Average Error: 52.4 → 6.3
Time: 31.4s
Precision: 64
\[4.930380657631324 \cdot 10^{-32} \lt a \lt 2.028240960365167 \cdot 10^{+31} \land 4.930380657631324 \cdot 10^{-32} \lt b \lt 2.028240960365167 \cdot 10^{+31} \land 4.930380657631324 \cdot 10^{-32} \lt c \lt 2.028240960365167 \cdot 10^{+31}\]
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
↓
\[\frac{\frac{c}{b} \cdot -2}{2}\]
\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 r549092 = b;
        double r549093 = -r549092;
        double r549094 = r549092 * r549092;
        double r549095 = 4.0;
        double r549096 = a;
        double r549097 = r549095 * r549096;
        double r549098 = c;
        double r549099 = r549097 * r549098;
        double r549100 = r549094 - r549099;
        double r549101 = sqrt(r549100);
        double r549102 = r549093 + r549101;
        double r549103 = 2.0;
        double r549104 = r549103 * r549096;
        double r549105 = r549102 / r549104;
        return r549105;
}
↓
double f(double __attribute__((unused)) a, double b, double c) {
        double r549106 = c;
        double r549107 = b;
        double r549108 = r549106 / r549107;
        double r549109 = -2.0;
        double r549110 = r549108 * r549109;
        double r549111 = 2.0;
        double r549112 = r549110 / r549111;
        return r549112;
}

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 52.4

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

  2. Simplified52.4

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

  3. Taylor expanded around inf 6.3

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

  4. Final simplification6.3

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

Reproduce

herbie shell --seed 2019151 
(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 a) c)))) (* 2 a)))