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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -7.668263498157483707441263748528829871939 \cdot 10^{-23}:\\ \;\;\;\;\frac{-1}{1 \cdot \left(\frac{b}{c} - \frac{a}{b}\right)}\\ \mathbf{elif}\;b \le 2.938039658404582626293093928685157937414 \cdot 10^{94}:\\ \;\;\;\;\frac{-1}{\frac{2}{b + \sqrt{\mathsf{fma}\left(c, \left(-a\right) \cdot 4, b \cdot b\right)}} \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\left(-1\right) \cdot \left(\frac{b}{a} - \frac{c}{b}\right)\\ \end{array}\]

\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 -7.668263498157483707441263748528829871939 \cdot 10^{-23}:\\
\;\;\;\;\frac{-1}{1 \cdot \left(\frac{b}{c} - \frac{a}{b}\right)}\\

\mathbf{elif}\;b \le 2.938039658404582626293093928685157937414 \cdot 10^{94}:\\
\;\;\;\;\frac{-1}{\frac{2}{b + \sqrt{\mathsf{fma}\left(c, \left(-a\right) \cdot 4, b \cdot b\right)}} \cdot a}\\

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

\end{array}

double f(double a, double b, double c) {
        double r59248 = b;
        double r59249 = -r59248;
        double r59250 = r59248 * r59248;
        double r59251 = 4.0;
        double r59252 = a;
        double r59253 = c;
        double r59254 = r59252 * r59253;
        double r59255 = r59251 * r59254;
        double r59256 = r59250 - r59255;
        double r59257 = sqrt(r59256);
        double r59258 = r59249 - r59257;
        double r59259 = 2.0;
        double r59260 = r59259 * r59252;
        double r59261 = r59258 / r59260;
        return r59261;
}

↓

double f(double a, double b, double c) {
        double r59262 = b;
        double r59263 = -7.668263498157484e-23;
        bool r59264 = r59262 <= r59263;
        double r59265 = -1.0;
        double r59266 = 1.0;
        double r59267 = c;
        double r59268 = r59262 / r59267;
        double r59269 = a;
        double r59270 = r59269 / r59262;
        double r59271 = r59268 - r59270;
        double r59272 = r59266 * r59271;
        double r59273 = r59265 / r59272;
        double r59274 = 2.9380396584045826e+94;
        bool r59275 = r59262 <= r59274;
        double r59276 = 2.0;
        double r59277 = -r59269;
        double r59278 = 4.0;
        double r59279 = r59277 * r59278;
        double r59280 = r59262 * r59262;
        double r59281 = fma(r59267, r59279, r59280);
        double r59282 = sqrt(r59281);
        double r59283 = r59262 + r59282;
        double r59284 = r59276 / r59283;
        double r59285 = r59284 * r59269;
        double r59286 = r59265 / r59285;
        double r59287 = -r59266;
        double r59288 = r59262 / r59269;
        double r59289 = r59267 / r59262;
        double r59290 = r59288 - r59289;
        double r59291 = r59287 * r59290;
        double r59292 = r59275 ? r59286 : r59291;
        double r59293 = r59264 ? r59273 : r59292;
        return r59293;
}

Original	34.4
Target	21.0
Herbie	10.8

Derivation

Split input into 3 regimes
if b < -7.668263498157484e-23
1. Initial program 55.0
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified55.0
  \[\leadsto \color{blue}{-\frac{b + \sqrt{\mathsf{fma}\left(\left(-a\right) \cdot c, 4, b \cdot b\right)}}{2 \cdot a}}\]
3. Using strategy rm
4. Applied clear-num55.0
  \[\leadsto -\color{blue}{\frac{1}{\frac{2 \cdot a}{b + \sqrt{\mathsf{fma}\left(\left(-a\right) \cdot c, 4, b \cdot b\right)}}}}\]
5. Simplified55.0
  \[\leadsto -\frac{1}{\color{blue}{\frac{2}{b + \sqrt{\mathsf{fma}\left(c, \left(-a\right) \cdot 4, b \cdot b\right)}} \cdot a}}\]
6. Taylor expanded around -inf 7.0
  \[\leadsto -\frac{1}{\color{blue}{1 \cdot \frac{b}{c} - 1 \cdot \frac{a}{b}}}\]
7. Simplified7.0
  \[\leadsto -\frac{1}{\color{blue}{1 \cdot \left(\frac{b}{c} - \frac{a}{b}\right)}}\]
if -7.668263498157484e-23 < b < 2.9380396584045826e+94
1. Initial program 15.6
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified15.6
  \[\leadsto \color{blue}{-\frac{b + \sqrt{\mathsf{fma}\left(\left(-a\right) \cdot c, 4, b \cdot b\right)}}{2 \cdot a}}\]
3. Using strategy rm
4. Applied clear-num15.7
  \[\leadsto -\color{blue}{\frac{1}{\frac{2 \cdot a}{b + \sqrt{\mathsf{fma}\left(\left(-a\right) \cdot c, 4, b \cdot b\right)}}}}\]
5. Simplified15.8
  \[\leadsto -\frac{1}{\color{blue}{\frac{2}{b + \sqrt{\mathsf{fma}\left(c, \left(-a\right) \cdot 4, b \cdot b\right)}} \cdot a}}\]
if 2.9380396584045826e+94 < b
1. Initial program 46.7
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified46.7
  \[\leadsto \color{blue}{-\frac{b + \sqrt{\mathsf{fma}\left(\left(-a\right) \cdot c, 4, b \cdot b\right)}}{2 \cdot a}}\]
3. Taylor expanded around inf 3.9
  \[\leadsto -\color{blue}{\left(1 \cdot \frac{b}{a} - 1 \cdot \frac{c}{b}\right)}\]
4. Simplified3.9
  \[\leadsto -\color{blue}{\left(\frac{b}{a} - \frac{c}{b}\right) \cdot 1}\]
Recombined 3 regimes into one program.
Final simplification10.8
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -7.668263498157483707441263748528829871939 \cdot 10^{-23}:\\ \;\;\;\;\frac{-1}{1 \cdot \left(\frac{b}{c} - \frac{a}{b}\right)}\\ \mathbf{elif}\;b \le 2.938039658404582626293093928685157937414 \cdot 10^{94}:\\ \;\;\;\;\frac{-1}{\frac{2}{b + \sqrt{\mathsf{fma}\left(c, \left(-a\right) \cdot 4, b \cdot b\right)}} \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\left(-1\right) \cdot \left(\frac{b}{a} - \frac{c}{b}\right)\\ \end{array}\]

Error

Target

Derivation

`if b < -7.668263498157484e-23`

`if -7.668263498157484e-23 < b < 2.9380396584045826e+94`

`if 2.9380396584045826e+94 < b`

Reproduce