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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -2.766818940874854722177248139872145176232 \cdot 10^{100}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 7.923524897992036987166355557663274472861 \cdot 10^{-153}:\\ \;\;\;\;\frac{\frac{1}{2 \cdot a}}{\frac{1}{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} \cdot -1\\ \end{array}\]

\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 -2.766818940874854722177248139872145176232 \cdot 10^{100}:\\
\;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\

\mathbf{elif}\;b \le 7.923524897992036987166355557663274472861 \cdot 10^{-153}:\\
\;\;\;\;\frac{\frac{1}{2 \cdot a}}{\frac{1}{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}}\\

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

\end{array}

double f(double a, double b, double c) {
        double r5083925 = b;
        double r5083926 = -r5083925;
        double r5083927 = r5083925 * r5083925;
        double r5083928 = 4.0;
        double r5083929 = a;
        double r5083930 = c;
        double r5083931 = r5083929 * r5083930;
        double r5083932 = r5083928 * r5083931;
        double r5083933 = r5083927 - r5083932;
        double r5083934 = sqrt(r5083933);
        double r5083935 = r5083926 + r5083934;
        double r5083936 = 2.0;
        double r5083937 = r5083936 * r5083929;
        double r5083938 = r5083935 / r5083937;
        return r5083938;
}

↓

double f(double a, double b, double c) {
        double r5083939 = b;
        double r5083940 = -2.7668189408748547e+100;
        bool r5083941 = r5083939 <= r5083940;
        double r5083942 = 1.0;
        double r5083943 = c;
        double r5083944 = r5083943 / r5083939;
        double r5083945 = a;
        double r5083946 = r5083939 / r5083945;
        double r5083947 = r5083944 - r5083946;
        double r5083948 = r5083942 * r5083947;
        double r5083949 = 7.923524897992037e-153;
        bool r5083950 = r5083939 <= r5083949;
        double r5083951 = 1.0;
        double r5083952 = 2.0;
        double r5083953 = r5083952 * r5083945;
        double r5083954 = r5083951 / r5083953;
        double r5083955 = r5083939 * r5083939;
        double r5083956 = 4.0;
        double r5083957 = r5083956 * r5083945;
        double r5083958 = r5083943 * r5083957;
        double r5083959 = r5083955 - r5083958;
        double r5083960 = sqrt(r5083959);
        double r5083961 = r5083960 - r5083939;
        double r5083962 = r5083951 / r5083961;
        double r5083963 = r5083954 / r5083962;
        double r5083964 = -1.0;
        double r5083965 = r5083944 * r5083964;
        double r5083966 = r5083950 ? r5083963 : r5083965;
        double r5083967 = r5083941 ? r5083948 : r5083966;
        return r5083967;
}

Original	34.6
Target	21.1
Herbie	10.7

Derivation

Split input into 3 regimes
if b < -2.7668189408748547e+100
1. Initial program 47.2
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified47.2
  \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - \left(a \cdot 4\right) \cdot c} - b}{2 \cdot a}}\]
3. Taylor expanded around -inf 4.0
  \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
4. Simplified4.0
  \[\leadsto \color{blue}{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 1}\]
if -2.7668189408748547e+100 < b < 7.923524897992037e-153
1. Initial program 10.9
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified10.8
  \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - \left(a \cdot 4\right) \cdot c} - b}{2 \cdot a}}\]
3. Taylor expanded around 0 10.9
  \[\leadsto \frac{\sqrt{\color{blue}{{b}^{2} - 4 \cdot \left(a \cdot c\right)}} - b}{2 \cdot a}\]
4. Simplified10.8
  \[\leadsto \frac{\sqrt{\color{blue}{b \cdot b - c \cdot \left(a \cdot 4\right)}} - b}{2 \cdot a}\]
5. Taylor expanded around 0 10.9
  \[\leadsto \frac{\sqrt{\color{blue}{{b}^{2} - 4 \cdot \left(a \cdot c\right)}} - b}{2 \cdot a}\]
6. Simplified10.8
  \[\leadsto \frac{\sqrt{\color{blue}{b \cdot b - c \cdot \left(4 \cdot a\right)}} - b}{2 \cdot a}\]
7. Using strategy rm
8. Applied clear-num11.0
  \[\leadsto \color{blue}{\frac{1}{\frac{2 \cdot a}{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}}}\]
9. Using strategy rm
10. Applied div-inv11.0
  \[\leadsto \frac{1}{\color{blue}{\left(2 \cdot a\right) \cdot \frac{1}{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}}}\]
11. Applied associate-/r*11.0
  \[\leadsto \color{blue}{\frac{\frac{1}{2 \cdot a}}{\frac{1}{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}}}\]
if 7.923524897992037e-153 < b
1. Initial program 50.5
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified50.5
  \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - \left(a \cdot 4\right) \cdot c} - b}{2 \cdot a}}\]
3. Taylor expanded around inf 12.7
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
Recombined 3 regimes into one program.
Final simplification10.7
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -2.766818940874854722177248139872145176232 \cdot 10^{100}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \mathbf{elif}\;b \le 7.923524897992036987166355557663274472861 \cdot 10^{-153}:\\ \;\;\;\;\frac{\frac{1}{2 \cdot a}}{\frac{1}{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} \cdot -1\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -2.7668189408748547e+100`

`if -2.7668189408748547e+100 < b < 7.923524897992037e-153`

`if 7.923524897992037e-153 < b`

Reproduce

In
Out