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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.6239127264630285 \cdot 10^{-63}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \mathbf{elif}\;b \le 7.052614559736995 \cdot 10^{+62}:\\ \;\;\;\;\frac{\frac{1}{a} \cdot \left(\left(-b\right) - \sqrt{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}\right)}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\ \end{array}\]

\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 -1.6239127264630285 \cdot 10^{-63}:\\
\;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\

\mathbf{elif}\;b \le 7.052614559736995 \cdot 10^{+62}:\\
\;\;\;\;\frac{\frac{1}{a} \cdot \left(\left(-b\right) - \sqrt{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}\right)}{2}\\

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

\end{array}

double f(double a, double b, double c) {
        double r3101768 = b;
        double r3101769 = -r3101768;
        double r3101770 = r3101768 * r3101768;
        double r3101771 = 4.0;
        double r3101772 = a;
        double r3101773 = c;
        double r3101774 = r3101772 * r3101773;
        double r3101775 = r3101771 * r3101774;
        double r3101776 = r3101770 - r3101775;
        double r3101777 = sqrt(r3101776);
        double r3101778 = r3101769 - r3101777;
        double r3101779 = 2.0;
        double r3101780 = r3101779 * r3101772;
        double r3101781 = r3101778 / r3101780;
        return r3101781;
}

↓

double f(double a, double b, double c) {
        double r3101782 = b;
        double r3101783 = -1.6239127264630285e-63;
        bool r3101784 = r3101782 <= r3101783;
        double r3101785 = -2.0;
        double r3101786 = c;
        double r3101787 = r3101786 / r3101782;
        double r3101788 = r3101785 * r3101787;
        double r3101789 = 2.0;
        double r3101790 = r3101788 / r3101789;
        double r3101791 = 7.052614559736995e+62;
        bool r3101792 = r3101782 <= r3101791;
        double r3101793 = 1.0;
        double r3101794 = a;
        double r3101795 = r3101793 / r3101794;
        double r3101796 = -r3101782;
        double r3101797 = -4.0;
        double r3101798 = r3101797 * r3101794;
        double r3101799 = r3101782 * r3101782;
        double r3101800 = fma(r3101798, r3101786, r3101799);
        double r3101801 = sqrt(r3101800);
        double r3101802 = r3101796 - r3101801;
        double r3101803 = r3101795 * r3101802;
        double r3101804 = r3101803 / r3101789;
        double r3101805 = r3101782 / r3101794;
        double r3101806 = r3101787 - r3101805;
        double r3101807 = r3101806 * r3101789;
        double r3101808 = r3101807 / r3101789;
        double r3101809 = r3101792 ? r3101804 : r3101808;
        double r3101810 = r3101784 ? r3101790 : r3101809;
        return r3101810;
}

Original	32.8
Target	20.1
Herbie	10.3

Derivation

Split input into 3 regimes
if b < -1.6239127264630285e-63
1. Initial program 52.2
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified52.3
  \[\leadsto \color{blue}{\frac{\frac{\left(-b\right) - \sqrt{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}}{a}}{2}}\]
3. Taylor expanded around -inf 8.6
  \[\leadsto \frac{\color{blue}{-2 \cdot \frac{c}{b}}}{2}\]
if -1.6239127264630285e-63 < b < 7.052614559736995e+62
1. Initial program 13.9
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified14.0
  \[\leadsto \color{blue}{\frac{\frac{\left(-b\right) - \sqrt{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}}{a}}{2}}\]
3. Using strategy rm
4. Applied clear-num14.1
  \[\leadsto \frac{\color{blue}{\frac{1}{\frac{a}{\left(-b\right) - \sqrt{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}}}}}{2}\]
5. Using strategy rm
6. Applied div-inv14.1
  \[\leadsto \frac{\frac{1}{\color{blue}{a \cdot \frac{1}{\left(-b\right) - \sqrt{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}}}}}{2}\]
7. Using strategy rm
8. Applied un-div-inv14.1
  \[\leadsto \frac{\frac{1}{\color{blue}{\frac{a}{\left(-b\right) - \sqrt{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}}}}}{2}\]
9. Applied associate-/r/14.1
  \[\leadsto \frac{\color{blue}{\frac{1}{a} \cdot \left(\left(-b\right) - \sqrt{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}\right)}}{2}\]
if 7.052614559736995e+62 < b
1. Initial program 38.1
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified38.0
  \[\leadsto \color{blue}{\frac{\frac{\left(-b\right) - \sqrt{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}}{a}}{2}}\]
3. Taylor expanded around inf 4.7
  \[\leadsto \frac{\color{blue}{2 \cdot \frac{c}{b} - 2 \cdot \frac{b}{a}}}{2}\]
4. Simplified4.7
  \[\leadsto \frac{\color{blue}{2 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}}{2}\]
Recombined 3 regimes into one program.
Final simplification10.3
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.6239127264630285 \cdot 10^{-63}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \mathbf{elif}\;b \le 7.052614559736995 \cdot 10^{+62}:\\ \;\;\;\;\frac{\frac{1}{a} \cdot \left(\left(-b\right) - \sqrt{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}\right)}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\ \end{array}\]

Error

Target

Derivation

`if b < -1.6239127264630285e-63`

`if -1.6239127264630285e-63 < b < 7.052614559736995e+62`

`if 7.052614559736995e+62 < b`

Reproduce