Average Error: 52.5 → 6.2
Time: 15.4s
Precision: 64
\[4.930380657631324 \cdot 10^{-32} \lt a \lt 2.028240960365167 \cdot 10^{+31} \land 4.930380657631324 \cdot 10^{-32} \lt b \lt 2.028240960365167 \cdot 10^{+31} \land 4.930380657631324 \cdot 10^{-32} \lt c \lt 2.028240960365167 \cdot 10^{+31}\]
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
↓
\[-\frac{c}{b}\]
\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 r501292 = b;
        double r501293 = -r501292;
        double r501294 = r501292 * r501292;
        double r501295 = 4.0;
        double r501296 = a;
        double r501297 = r501295 * r501296;
        double r501298 = c;
        double r501299 = r501297 * r501298;
        double r501300 = r501294 - r501299;
        double r501301 = sqrt(r501300);
        double r501302 = r501293 + r501301;
        double r501303 = 2.0;
        double r501304 = r501303 * r501296;
        double r501305 = r501302 / r501304;
        return r501305;
}
↓
double f(double __attribute__((unused)) a, double b, double c) {
        double r501306 = c;
        double r501307 = b;
        double r501308 = r501306 / r501307;
        double r501309 = -r501308;
        return r501309;
}

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. Simplified6.2

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

  5. Final simplification6.2

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

Reproduce

herbie shell --seed 2019129 
(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)))