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

↓

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

\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{c}{b}\\

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

\mathbf{else}:\\
\;\;\;\;\frac{c}{b} - \frac{b}{a}\\

\end{array}

double f(double a, double b, double c) {
        double r3679201 = b;
        double r3679202 = -r3679201;
        double r3679203 = r3679201 * r3679201;
        double r3679204 = 4.0;
        double r3679205 = a;
        double r3679206 = c;
        double r3679207 = r3679205 * r3679206;
        double r3679208 = r3679204 * r3679207;
        double r3679209 = r3679203 - r3679208;
        double r3679210 = sqrt(r3679209);
        double r3679211 = r3679202 - r3679210;
        double r3679212 = 2.0;
        double r3679213 = r3679212 * r3679205;
        double r3679214 = r3679211 / r3679213;
        return r3679214;
}

↓

double f(double a, double b, double c) {
        double r3679215 = b;
        double r3679216 = -1.6239127264630285e-63;
        bool r3679217 = r3679215 <= r3679216;
        double r3679218 = c;
        double r3679219 = r3679218 / r3679215;
        double r3679220 = -r3679219;
        double r3679221 = 7.052614559736995e+62;
        bool r3679222 = r3679215 <= r3679221;
        double r3679223 = -0.5;
        double r3679224 = a;
        double r3679225 = r3679223 / r3679224;
        double r3679226 = r3679215 * r3679215;
        double r3679227 = 4.0;
        double r3679228 = r3679227 * r3679224;
        double r3679229 = r3679228 * r3679218;
        double r3679230 = r3679226 - r3679229;
        double r3679231 = sqrt(r3679230);
        double r3679232 = r3679225 * r3679231;
        double r3679233 = r3679225 * r3679215;
        double r3679234 = r3679232 + r3679233;
        double r3679235 = r3679215 / r3679224;
        double r3679236 = r3679219 - r3679235;
        double r3679237 = r3679222 ? r3679234 : r3679236;
        double r3679238 = r3679217 ? r3679220 : r3679237;
        return r3679238;
}

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. Taylor expanded around -inf 8.6
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
3. Simplified8.6
  \[\leadsto \color{blue}{-\frac{c}{b}}\]
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. Using strategy rm
3. Applied clear-num14.0
  \[\leadsto \color{blue}{\frac{1}{\frac{2 \cdot a}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}}\]
4. Using strategy rm
5. Applied div-inv14.1
  \[\leadsto \frac{1}{\color{blue}{\left(2 \cdot a\right) \cdot \frac{1}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}}\]
6. Applied add-cube-cbrt14.1
  \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\left(2 \cdot a\right) \cdot \frac{1}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}\]
7. Applied times-frac14.1
  \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{2 \cdot a} \cdot \frac{\sqrt[3]{1}}{\frac{1}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}}\]
8. Simplified14.1
  \[\leadsto \color{blue}{\frac{\frac{1}{2}}{a}} \cdot \frac{\sqrt[3]{1}}{\frac{1}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}\]
9. Simplified14.0
  \[\leadsto \frac{\frac{1}{2}}{a} \cdot \color{blue}{\left(-\left(b + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right)\right)}\]
10. Using strategy rm
11. Applied distribute-neg-in14.0
  \[\leadsto \frac{\frac{1}{2}}{a} \cdot \color{blue}{\left(\left(-b\right) + \left(-\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right)\right)}\]
12. Applied distribute-rgt-in14.1
  \[\leadsto \color{blue}{\left(-b\right) \cdot \frac{\frac{1}{2}}{a} + \left(-\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right) \cdot \frac{\frac{1}{2}}{a}}\]
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. Taylor expanded around inf 4.7
  \[\leadsto \color{blue}{\frac{c}{b} - \frac{b}{a}}\]
Recombined 3 regimes into one program.
Final simplification10.3
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.6239127264630285 \cdot 10^{-63}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le 7.052614559736995 \cdot 10^{+62}:\\ \;\;\;\;\frac{\frac{-1}{2}}{a} \cdot \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} + \frac{\frac{-1}{2}}{a} \cdot b\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -1.6239127264630285e-63`

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

`if 7.052614559736995e+62 < b`

Reproduce

In
Out