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

↓

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

\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(-\sqrt{\mathsf{fma}\left(c, a \cdot -4, b \cdot b\right)}\right) - b\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 r2789014 = b;
        double r2789015 = -r2789014;
        double r2789016 = r2789014 * r2789014;
        double r2789017 = 4.0;
        double r2789018 = a;
        double r2789019 = c;
        double r2789020 = r2789018 * r2789019;
        double r2789021 = r2789017 * r2789020;
        double r2789022 = r2789016 - r2789021;
        double r2789023 = sqrt(r2789022);
        double r2789024 = r2789015 - r2789023;
        double r2789025 = 2.0;
        double r2789026 = r2789025 * r2789018;
        double r2789027 = r2789024 / r2789026;
        return r2789027;
}

↓

double f(double a, double b, double c) {
        double r2789028 = b;
        double r2789029 = -1.6239127264630285e-63;
        bool r2789030 = r2789028 <= r2789029;
        double r2789031 = -2.0;
        double r2789032 = c;
        double r2789033 = r2789032 / r2789028;
        double r2789034 = r2789031 * r2789033;
        double r2789035 = 2.0;
        double r2789036 = r2789034 / r2789035;
        double r2789037 = 7.052614559736995e+62;
        bool r2789038 = r2789028 <= r2789037;
        double r2789039 = 1.0;
        double r2789040 = a;
        double r2789041 = r2789039 / r2789040;
        double r2789042 = -4.0;
        double r2789043 = r2789040 * r2789042;
        double r2789044 = r2789028 * r2789028;
        double r2789045 = fma(r2789032, r2789043, r2789044);
        double r2789046 = sqrt(r2789045);
        double r2789047 = -r2789046;
        double r2789048 = r2789047 - r2789028;
        double r2789049 = r2789041 * r2789048;
        double r2789050 = r2789049 / r2789035;
        double r2789051 = r2789028 / r2789040;
        double r2789052 = r2789033 - r2789051;
        double r2789053 = r2789052 * r2789035;
        double r2789054 = r2789053 / r2789035;
        double r2789055 = r2789038 ? r2789050 : r2789054;
        double r2789056 = r2789030 ? r2789036 : r2789055;
        return r2789056;
}

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 add-cube-cbrt14.1
  \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{a \cdot \frac{1}{\left(-b\right) - \sqrt{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}}}}{2}\]
9. Applied times-frac14.1
  \[\leadsto \frac{\color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{a} \cdot \frac{\sqrt[3]{1}}{\frac{1}{\left(-b\right) - \sqrt{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}}}}}{2}\]
10. Simplified14.1
  \[\leadsto \frac{\color{blue}{\frac{1}{a}} \cdot \frac{\sqrt[3]{1}}{\frac{1}{\left(-b\right) - \sqrt{\mathsf{fma}\left(-4 \cdot a, c, b \cdot b\right)}}}}{2}\]
11. Simplified14.1
  \[\leadsto \frac{\frac{1}{a} \cdot \color{blue}{\left(\left(-\sqrt{\mathsf{fma}\left(c, -4 \cdot a, b \cdot b\right)}\right) - b\right)}}{2}\]
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
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.6239127264630285 \cdot 10^{-63}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \mathbf{elif}\;b \le 7.052614559736995 \cdot 10^{+62}:\\ \;\;\;\;\frac{\frac{1}{a} \cdot \left(\left(-\sqrt{\mathsf{fma}\left(c, a \cdot -4, b \cdot b\right)}\right) - b\right)}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\ \end{array}\]

Error

Target

Derivation

`if b < -1.6239127264630285e-63`

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

`if 7.052614559736995e+62 < b`

Reproduce