Average Error: 43.9 → 12.0
Time: 20.0s
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 r1889484 = b;
        double r1889485 = -r1889484;
        double r1889486 = r1889484 * r1889484;
        double r1889487 = 4.0;
        double r1889488 = a;
        double r1889489 = r1889487 * r1889488;
        double r1889490 = c;
        double r1889491 = r1889489 * r1889490;
        double r1889492 = r1889486 - r1889491;
        double r1889493 = sqrt(r1889492);
        double r1889494 = r1889485 + r1889493;
        double r1889495 = 2.0;
        double r1889496 = r1889495 * r1889488;
        double r1889497 = r1889494 / r1889496;
        return r1889497;
}
↓
double f(double __attribute__((unused)) a, double b, double c) {
        double r1889498 = c;
        double r1889499 = b;
        double r1889500 = r1889498 / r1889499;
        double r1889501 = -1.0;
        double r1889502 = r1889500 * r1889501;
        return r1889502;
}

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 43.9

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

  2. Simplified43.9

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

  3. Taylor expanded around inf 12.0

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

  4. Final simplification12.0

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

Reproduce

herbie shell --seed 2019174 
(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)))