double r77081 = r77075 * r77080;
        double r77082 = 2.0569776426586135e-106;
        bool r77083 = r77072 <= r77082;
        double r77084 = r77072 * r77072;
        double r77085 = 4.0;
        double r77086 = r77078 * r77076;
        double r77087 = r77085 * r77086;
        double r77088 = r77084 - r77087;
        double r77089 = sqrt(r77088);
        double r77090 = r77089 - r77072;
        double r77091 = 1.0;
        double r77092 = 2.0;
        double r77093 = r77091 / r77092;
        double r77094 = r77078 / r77093;
        double r77095 = r77090 / r77094;
        double r77096 = -1.0;
        double r77097 = r77096 * r77077;
        double r77098 = r77083 ? r77095 : r77097;
        double r77099 = r77074 ? r77081 : r77098;
        return r77099;
}

Original	33.8
Target	21.2
Herbie	9.8

Derivation

Split input into 3 regimes
if b < -7.93152454634662e+153
1. Initial program 63.8
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified63.8
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}}{a}}\]
3. Taylor expanded around -inf 1.9
  \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
4. Simplified1.9
  \[\leadsto \color{blue}{1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}\]
if -7.93152454634662e+153 < b < 2.0569776426586135e-106
1. Initial program 11.2
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified11.2
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied *-un-lft-identity11.2
  \[\leadsto \frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{\color{blue}{1 \cdot 2}}}{a}\]
5. Applied *-un-lft-identity11.2
  \[\leadsto \frac{\frac{\color{blue}{1 \cdot \left(\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b\right)}}{1 \cdot 2}}{a}\]
6. Applied times-frac11.2
  \[\leadsto \frac{\color{blue}{\frac{1}{1} \cdot \frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}}}{a}\]
7. Applied associate-/l*11.3
  \[\leadsto \color{blue}{\frac{\frac{1}{1}}{\frac{a}{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}}}}\]
8. Using strategy rm
9. Applied div-inv11.3
  \[\leadsto \frac{\frac{1}{1}}{\frac{a}{\color{blue}{\left(\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b\right) \cdot \frac{1}{2}}}}\]
10. Applied *-un-lft-identity11.3
  \[\leadsto \frac{\frac{1}{1}}{\frac{\color{blue}{1 \cdot a}}{\left(\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b\right) \cdot \frac{1}{2}}}\]
11. Applied times-frac11.4
  \[\leadsto \frac{\frac{1}{1}}{\color{blue}{\frac{1}{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b} \cdot \frac{a}{\frac{1}{2}}}}\]
12. Applied associate-/r*11.3
  \[\leadsto \color{blue}{\frac{\frac{\frac{1}{1}}{\frac{1}{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}}}{\frac{a}{\frac{1}{2}}}}\]
13. Simplified11.2
  \[\leadsto \frac{\color{blue}{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}}{\frac{a}{\frac{1}{2}}}\]
if 2.0569776426586135e-106 < b
1. Initial program 52.0
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified52.0
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{2}}{a}}\]
3. Taylor expanded around inf 10.3
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
Recombined 3 regimes into one program.
Final simplification9.8
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -7.93152454634661985 \cdot 10^{153}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 2.0569776426586135 \cdot 10^{-106}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{\frac{a}{\frac{1}{2}}}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

Falling back on racket egraph because egg-herbie package not installed (more)

Error

Try it out

Target

Derivation

`if b < -7.93152454634662e+153`

`if -7.93152454634662e+153 < b < 2.0569776426586135e-106`

`if 2.0569776426586135e-106 < b`

Reproduce

In
Out