Average Error: 34.0 → 10.6
Time: 17.2s
Precision: 64
\[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -2.900769547116861 \cdot 10^{+46}:\\ \;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\ \mathbf{elif}\;b \le 1.6528810740721013 \cdot 10^{-142}:\\ \;\;\;\;\frac{\frac{1}{a} \cdot \left(\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b\right)}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \end{array}\]
\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 -2.900769547116861 \cdot 10^{+46}:\\
\;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\

\mathbf{elif}\;b \le 1.6528810740721013 \cdot 10^{-142}:\\
\;\;\;\;\frac{\frac{1}{a} \cdot \left(\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b\right)}{2}\\

\mathbf{else}:\\
\;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\

\end{array}
double f(double a, double b, double c) {
        double r3625235 = b;
        double r3625236 = -r3625235;
        double r3625237 = r3625235 * r3625235;
        double r3625238 = 4.0;
        double r3625239 = a;
        double r3625240 = c;
        double r3625241 = r3625239 * r3625240;
        double r3625242 = r3625238 * r3625241;
        double r3625243 = r3625237 - r3625242;
        double r3625244 = sqrt(r3625243);
        double r3625245 = r3625236 + r3625244;
        double r3625246 = 2.0;
        double r3625247 = r3625246 * r3625239;
        double r3625248 = r3625245 / r3625247;
        return r3625248;
}
↓
double f(double a, double b, double c) {
        double r3625249 = b;
        double r3625250 = -2.900769547116861e+46;
        bool r3625251 = r3625249 <= r3625250;
        double r3625252 = c;
        double r3625253 = r3625252 / r3625249;
        double r3625254 = a;
        double r3625255 = r3625249 / r3625254;
        double r3625256 = r3625253 - r3625255;
        double r3625257 = 2.0;
        double r3625258 = r3625256 * r3625257;
        double r3625259 = r3625258 / r3625257;
        double r3625260 = 1.6528810740721013e-142;
        bool r3625261 = r3625249 <= r3625260;
        double r3625262 = 1.0;
        double r3625263 = r3625262 / r3625254;
        double r3625264 = r3625249 * r3625249;
        double r3625265 = 4.0;
        double r3625266 = r3625265 * r3625254;
        double r3625267 = r3625252 * r3625266;
        double r3625268 = r3625264 - r3625267;
        double r3625269 = sqrt(r3625268);
        double r3625270 = r3625269 - r3625249;
        double r3625271 = r3625263 * r3625270;
        double r3625272 = r3625271 / r3625257;
        double r3625273 = -2.0;
        double r3625274 = r3625273 * r3625253;
        double r3625275 = r3625274 / r3625257;
        double r3625276 = r3625261 ? r3625272 : r3625275;
        double r3625277 = r3625251 ? r3625259 : r3625276;
        return r3625277;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original34.0
Target20.7
Herbie10.6
\[\begin{array}{l} \mathbf{if}\;b \lt 0:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if b < -2.900769547116861e+46

    1. Initial program 35.9

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

    2. Simplified35.9

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

    3. Taylor expanded around -inf 5.3

      \[\leadsto \frac{\color{blue}{2 \cdot \frac{c}{b} - 2 \cdot \frac{b}{a}}}{2}\]

    4. Simplified5.3

      \[\leadsto \frac{\color{blue}{2 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}}{2}\]

    if -2.900769547116861e+46 < b < 1.6528810740721013e-142

    1. Initial program 11.5

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

    2. Simplified11.5

      \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{a}}{2}}\]
    3. Using strategy rm

    4. Applied div-inv11.7

      \[\leadsto \frac{\color{blue}{\left(\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b\right) \cdot \frac{1}{a}}}{2}\]

    if 1.6528810740721013e-142 < b

    1. Initial program 50.1

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

    2. Simplified50.1

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

    3. Taylor expanded around inf 12.0

      \[\leadsto \frac{\color{blue}{-2 \cdot \frac{c}{b}}}{2}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification10.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -2.900769547116861 \cdot 10^{+46}:\\ \;\;\;\;\frac{\left(\frac{c}{b} - \frac{b}{a}\right) \cdot 2}{2}\\ \mathbf{elif}\;b \le 1.6528810740721013 \cdot 10^{-142}:\\ \;\;\;\;\frac{\frac{1}{a} \cdot \left(\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b\right)}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{c}{b}}{2}\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (a b c)
  :name "quadp (p42, positive)"

  :herbie-target
  (if (< b 0) (/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a)) (/ c (* a (/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a)))))

  (/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a)))