Average Error: 33.1 → 10.7
Time: 26.6s
Precision: 64
\[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -2.7503548021140933 \cdot 10^{-65}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le -9.861592941135515 \cdot 10^{-102}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a \cdot 2}\\ \mathbf{elif}\;b \le -4.884190020998732 \cdot 10^{-159}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le 7.377921431051488 \cdot 10^{+75}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\]
\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 -2.7503548021140933 \cdot 10^{-65}:\\
\;\;\;\;-\frac{c}{b}\\

\mathbf{elif}\;b \le -9.861592941135515 \cdot 10^{-102}:\\
\;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a \cdot 2}\\

\mathbf{elif}\;b \le -4.884190020998732 \cdot 10^{-159}:\\
\;\;\;\;-\frac{c}{b}\\

\mathbf{elif}\;b \le 7.377921431051488 \cdot 10^{+75}:\\
\;\;\;\;\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 r2446598 = b;
        double r2446599 = -r2446598;
        double r2446600 = r2446598 * r2446598;
        double r2446601 = 4.0;
        double r2446602 = a;
        double r2446603 = c;
        double r2446604 = r2446602 * r2446603;
        double r2446605 = r2446601 * r2446604;
        double r2446606 = r2446600 - r2446605;
        double r2446607 = sqrt(r2446606);
        double r2446608 = r2446599 - r2446607;
        double r2446609 = 2.0;
        double r2446610 = r2446609 * r2446602;
        double r2446611 = r2446608 / r2446610;
        return r2446611;
}
↓
double f(double a, double b, double c) {
        double r2446612 = b;
        double r2446613 = -2.7503548021140933e-65;
        bool r2446614 = r2446612 <= r2446613;
        double r2446615 = c;
        double r2446616 = r2446615 / r2446612;
        double r2446617 = -r2446616;
        double r2446618 = -9.861592941135515e-102;
        bool r2446619 = r2446612 <= r2446618;
        double r2446620 = -r2446612;
        double r2446621 = r2446612 * r2446612;
        double r2446622 = a;
        double r2446623 = r2446615 * r2446622;
        double r2446624 = 4.0;
        double r2446625 = r2446623 * r2446624;
        double r2446626 = r2446621 - r2446625;
        double r2446627 = sqrt(r2446626);
        double r2446628 = r2446620 - r2446627;
        double r2446629 = 2.0;
        double r2446630 = r2446622 * r2446629;
        double r2446631 = r2446628 / r2446630;
        double r2446632 = -4.884190020998732e-159;
        bool r2446633 = r2446612 <= r2446632;
        double r2446634 = 7.377921431051488e+75;
        bool r2446635 = r2446612 <= r2446634;
        double r2446636 = r2446612 / r2446622;
        double r2446637 = r2446616 - r2446636;
        double r2446638 = r2446635 ? r2446631 : r2446637;
        double r2446639 = r2446633 ? r2446617 : r2446638;
        double r2446640 = r2446619 ? r2446631 : r2446639;
        double r2446641 = r2446614 ? r2446617 : r2446640;
        return r2446641;
}

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

Original33.1
Target20.8
Herbie10.7
\[\begin{array}{l} \mathbf{if}\;b \lt 0:\\ \;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if b < -2.7503548021140933e-65 or -9.861592941135515e-102 < b < -4.884190020998732e-159

    1. Initial program 49.8

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

    2. Taylor expanded around -inf 49.8

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

    3. Simplified49.8

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

    4. Taylor expanded around -inf 11.9

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

    5. Simplified11.9

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

    if -2.7503548021140933e-65 < b < -9.861592941135515e-102 or -4.884190020998732e-159 < b < 7.377921431051488e+75

    1. Initial program 12.4

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

    2. Taylor expanded around -inf 12.4

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

    3. Simplified12.4

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

    if 7.377921431051488e+75 < b

    1. Initial program 39.3

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

    2. Taylor expanded around inf 4.2

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

  4. Final simplification10.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -2.7503548021140933 \cdot 10^{-65}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le -9.861592941135515 \cdot 10^{-102}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a \cdot 2}\\ \mathbf{elif}\;b \le -4.884190020998732 \cdot 10^{-159}:\\ \;\;\;\;-\frac{c}{b}\\ \mathbf{elif}\;b \le 7.377921431051488 \cdot 10^{+75}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019144 
(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)))