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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -2.025649824816678368861606895534923213042 \cdot 10^{153}:\\ \;\;\;\;\left(1 \cdot \frac{c}{b} - \frac{b}{a} \cdot 0.5\right) - \frac{\frac{b}{2}}{a}\\ \mathbf{elif}\;b \le 3.047677256636077515553757160900796353717 \cdot 10^{-81}:\\ \;\;\;\;\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{2}}{a} - \frac{\frac{b}{2}}{a}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;b \le -2.025649824816678368861606895534923213042 \cdot 10^{153}:\\
\;\;\;\;\left(1 \cdot \frac{c}{b} - \frac{b}{a} \cdot 0.5\right) - \frac{\frac{b}{2}}{a}\\

\mathbf{elif}\;b \le 3.047677256636077515553757160900796353717 \cdot 10^{-81}:\\
\;\;\;\;\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{2}}{a} - \frac{\frac{b}{2}}{a}\\

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

\end{array}

double f(double a, double b, double c) {
        double r4774260 = b;
        double r4774261 = -r4774260;
        double r4774262 = r4774260 * r4774260;
        double r4774263 = 4.0;
        double r4774264 = a;
        double r4774265 = r4774263 * r4774264;
        double r4774266 = c;
        double r4774267 = r4774265 * r4774266;
        double r4774268 = r4774262 - r4774267;
        double r4774269 = sqrt(r4774268);
        double r4774270 = r4774261 + r4774269;
        double r4774271 = 2.0;
        double r4774272 = r4774271 * r4774264;
        double r4774273 = r4774270 / r4774272;
        return r4774273;
}

↓

double f(double a, double b, double c) {
        double r4774274 = b;
        double r4774275 = -2.0256498248166784e+153;
        bool r4774276 = r4774274 <= r4774275;
        double r4774277 = 1.0;
        double r4774278 = c;
        double r4774279 = r4774278 / r4774274;
        double r4774280 = r4774277 * r4774279;
        double r4774281 = a;
        double r4774282 = r4774274 / r4774281;
        double r4774283 = 0.5;
        double r4774284 = r4774282 * r4774283;
        double r4774285 = r4774280 - r4774284;
        double r4774286 = 2.0;
        double r4774287 = r4774274 / r4774286;
        double r4774288 = r4774287 / r4774281;
        double r4774289 = r4774285 - r4774288;
        double r4774290 = 3.0476772566360775e-81;
        bool r4774291 = r4774274 <= r4774290;
        double r4774292 = r4774274 * r4774274;
        double r4774293 = r4774278 * r4774281;
        double r4774294 = 4.0;
        double r4774295 = r4774293 * r4774294;
        double r4774296 = r4774292 - r4774295;
        double r4774297 = sqrt(r4774296);
        double r4774298 = r4774297 / r4774286;
        double r4774299 = r4774298 / r4774281;
        double r4774300 = r4774299 - r4774288;
        double r4774301 = -1.0;
        double r4774302 = r4774301 * r4774279;
        double r4774303 = r4774291 ? r4774300 : r4774302;
        double r4774304 = r4774276 ? r4774289 : r4774303;
        return r4774304;
}

Original	33.8
Target	20.6
Herbie	10.3

Derivation

Split input into 3 regimes
if b < -2.0256498248166784e+153
1. Initial program 63.6
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified63.6
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied div-sub63.6
  \[\leadsto \frac{\color{blue}{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{2} - \frac{b}{2}}}{a}\]
5. Applied div-sub63.6
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{2}}{a} - \frac{\frac{b}{2}}{a}}\]
6. Taylor expanded around -inf 2.0
  \[\leadsto \color{blue}{\left(1 \cdot \frac{c}{b} - 0.5 \cdot \frac{b}{a}\right)} - \frac{\frac{b}{2}}{a}\]
if -2.0256498248166784e+153 < b < 3.0476772566360775e-81
1. Initial program 11.9
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified11.9
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied div-sub11.9
  \[\leadsto \frac{\color{blue}{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{2} - \frac{b}{2}}}{a}\]
5. Applied div-sub11.9
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{2}}{a} - \frac{\frac{b}{2}}{a}}\]
if 3.0476772566360775e-81 < b
1. Initial program 52.2
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified52.2
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{2}}{a}}\]
3. Taylor expanded around inf 10.5
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
Recombined 3 regimes into one program.
Final simplification10.3
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -2.025649824816678368861606895534923213042 \cdot 10^{153}:\\ \;\;\;\;\left(1 \cdot \frac{c}{b} - \frac{b}{a} \cdot 0.5\right) - \frac{\frac{b}{2}}{a}\\ \mathbf{elif}\;b \le 3.047677256636077515553757160900796353717 \cdot 10^{-81}:\\ \;\;\;\;\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{2}}{a} - \frac{\frac{b}{2}}{a}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -2.0256498248166784e+153`

`if -2.0256498248166784e+153 < b < 3.0476772566360775e-81`

`if 3.0476772566360775e-81 < b`

Reproduce

In
Out