Average Error: 52.7 → 6.0
Time: 18.9s
Precision: 64
\[4.930380657631324 \cdot 10^{-32} \lt a \lt 2.028240960365167 \cdot 10^{+31} \land 4.930380657631324 \cdot 10^{-32} \lt b \lt 2.028240960365167 \cdot 10^{+31} \land 4.930380657631324 \cdot 10^{-32} \lt c \lt 2.028240960365167 \cdot 10^{+31}\]
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]
↓
\[\frac{c}{b} \cdot \frac{-1}{2}\]
\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}
↓
\frac{c}{b} \cdot \frac{-1}{2}
double f(double a, double b, double c, double __attribute__((unused)) d) {
        double r2455253 = b;
        double r2455254 = -r2455253;
        double r2455255 = r2455253 * r2455253;
        double r2455256 = 3.0;
        double r2455257 = a;
        double r2455258 = r2455256 * r2455257;
        double r2455259 = c;
        double r2455260 = r2455258 * r2455259;
        double r2455261 = r2455255 - r2455260;
        double r2455262 = sqrt(r2455261);
        double r2455263 = r2455254 + r2455262;
        double r2455264 = r2455263 / r2455258;
        return r2455264;
}
↓
double f(double __attribute__((unused)) a, double b, double c, double __attribute__((unused)) d) {
        double r2455265 = c;
        double r2455266 = b;
        double r2455267 = r2455265 / r2455266;
        double r2455268 = -0.5;
        double r2455269 = r2455267 * r2455268;
        return r2455269;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 52.7

    \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]

  2. Taylor expanded around inf 6.0

    \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{c}{b}}\]

  3. Final simplification6.0

    \[\leadsto \frac{c}{b} \cdot \frac{-1}{2}\]

Reproduce

herbie shell --seed 2019134 +o rules:numerics
(FPCore (a b c d)
  :name "Cubic critical, 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) (* (* 3 a) c)))) (* 3 a)))