Average Error: 52.3 → 6.3
Time: 17.3s
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 r2850420 = b;
        double r2850421 = -r2850420;
        double r2850422 = r2850420 * r2850420;
        double r2850423 = 3.0;
        double r2850424 = a;
        double r2850425 = r2850423 * r2850424;
        double r2850426 = c;
        double r2850427 = r2850425 * r2850426;
        double r2850428 = r2850422 - r2850427;
        double r2850429 = sqrt(r2850428);
        double r2850430 = r2850421 + r2850429;
        double r2850431 = r2850430 / r2850425;
        return r2850431;
}
↓
double f(double __attribute__((unused)) a, double b, double c, double __attribute__((unused)) d) {
        double r2850432 = c;
        double r2850433 = b;
        double r2850434 = r2850432 / r2850433;
        double r2850435 = -0.5;
        double r2850436 = r2850434 * r2850435;
        return r2850436;
}

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 52.3

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

  2. Simplified52.3

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

  3. Taylor expanded around inf 6.3

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

  4. Final simplification6.3

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

Reproduce

herbie shell --seed 2019130 
(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)))