Average Error: 43.6 → 12.1
Time: 24.6s
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 r1362175 = b;
        double r1362176 = -r1362175;
        double r1362177 = r1362175 * r1362175;
        double r1362178 = 4.0;
        double r1362179 = a;
        double r1362180 = r1362178 * r1362179;
        double r1362181 = c;
        double r1362182 = r1362180 * r1362181;
        double r1362183 = r1362177 - r1362182;
        double r1362184 = sqrt(r1362183);
        double r1362185 = r1362176 + r1362184;
        double r1362186 = 2.0;
        double r1362187 = r1362186 * r1362179;
        double r1362188 = r1362185 / r1362187;
        return r1362188;
}
↓
double f(double __attribute__((unused)) a, double b, double c) {
        double r1362189 = c;
        double r1362190 = b;
        double r1362191 = r1362189 / r1362190;
        double r1362192 = -2.0;
        double r1362193 = r1362191 * r1362192;
        double r1362194 = 2.0;
        double r1362195 = r1362193 / r1362194;
        return r1362195;
}

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 43.6

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

  2. Simplified43.6

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

  3. Taylor expanded around inf 12.1

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

  4. Final simplification12.1

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

Reproduce

herbie shell --seed 2019144 
(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)))