Average Error: 44.0 → 12.0
Time: 14.4s
Precision: 64
\[1.1102230246251565 \cdot 10^{-16} \lt a \lt 9007199254740992.0 \land 1.1102230246251565 \cdot 10^{-16} \lt b \lt 9007199254740992.0 \land 1.1102230246251565 \cdot 10^{-16} \lt c \lt 9007199254740992.0\]
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
↓
\[\frac{\frac{c}{b} \cdot -2}{2}\]
\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}
↓
\frac{\frac{c}{b} \cdot -2}{2}
double f(double a, double b, double c) {
        double r539632 = b;
        double r539633 = -r539632;
        double r539634 = r539632 * r539632;
        double r539635 = 4.0;
        double r539636 = a;
        double r539637 = r539635 * r539636;
        double r539638 = c;
        double r539639 = r539637 * r539638;
        double r539640 = r539634 - r539639;
        double r539641 = sqrt(r539640);
        double r539642 = r539633 + r539641;
        double r539643 = 2.0;
        double r539644 = r539643 * r539636;
        double r539645 = r539642 / r539644;
        return r539645;
}
↓
double f(double __attribute__((unused)) a, double b, double c) {
        double r539646 = c;
        double r539647 = b;
        double r539648 = r539646 / r539647;
        double r539649 = -2.0;
        double r539650 = r539648 * r539649;
        double r539651 = 2.0;
        double r539652 = r539650 / r539651;
        return r539652;
}

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

Derivation

  1. Initial program 44.0

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

  2. Simplified44.0

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

  3. Taylor expanded around inf 12.0

    \[\leadsto \frac{\color{blue}{-2 \cdot \frac{c}{b}}}{2}\]

  4. Final simplification12.0

    \[\leadsto \frac{\frac{c}{b} \cdot -2}{2}\]

Reproduce

herbie shell --seed 2019153 
(FPCore (a b c)
  :name "Quadratic roots, medium range"
  :pre (and (< 1.1102230246251565e-16 a 9007199254740992.0) (< 1.1102230246251565e-16 b 9007199254740992.0) (< 1.1102230246251565e-16 c 9007199254740992.0))
  (/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)))