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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.390658213785421360285622940547871300736 \cdot 10^{101}:\\ \;\;\;\;\frac{\left(\frac{c}{\frac{b}{a}} - b\right) \cdot 1}{a}\\ \mathbf{elif}\;b \le 4.330541687749954965862284767620099540245 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{1}{\frac{2}{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{1}{b} - \frac{1 \cdot b}{c \cdot a}}}{a}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;b \le -1.390658213785421360285622940547871300736 \cdot 10^{101}:\\
\;\;\;\;\frac{\left(\frac{c}{\frac{b}{a}} - b\right) \cdot 1}{a}\\

\mathbf{elif}\;b \le 4.330541687749954965862284767620099540245 \cdot 10^{-17}:\\
\;\;\;\;\frac{\frac{1}{\frac{2}{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}}}{a}\\

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

\end{array}

double f(double a, double b, double c) {
        double r4190042 = b;
        double r4190043 = -r4190042;
        double r4190044 = r4190042 * r4190042;
        double r4190045 = 4.0;
        double r4190046 = a;
        double r4190047 = r4190045 * r4190046;
        double r4190048 = c;
        double r4190049 = r4190047 * r4190048;
        double r4190050 = r4190044 - r4190049;
        double r4190051 = sqrt(r4190050);
        double r4190052 = r4190043 + r4190051;
        double r4190053 = 2.0;
        double r4190054 = r4190053 * r4190046;
        double r4190055 = r4190052 / r4190054;
        return r4190055;
}

↓

double f(double a, double b, double c) {
        double r4190056 = b;
        double r4190057 = -1.3906582137854214e+101;
        bool r4190058 = r4190056 <= r4190057;
        double r4190059 = c;
        double r4190060 = a;
        double r4190061 = r4190056 / r4190060;
        double r4190062 = r4190059 / r4190061;
        double r4190063 = r4190062 - r4190056;
        double r4190064 = 1.0;
        double r4190065 = r4190063 * r4190064;
        double r4190066 = r4190065 / r4190060;
        double r4190067 = 4.330541687749955e-17;
        bool r4190068 = r4190056 <= r4190067;
        double r4190069 = 1.0;
        double r4190070 = 2.0;
        double r4190071 = r4190056 * r4190056;
        double r4190072 = r4190059 * r4190060;
        double r4190073 = 4.0;
        double r4190074 = r4190072 * r4190073;
        double r4190075 = r4190071 - r4190074;
        double r4190076 = sqrt(r4190075);
        double r4190077 = r4190076 - r4190056;
        double r4190078 = r4190070 / r4190077;
        double r4190079 = r4190069 / r4190078;
        double r4190080 = r4190079 / r4190060;
        double r4190081 = r4190064 / r4190056;
        double r4190082 = r4190064 * r4190056;
        double r4190083 = r4190082 / r4190072;
        double r4190084 = r4190081 - r4190083;
        double r4190085 = r4190069 / r4190084;
        double r4190086 = r4190085 / r4190060;
        double r4190087 = r4190068 ? r4190080 : r4190086;
        double r4190088 = r4190058 ? r4190066 : r4190087;
        return r4190088;
}

Original	34.4
Target	21.3
Herbie	14.1

Derivation

Split input into 3 regimes
if b < -1.3906582137854214e+101
1. Initial program 48.2
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified48.2
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{2}}{a}}\]
3. Taylor expanded around -inf 10.3
  \[\leadsto \frac{\color{blue}{1 \cdot \frac{a \cdot c}{b} - 1 \cdot b}}{a}\]
4. Simplified3.5
  \[\leadsto \frac{\color{blue}{1 \cdot \left(\frac{c}{\frac{b}{a}} - b\right)}}{a}\]
if -1.3906582137854214e+101 < b < 4.330541687749955e-17
1. Initial program 15.2
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified15.2
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied clear-num15.3
  \[\leadsto \frac{\color{blue}{\frac{1}{\frac{2}{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}}}}{a}\]
if 4.330541687749955e-17 < b
1. Initial program 55.6
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified55.6
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied clear-num55.6
  \[\leadsto \frac{\color{blue}{\frac{1}{\frac{2}{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}}}}{a}\]
5. Taylor expanded around inf 17.3
  \[\leadsto \frac{\frac{1}{\color{blue}{1 \cdot \frac{1}{b} - 1 \cdot \frac{b}{a \cdot c}}}}{a}\]
6. Simplified17.3
  \[\leadsto \frac{\frac{1}{\color{blue}{\frac{1}{b} - \frac{b \cdot 1}{c \cdot a}}}}{a}\]
Recombined 3 regimes into one program.
Final simplification14.1
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.390658213785421360285622940547871300736 \cdot 10^{101}:\\ \;\;\;\;\frac{\left(\frac{c}{\frac{b}{a}} - b\right) \cdot 1}{a}\\ \mathbf{elif}\;b \le 4.330541687749954965862284767620099540245 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{1}{\frac{2}{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{1}{b} - \frac{1 \cdot b}{c \cdot a}}}{a}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -1.3906582137854214e+101`

`if -1.3906582137854214e+101 < b < 4.330541687749955e-17`

`if 4.330541687749955e-17 < b`

Reproduce

In
Out