Average Error: 33.2 → 9.9
Time: 19.1s
Precision: 64
\[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -4.600306435637794 \cdot 10^{+151}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 5.930445637544082 \cdot 10^{-86}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]
\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 -4.600306435637794 \cdot 10^{+151}:\\
\;\;\;\;\frac{c}{b} - \frac{b}{a}\\

\mathbf{elif}\;b \le 5.930445637544082 \cdot 10^{-86}:\\
\;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a \cdot 2}\\

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

\end{array}
double f(double a, double b, double c) {
        double r3603813 = b;
        double r3603814 = -r3603813;
        double r3603815 = r3603813 * r3603813;
        double r3603816 = 4.0;
        double r3603817 = a;
        double r3603818 = c;
        double r3603819 = r3603817 * r3603818;
        double r3603820 = r3603816 * r3603819;
        double r3603821 = r3603815 - r3603820;
        double r3603822 = sqrt(r3603821);
        double r3603823 = r3603814 + r3603822;
        double r3603824 = 2.0;
        double r3603825 = r3603824 * r3603817;
        double r3603826 = r3603823 / r3603825;
        return r3603826;
}
↓
double f(double a, double b, double c) {
        double r3603827 = b;
        double r3603828 = -4.600306435637794e+151;
        bool r3603829 = r3603827 <= r3603828;
        double r3603830 = c;
        double r3603831 = r3603830 / r3603827;
        double r3603832 = a;
        double r3603833 = r3603827 / r3603832;
        double r3603834 = r3603831 - r3603833;
        double r3603835 = 5.930445637544082e-86;
        bool r3603836 = r3603827 <= r3603835;
        double r3603837 = -r3603827;
        double r3603838 = r3603827 * r3603827;
        double r3603839 = r3603830 * r3603832;
        double r3603840 = 4.0;
        double r3603841 = r3603839 * r3603840;
        double r3603842 = r3603838 - r3603841;
        double r3603843 = sqrt(r3603842);
        double r3603844 = r3603837 + r3603843;
        double r3603845 = 2.0;
        double r3603846 = r3603832 * r3603845;
        double r3603847 = r3603844 / r3603846;
        double r3603848 = -r3603831;
        double r3603849 = r3603836 ? r3603847 : r3603848;
        double r3603850 = r3603829 ? r3603834 : r3603849;
        return r3603850;
}

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

Original33.2
Target20.6
Herbie9.9
\[\begin{array}{l} \mathbf{if}\;b \lt 0:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if b < -4.600306435637794e+151

    1. Initial program 59.7

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

    2. Taylor expanded around -inf 2.2

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

    if -4.600306435637794e+151 < b < 5.930445637544082e-86

    1. Initial program 11.6

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

    if 5.930445637544082e-86 < b

    1. Initial program 52.2

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

    2. Taylor expanded around inf 9.9

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

    3. Simplified9.9

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

  4. Final simplification9.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -4.600306435637794 \cdot 10^{+151}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \le 5.930445637544082 \cdot 10^{-86}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-\frac{c}{b}\\ \end{array}\]

Reproduce

herbie shell --seed 2019162 
(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)))