Average Error: 33.6 → 10.3
Time: 18.4s
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 r3589753 = b;
        double r3589754 = -r3589753;
        double r3589755 = r3589753 * r3589753;
        double r3589756 = 4.0;
        double r3589757 = a;
        double r3589758 = c;
        double r3589759 = r3589757 * r3589758;
        double r3589760 = r3589756 * r3589759;
        double r3589761 = r3589755 - r3589760;
        double r3589762 = sqrt(r3589761);
        double r3589763 = r3589754 - r3589762;
        double r3589764 = 2.0;
        double r3589765 = r3589764 * r3589757;
        double r3589766 = r3589763 / r3589765;
        return r3589766;
}
↓
double f(double a, double b, double c) {
        double r3589767 = b;
        double r3589768 = -1.264659490877098e-67;
        bool r3589769 = r3589767 <= r3589768;
        double r3589770 = c;
        double r3589771 = r3589770 / r3589767;
        double r3589772 = -r3589771;
        double r3589773 = 0.17389787404847717;
        bool r3589774 = r3589767 <= r3589773;
        double r3589775 = -r3589767;
        double r3589776 = a;
        double r3589777 = -4.0;
        double r3589778 = r3589776 * r3589777;
        double r3589779 = r3589778 * r3589770;
        double r3589780 = r3589767 * r3589767;
        double r3589781 = r3589779 + r3589780;
        double r3589782 = sqrt(r3589781);
        double r3589783 = r3589775 - r3589782;
        double r3589784 = 2.0;
        double r3589785 = r3589776 * r3589784;
        double r3589786 = r3589783 / r3589785;
        double r3589787 = r3589767 / r3589776;
        double r3589788 = r3589771 - r3589787;
        double r3589789 = r3589774 ? r3589786 : r3589788;
        double r3589790 = r3589769 ? r3589772 : r3589789;
        return r3589790;
}

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 "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)))