Average Error: 44.0 → 11.9
Time: 16.4s
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 r591957 = b;
        double r591958 = -r591957;
        double r591959 = r591957 * r591957;
        double r591960 = 4.0;
        double r591961 = a;
        double r591962 = r591960 * r591961;
        double r591963 = c;
        double r591964 = r591962 * r591963;
        double r591965 = r591959 - r591964;
        double r591966 = sqrt(r591965);
        double r591967 = r591958 + r591966;
        double r591968 = 2.0;
        double r591969 = r591968 * r591961;
        double r591970 = r591967 / r591969;
        return r591970;
}
↓
double f(double __attribute__((unused)) a, double b, double c) {
        double r591971 = c;
        double r591972 = b;
        double r591973 = r591971 / r591972;
        double r591974 = -2.0;
        double r591975 = r591973 * r591974;
        double r591976 = 2.0;
        double r591977 = r591975 / r591976;
        return r591977;
}

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 11.9

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

  4. Final simplification11.9

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

Reproduce

herbie shell --seed 2019155 
(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)))