Average Error: 33.0 → 10.6
Time: 14.2s
Precision: 64
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -3.794505329565205 \cdot 10^{+146}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 1.6194276288860963:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]
\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 -3.794505329565205 \cdot 10^{+146}:\\
\;\;\;\;\frac{c}{b} - \frac{b}{a}\\

\mathbf{elif}\;b \le 1.6194276288860963:\\
\;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}{a \cdot 2}\\

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

\end{array}
double f(double a, double b, double c) {
        double r4184296 = b;
        double r4184297 = -r4184296;
        double r4184298 = r4184296 * r4184296;
        double r4184299 = 4.0;
        double r4184300 = a;
        double r4184301 = r4184299 * r4184300;
        double r4184302 = c;
        double r4184303 = r4184301 * r4184302;
        double r4184304 = r4184298 - r4184303;
        double r4184305 = sqrt(r4184304);
        double r4184306 = r4184297 + r4184305;
        double r4184307 = 2.0;
        double r4184308 = r4184307 * r4184300;
        double r4184309 = r4184306 / r4184308;
        return r4184309;
}
↓
double f(double a, double b, double c) {
        double r4184310 = b;
        double r4184311 = -3.794505329565205e+146;
        bool r4184312 = r4184310 <= r4184311;
        double r4184313 = c;
        double r4184314 = r4184313 / r4184310;
        double r4184315 = a;
        double r4184316 = r4184310 / r4184315;
        double r4184317 = r4184314 - r4184316;
        double r4184318 = 1.6194276288860963;
        bool r4184319 = r4184310 <= r4184318;
        double r4184320 = -r4184310;
        double r4184321 = r4184310 * r4184310;
        double r4184322 = 4.0;
        double r4184323 = r4184322 * r4184315;
        double r4184324 = r4184313 * r4184323;
        double r4184325 = r4184321 - r4184324;
        double r4184326 = sqrt(r4184325);
        double r4184327 = r4184320 + r4184326;
        double r4184328 = 2.0;
        double r4184329 = r4184315 * r4184328;
        double r4184330 = r4184327 / r4184329;
        double r4184331 = -r4184314;
        double r4184332 = r4184319 ? r4184330 : r4184331;
        double r4184333 = r4184312 ? r4184317 : r4184332;
        return r4184333;
}

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

Original33.0
Target20.2
Herbie10.6
\[\begin{array}{l} \mathbf{if}\;b \lt 0:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if b < -3.794505329565205e+146

    1. Initial program 58.0

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

    2. Taylor expanded around -inf 3.1

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

    if -3.794505329565205e+146 < b < 1.6194276288860963

    1. Initial program 15.0

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

    if 1.6194276288860963 < b

    1. Initial program 54.4

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

    2. Taylor expanded around inf 5.9

      \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]

    3. Simplified5.9

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

  4. Final simplification10.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -3.794505329565205 \cdot 10^{+146}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 1.6194276288860963:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]

Reproduce

herbie shell --seed 2019129 
(FPCore (a b c)
  :name "The quadratic formula (r1)"

  :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)))