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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.2890050783826923 \cdot 10^{-183}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \mathbf{elif}\;b \le 2.88466596167667 \cdot 10^{+141}:\\ \;\;\;\;\frac{\frac{\left(-b\right) - \sqrt{\left(a \cdot -4\right) \cdot c + b \cdot b}}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{a} \cdot \left(\left(c \cdot \frac{a}{b} - b\right) \cdot 2\right)}{2}\\ \end{array}\]

\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 -1.2890050783826923 \cdot 10^{-183}:\\
\;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\

\mathbf{elif}\;b \le 2.88466596167667 \cdot 10^{+141}:\\
\;\;\;\;\frac{\frac{\left(-b\right) - \sqrt{\left(a \cdot -4\right) \cdot c + b \cdot b}}{a}}{2}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{1}{a} \cdot \left(\left(c \cdot \frac{a}{b} - b\right) \cdot 2\right)}{2}\\

\end{array}

double f(double a, double b, double c) {
        double r2225914 = b;
        double r2225915 = -r2225914;
        double r2225916 = r2225914 * r2225914;
        double r2225917 = 4.0;
        double r2225918 = a;
        double r2225919 = c;
        double r2225920 = r2225918 * r2225919;
        double r2225921 = r2225917 * r2225920;
        double r2225922 = r2225916 - r2225921;
        double r2225923 = sqrt(r2225922);
        double r2225924 = r2225915 - r2225923;
        double r2225925 = 2.0;
        double r2225926 = r2225925 * r2225918;
        double r2225927 = r2225924 / r2225926;
        return r2225927;
}

↓

double f(double a, double b, double c) {
        double r2225928 = b;
        double r2225929 = -1.2890050783826923e-183;
        bool r2225930 = r2225928 <= r2225929;
        double r2225931 = -2.0;
        double r2225932 = c;
        double r2225933 = r2225932 / r2225928;
        double r2225934 = r2225931 * r2225933;
        double r2225935 = 2.0;
        double r2225936 = r2225934 / r2225935;
        double r2225937 = 2.88466596167667e+141;
        bool r2225938 = r2225928 <= r2225937;
        double r2225939 = -r2225928;
        double r2225940 = a;
        double r2225941 = -4.0;
        double r2225942 = r2225940 * r2225941;
        double r2225943 = r2225942 * r2225932;
        double r2225944 = r2225928 * r2225928;
        double r2225945 = r2225943 + r2225944;
        double r2225946 = sqrt(r2225945);
        double r2225947 = r2225939 - r2225946;
        double r2225948 = r2225947 / r2225940;
        double r2225949 = r2225948 / r2225935;
        double r2225950 = 1.0;
        double r2225951 = r2225950 / r2225940;
        double r2225952 = r2225940 / r2225928;
        double r2225953 = r2225932 * r2225952;
        double r2225954 = r2225953 - r2225928;
        double r2225955 = r2225954 * r2225935;
        double r2225956 = r2225951 * r2225955;
        double r2225957 = r2225956 / r2225935;
        double r2225958 = r2225938 ? r2225949 : r2225957;
        double r2225959 = r2225930 ? r2225936 : r2225958;
        return r2225959;
}

Original	33.6
Target	20.5
Herbie	11.2

Derivation

Split input into 3 regimes
if b < -1.2890050783826923e-183
1. Initial program 48.2
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified48.2
  \[\leadsto \color{blue}{\frac{\frac{\left(-b\right) - \sqrt{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}}{a}}{2}}\]
3. Taylor expanded around -inf 14.3
  \[\leadsto \frac{\color{blue}{-2 \cdot \frac{c}{b}}}{2}\]
if -1.2890050783826923e-183 < b < 2.88466596167667e+141
1. Initial program 10.0
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified10.0
  \[\leadsto \color{blue}{\frac{\frac{\left(-b\right) - \sqrt{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}}{a}}{2}}\]
3. Using strategy rm
4. Applied fma-udef10.0
  \[\leadsto \frac{\frac{\left(-b\right) - \sqrt{\color{blue}{\left(-4 \cdot a\right) \cdot c + b \cdot b}}}{a}}{2}\]
if 2.88466596167667e+141 < b
1. Initial program 56.5
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified56.5
  \[\leadsto \color{blue}{\frac{\frac{\left(-b\right) - \sqrt{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}}{a}}{2}}\]
3. Using strategy rm
4. Applied div-inv56.5
  \[\leadsto \frac{\color{blue}{\left(\left(-b\right) - \sqrt{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}\right) \cdot \frac{1}{a}}}{2}\]
5. Using strategy rm
6. Applied add-cube-cbrt56.5
  \[\leadsto \frac{\left(\left(-b\right) - \sqrt{\color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)} \cdot \sqrt[3]{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}}}\right) \cdot \frac{1}{a}}{2}\]
7. Applied sqrt-prod56.5
  \[\leadsto \frac{\left(\left(-b\right) - \color{blue}{\sqrt{\sqrt[3]{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)} \cdot \sqrt[3]{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}} \cdot \sqrt{\sqrt[3]{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}}}\right) \cdot \frac{1}{a}}{2}\]
8. Taylor expanded around inf 10.1
  \[\leadsto \frac{\color{blue}{\left(2 \cdot \frac{a \cdot c}{b} - 2 \cdot b\right)} \cdot \frac{1}{a}}{2}\]
9. Simplified2.6
  \[\leadsto \frac{\color{blue}{\left(\left(\frac{a}{b} \cdot c - b\right) \cdot 2\right)} \cdot \frac{1}{a}}{2}\]
Recombined 3 regimes into one program.
Final simplification11.2
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.2890050783826923 \cdot 10^{-183}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \mathbf{elif}\;b \le 2.88466596167667 \cdot 10^{+141}:\\ \;\;\;\;\frac{\frac{\left(-b\right) - \sqrt{\left(a \cdot -4\right) \cdot c + b \cdot b}}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{a} \cdot \left(\left(c \cdot \frac{a}{b} - b\right) \cdot 2\right)}{2}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -1.2890050783826923e-183`

`if -1.2890050783826923e-183 < b < 2.88466596167667e+141`

`if 2.88466596167667e+141 < b`

Reproduce

In
Out