Average Error: 52.0 → 6.5
Time: 18.9s
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 r699097 = b;
        double r699098 = -r699097;
        double r699099 = r699097 * r699097;
        double r699100 = 4.0;
        double r699101 = a;
        double r699102 = r699100 * r699101;
        double r699103 = c;
        double r699104 = r699102 * r699103;
        double r699105 = r699099 - r699104;
        double r699106 = sqrt(r699105);
        double r699107 = r699098 + r699106;
        double r699108 = 2.0;
        double r699109 = r699108 * r699101;
        double r699110 = r699107 / r699109;
        return r699110;
}
↓
double f(double __attribute__((unused)) a, double b, double c) {
        double r699111 = c;
        double r699112 = b;
        double r699113 = r699111 / r699112;
        double r699114 = -2.0;
        double r699115 = r699113 * r699114;
        double r699116 = 2.0;
        double r699117 = r699115 / r699116;
        return r699117;
}

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 52.0

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

  2. Simplified52.0

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

  3. Taylor expanded around inf 6.5

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

  4. Final simplification6.5

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

Reproduce

herbie shell --seed 2019162 
(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)))