Average Error: 52.7 → 6.0
Time: 17.1s
Precision: 64
\[4.930380657631324 \cdot 10^{-32} \lt a \lt 2.028240960365167 \cdot 10^{+31} \land 4.930380657631324 \cdot 10^{-32} \lt b \lt 2.028240960365167 \cdot 10^{+31} \land 4.930380657631324 \cdot 10^{-32} \lt c \lt 2.028240960365167 \cdot 10^{+31}\]
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
↓
\[-\frac{c}{b}\]
\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}
↓
-\frac{c}{b}
double f(double a, double b, double c) {
        double r549409 = b;
        double r549410 = -r549409;
        double r549411 = r549409 * r549409;
        double r549412 = 4.0;
        double r549413 = a;
        double r549414 = r549412 * r549413;
        double r549415 = c;
        double r549416 = r549414 * r549415;
        double r549417 = r549411 - r549416;
        double r549418 = sqrt(r549417);
        double r549419 = r549410 + r549418;
        double r549420 = 2.0;
        double r549421 = r549420 * r549413;
        double r549422 = r549419 / r549421;
        return r549422;
}
↓
double f(double __attribute__((unused)) a, double b, double c) {
        double r549423 = c;
        double r549424 = b;
        double r549425 = r549423 / r549424;
        double r549426 = -r549425;
        return r549426;
}

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 52.7

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

  2. Simplified52.7

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

  3. Taylor expanded around inf 6.0

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

  4. Simplified6.0

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

  5. Final simplification6.0

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

Reproduce

herbie shell --seed 2019133 
(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)))