Average Error: 52.5 → 6.2
Time: 23.7s
Precision: 64
\[4.930380657631323783823303533017413935458 \cdot 10^{-32} \lt a \lt 20282409603651670423947251286016 \land 4.930380657631323783823303533017413935458 \cdot 10^{-32} \lt b \lt 20282409603651670423947251286016 \land 4.930380657631323783823303533017413935458 \cdot 10^{-32} \lt c \lt 20282409603651670423947251286016\]
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
↓
\[\frac{c}{b} \cdot -1\]
\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 r881173 = b;
        double r881174 = -r881173;
        double r881175 = r881173 * r881173;
        double r881176 = 4.0;
        double r881177 = a;
        double r881178 = r881176 * r881177;
        double r881179 = c;
        double r881180 = r881178 * r881179;
        double r881181 = r881175 - r881180;
        double r881182 = sqrt(r881181);
        double r881183 = r881174 + r881182;
        double r881184 = 2.0;
        double r881185 = r881184 * r881177;
        double r881186 = r881183 / r881185;
        return r881186;
}
↓
double f(double __attribute__((unused)) a, double b, double c) {
        double r881187 = c;
        double r881188 = b;
        double r881189 = r881187 / r881188;
        double r881190 = -1.0;
        double r881191 = r881189 * r881190;
        return r881191;
}

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 52.5

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

  2. Simplified52.5

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

  3. Taylor expanded around inf 6.2

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

  4. Final simplification6.2

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

Reproduce

herbie shell --seed 2019200 
(FPCore (a b c)
  :name "Quadratic roots, wide range"
  :pre (and (< 4.930380657631324e-32 a 2.028240960365167e+31) (< 4.930380657631324e-32 b 2.028240960365167e+31) (< 4.930380657631324e-32 c 2.028240960365167e+31))
  (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)))