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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -4.829903230896134050158793286773621805382 \cdot 10^{148}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 1.058331905530479345989188577279018272684 \cdot 10^{-144}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\ \mathbf{elif}\;b \le 400482480739649191422756162656796672:\\ \;\;\;\;\frac{\frac{0 + 4 \cdot \left(a \cdot c\right)}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

\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 -4.829903230896134050158793286773621805382 \cdot 10^{148}:\\
\;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\

\mathbf{elif}\;b \le 1.058331905530479345989188577279018272684 \cdot 10^{-144}:\\
\;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\

\mathbf{elif}\;b \le 400482480739649191422756162656796672:\\
\;\;\;\;\frac{\frac{0 + 4 \cdot \left(a \cdot c\right)}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\\

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

\end{array}

double f(double a, double b, double c) {
        double r54935 = b;
        double r54936 = -r54935;
        double r54937 = r54935 * r54935;
        double r54938 = 4.0;
        double r54939 = a;
        double r54940 = c;
        double r54941 = r54939 * r54940;
        double r54942 = r54938 * r54941;
        double r54943 = r54937 - r54942;
        double r54944 = sqrt(r54943);
        double r54945 = r54936 + r54944;
        double r54946 = 2.0;
        double r54947 = r54946 * r54939;
        double r54948 = r54945 / r54947;
        return r54948;
}

↓

double f(double a, double b, double c) {
        double r54949 = b;
        double r54950 = -4.829903230896134e+148;
        bool r54951 = r54949 <= r54950;
        double r54952 = 1.0;
        double r54953 = c;
        double r54954 = r54953 / r54949;
        double r54955 = a;
        double r54956 = r54949 / r54955;
        double r54957 = r54954 - r54956;
        double r54958 = r54952 * r54957;
        double r54959 = 1.0583319055304793e-144;
        bool r54960 = r54949 <= r54959;
        double r54961 = -r54949;
        double r54962 = r54949 * r54949;
        double r54963 = 4.0;
        double r54964 = r54955 * r54953;
        double r54965 = r54963 * r54964;
        double r54966 = r54962 - r54965;
        double r54967 = sqrt(r54966);
        double r54968 = r54961 + r54967;
        double r54969 = 2.0;
        double r54970 = r54969 * r54955;
        double r54971 = r54968 / r54970;
        double r54972 = 4.004824807396492e+35;
        bool r54973 = r54949 <= r54972;
        double r54974 = 0.0;
        double r54975 = r54974 + r54965;
        double r54976 = r54961 - r54967;
        double r54977 = r54975 / r54976;
        double r54978 = r54977 / r54970;
        double r54979 = -1.0;
        double r54980 = r54979 * r54954;
        double r54981 = r54973 ? r54978 : r54980;
        double r54982 = r54960 ? r54971 : r54981;
        double r54983 = r54951 ? r54958 : r54982;
        return r54983;
}

Original	34.2
Target	20.9
Herbie	8.9

Derivation

Split input into 4 regimes
if b < -4.829903230896134e+148
1. Initial program 61.7
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Taylor expanded around -inf 2.8
  \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
3. Simplified2.8
  \[\leadsto \color{blue}{1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}\]
if -4.829903230896134e+148 < b < 1.0583319055304793e-144
1. Initial program 11.1
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
if 1.0583319055304793e-144 < b < 4.004824807396492e+35
1. Initial program 35.7
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Using strategy rm
3. Applied flip-+35.7
  \[\leadsto \frac{\color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} \cdot \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a}\]
4. Simplified16.7
  \[\leadsto \frac{\frac{\color{blue}{0 + 4 \cdot \left(a \cdot c\right)}}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\]
if 4.004824807396492e+35 < b
1. Initial program 56.6
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Taylor expanded around inf 4.3
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
Recombined 4 regimes into one program.
Final simplification8.9
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -4.829903230896134050158793286773621805382 \cdot 10^{148}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 1.058331905530479345989188577279018272684 \cdot 10^{-144}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\ \mathbf{elif}\;b \le 400482480739649191422756162656796672:\\ \;\;\;\;\frac{\frac{0 + 4 \cdot \left(a \cdot c\right)}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -4.829903230896134e+148`

`if -4.829903230896134e+148 < b < 1.0583319055304793e-144`

`if 1.0583319055304793e-144 < b < 4.004824807396492e+35`

`if 4.004824807396492e+35 < b`

Reproduce

In
Out