Average Error: 34.0 → 10.5
Time: 14.5s
Precision: 64
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -2.900769547116861 \cdot 10^{+46}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 1.6528810740721013 \cdot 10^{-142}:\\ \;\;\;\;\left(\left(-b\right) + \sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)}\right) \cdot \frac{\frac{1}{2}}{a}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]
\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 -2.900769547116861 \cdot 10^{+46}:\\
\;\;\;\;\frac{c}{b} - \frac{b}{a}\\

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

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

\end{array}
double f(double a, double b, double c) {
        double r5651299 = b;
        double r5651300 = -r5651299;
        double r5651301 = r5651299 * r5651299;
        double r5651302 = 4.0;
        double r5651303 = a;
        double r5651304 = r5651302 * r5651303;
        double r5651305 = c;
        double r5651306 = r5651304 * r5651305;
        double r5651307 = r5651301 - r5651306;
        double r5651308 = sqrt(r5651307);
        double r5651309 = r5651300 + r5651308;
        double r5651310 = 2.0;
        double r5651311 = r5651310 * r5651303;
        double r5651312 = r5651309 / r5651311;
        return r5651312;
}
↓
double f(double a, double b, double c) {
        double r5651313 = b;
        double r5651314 = -2.900769547116861e+46;
        bool r5651315 = r5651313 <= r5651314;
        double r5651316 = c;
        double r5651317 = r5651316 / r5651313;
        double r5651318 = a;
        double r5651319 = r5651313 / r5651318;
        double r5651320 = r5651317 - r5651319;
        double r5651321 = 1.6528810740721013e-142;
        bool r5651322 = r5651313 <= r5651321;
        double r5651323 = -r5651313;
        double r5651324 = r5651313 * r5651313;
        double r5651325 = 4.0;
        double r5651326 = r5651325 * r5651318;
        double r5651327 = r5651316 * r5651326;
        double r5651328 = r5651324 - r5651327;
        double r5651329 = sqrt(r5651328);
        double r5651330 = r5651323 + r5651329;
        double r5651331 = 0.5;
        double r5651332 = r5651331 / r5651318;
        double r5651333 = r5651330 * r5651332;
        double r5651334 = -r5651317;
        double r5651335 = r5651322 ? r5651333 : r5651334;
        double r5651336 = r5651315 ? r5651320 : r5651335;
        return r5651336;
}

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
Herbie10.5
\[\begin{array}{l} \mathbf{if}\;b \lt 0:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if b < -2.900769547116861e+46

    1. Initial program 35.9

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

    2. Taylor expanded around -inf 5.3

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

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

    1. Initial program 11.5

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

    3. Applied div-inv11.7

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

    4. Simplified11.7

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

    if 1.6528810740721013e-142 < b

    1. Initial program 50.1

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

    2. Taylor expanded around inf 12.0

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

    3. Simplified12.0

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

  4. Final simplification10.5

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

Reproduce

herbie shell --seed 2019168 
(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)))