Average Error: 43.7 → 12.1
Time: 19.9s
Precision: 64
\[1.1102230246251565404236316680908203125 \cdot 10^{-16} \lt a \lt 9007199254740992 \land 1.1102230246251565404236316680908203125 \cdot 10^{-16} \lt b \lt 9007199254740992 \land 1.1102230246251565404236316680908203125 \cdot 10^{-16} \lt c \lt 9007199254740992\]
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
↓
\[\frac{c}{b} \cdot -1\]
\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}
↓
\frac{c}{b} \cdot -1
double f(double a, double b, double c) {
        double r1437825 = b;
        double r1437826 = -r1437825;
        double r1437827 = r1437825 * r1437825;
        double r1437828 = 4.0;
        double r1437829 = a;
        double r1437830 = r1437828 * r1437829;
        double r1437831 = c;
        double r1437832 = r1437830 * r1437831;
        double r1437833 = r1437827 - r1437832;
        double r1437834 = sqrt(r1437833);
        double r1437835 = r1437826 + r1437834;
        double r1437836 = 2.0;
        double r1437837 = r1437836 * r1437829;
        double r1437838 = r1437835 / r1437837;
        return r1437838;
}
↓
double f(double __attribute__((unused)) a, double b, double c) {
        double r1437839 = c;
        double r1437840 = b;
        double r1437841 = r1437839 / r1437840;
        double r1437842 = -1.0;
        double r1437843 = r1437841 * r1437842;
        return r1437843;
}

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 43.7

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

  2. Simplified43.7

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

  3. Taylor expanded around inf 12.1

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

  4. Final simplification12.1

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

Reproduce

herbie shell --seed 2019192 
(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) (* (* 4.0 a) c)))) (* 2.0 a)))