Average Error: 33.0 → 9.5
Time: 19.6s
Precision: 64
\[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -1.376414644198452 \cdot 10^{-55}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le 2.3362227636224895 \cdot 10^{+83}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\]
\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 -1.376414644198452 \cdot 10^{-55}:\\
\;\;\;\;-\frac{c}{b}\\

\mathbf{elif}\;b \le 2.3362227636224895 \cdot 10^{+83}:\\
\;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a \cdot 2}\\

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

\end{array}
double f(double a, double b, double c) {
        double r2215688 = b;
        double r2215689 = -r2215688;
        double r2215690 = r2215688 * r2215688;
        double r2215691 = 4.0;
        double r2215692 = a;
        double r2215693 = c;
        double r2215694 = r2215692 * r2215693;
        double r2215695 = r2215691 * r2215694;
        double r2215696 = r2215690 - r2215695;
        double r2215697 = sqrt(r2215696);
        double r2215698 = r2215689 - r2215697;
        double r2215699 = 2.0;
        double r2215700 = r2215699 * r2215692;
        double r2215701 = r2215698 / r2215700;
        return r2215701;
}
↓
double f(double a, double b, double c) {
        double r2215702 = b;
        double r2215703 = -1.376414644198452e-55;
        bool r2215704 = r2215702 <= r2215703;
        double r2215705 = c;
        double r2215706 = r2215705 / r2215702;
        double r2215707 = -r2215706;
        double r2215708 = 2.3362227636224895e+83;
        bool r2215709 = r2215702 <= r2215708;
        double r2215710 = -r2215702;
        double r2215711 = r2215702 * r2215702;
        double r2215712 = a;
        double r2215713 = r2215705 * r2215712;
        double r2215714 = 4.0;
        double r2215715 = r2215713 * r2215714;
        double r2215716 = r2215711 - r2215715;
        double r2215717 = sqrt(r2215716);
        double r2215718 = r2215710 - r2215717;
        double r2215719 = 2.0;
        double r2215720 = r2215712 * r2215719;
        double r2215721 = r2215718 / r2215720;
        double r2215722 = r2215702 / r2215712;
        double r2215723 = r2215706 - r2215722;
        double r2215724 = r2215709 ? r2215721 : r2215723;
        double r2215725 = r2215704 ? r2215707 : r2215724;
        return r2215725;
}

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
Target20.5
Herbie9.5
\[\begin{array}{l} \mathbf{if}\;b \lt 0:\\ \;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if b < -1.376414644198452e-55

    1. Initial program 53.4

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

    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 -1.376414644198452e-55 < b < 2.3362227636224895e+83

    1. Initial program 12.9

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

    2. Taylor expanded around inf 12.9

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

    3. Simplified12.9

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

    if 2.3362227636224895e+83 < b

    1. Initial program 41.5

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

    2. Taylor expanded around inf 41.5

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

    3. Simplified41.5

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

    4. Taylor expanded around inf 3.8

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

  4. Final simplification9.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.376414644198452 \cdot 10^{-55}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le 2.3362227636224895 \cdot 10^{+83}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019137 
(FPCore (a b c)
  :name "quadm (p42, negative)"

  :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)))