Average Error: 52.5 → 6.2
Time: 18.6s
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 r808430 = b;
        double r808431 = -r808430;
        double r808432 = r808430 * r808430;
        double r808433 = 4.0;
        double r808434 = a;
        double r808435 = r808433 * r808434;
        double r808436 = c;
        double r808437 = r808435 * r808436;
        double r808438 = r808432 - r808437;
        double r808439 = sqrt(r808438);
        double r808440 = r808431 + r808439;
        double r808441 = 2.0;
        double r808442 = r808441 * r808434;
        double r808443 = r808440 / r808442;
        return r808443;
}
↓
double f(double __attribute__((unused)) a, double b, double c) {
        double r808444 = c;
        double r808445 = b;
        double r808446 = r808444 / r808445;
        double r808447 = -1.0;
        double r808448 = r808446 * r808447;
        return r808448;
}

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

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

  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 2019174 
(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)))