Average Error: 33.6 → 10.3
Time: 16.6s
Precision: 64
\[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -1.264659490877098 \cdot 10^{-67}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le 0.17389787404847717:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{\left(a \cdot -4\right) \cdot c + b \cdot b}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\]
\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 -1.264659490877098 \cdot 10^{-67}:\\
\;\;\;\;-\frac{c}{b}\\

\mathbf{elif}\;b \le 0.17389787404847717:\\
\;\;\;\;\frac{\left(-b\right) - \sqrt{\left(a \cdot -4\right) \cdot c + b \cdot b}}{a \cdot 2}\\

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

\end{array}
double f(double a, double b, double c) {
        double r4259967 = b;
        double r4259968 = -r4259967;
        double r4259969 = r4259967 * r4259967;
        double r4259970 = 4.0;
        double r4259971 = a;
        double r4259972 = c;
        double r4259973 = r4259971 * r4259972;
        double r4259974 = r4259970 * r4259973;
        double r4259975 = r4259969 - r4259974;
        double r4259976 = sqrt(r4259975);
        double r4259977 = r4259968 - r4259976;
        double r4259978 = 2.0;
        double r4259979 = r4259978 * r4259971;
        double r4259980 = r4259977 / r4259979;
        return r4259980;
}
↓
double f(double a, double b, double c) {
        double r4259981 = b;
        double r4259982 = -1.264659490877098e-67;
        bool r4259983 = r4259981 <= r4259982;
        double r4259984 = c;
        double r4259985 = r4259984 / r4259981;
        double r4259986 = -r4259985;
        double r4259987 = 0.17389787404847717;
        bool r4259988 = r4259981 <= r4259987;
        double r4259989 = -r4259981;
        double r4259990 = a;
        double r4259991 = -4.0;
        double r4259992 = r4259990 * r4259991;
        double r4259993 = r4259992 * r4259984;
        double r4259994 = r4259981 * r4259981;
        double r4259995 = r4259993 + r4259994;
        double r4259996 = sqrt(r4259995);
        double r4259997 = r4259989 - r4259996;
        double r4259998 = 2.0;
        double r4259999 = r4259990 * r4259998;
        double r4260000 = r4259997 / r4259999;
        double r4260001 = r4259981 / r4259990;
        double r4260002 = r4259985 - r4260001;
        double r4260003 = r4259988 ? r4260000 : r4260002;
        double r4260004 = r4259983 ? r4259986 : r4260003;
        return r4260004;
}

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

Original33.6
Target20.9
Herbie10.3
\[\begin{array}{l} \mathbf{if}\;b \lt 0:\\ \;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if b < -1.264659490877098e-67

    1. Initial program 52.9

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

    2. Taylor expanded around -inf 8.1

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

    3. Simplified8.1

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

    if -1.264659490877098e-67 < b < 0.17389787404847717

    1. Initial program 15.0

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

    3. Applied sub-neg15.0

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

    4. Simplified15.0

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

    if 0.17389787404847717 < b

    1. Initial program 29.8

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

    2. Taylor expanded around inf 7.3

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

  4. Final simplification10.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.264659490877098 \cdot 10^{-67}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le 0.17389787404847717:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{\left(a \cdot -4\right) \cdot c + b \cdot b}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (a b c)
  :name "The quadratic formula (r2)"

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

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