Average Error: 52.7 → 6.0
Time: 20.7s
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 r2284607 = b;
        double r2284608 = -r2284607;
        double r2284609 = r2284607 * r2284607;
        double r2284610 = 3.0;
        double r2284611 = a;
        double r2284612 = r2284610 * r2284611;
        double r2284613 = c;
        double r2284614 = r2284612 * r2284613;
        double r2284615 = r2284609 - r2284614;
        double r2284616 = sqrt(r2284615);
        double r2284617 = r2284608 + r2284616;
        double r2284618 = r2284617 / r2284612;
        return r2284618;
}
↓
double f(double __attribute__((unused)) a, double b, double c, double __attribute__((unused)) d) {
        double r2284619 = c;
        double r2284620 = b;
        double r2284621 = r2284619 / r2284620;
        double r2284622 = -0.5;
        double r2284623 = r2284621 * r2284622;
        return r2284623;
}

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. Simplified52.7

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

  3. Taylor expanded around inf 6.0

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

  4. Final simplification6.0

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

Reproduce

herbie shell --seed 2019134 
(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)))