Average Error: 52.2 → 6.4
Time: 32.4s
Precision: 64
\[4.930380657631324 \cdot 10^{-32} \lt a \lt 2.028240960365167 \cdot 10^{+31} \land 4.930380657631324 \cdot 10^{-32} \lt b \lt 2.028240960365167 \cdot 10^{+31} \land 4.930380657631324 \cdot 10^{-32} \lt c \lt 2.028240960365167 \cdot 10^{+31}\]
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]
↓
\[\frac{c}{b} \cdot \frac{-1}{2}\]
\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 r3445789 = b;
        double r3445790 = -r3445789;
        double r3445791 = r3445789 * r3445789;
        double r3445792 = 3.0;
        double r3445793 = a;
        double r3445794 = r3445792 * r3445793;
        double r3445795 = c;
        double r3445796 = r3445794 * r3445795;
        double r3445797 = r3445791 - r3445796;
        double r3445798 = sqrt(r3445797);
        double r3445799 = r3445790 + r3445798;
        double r3445800 = r3445799 / r3445794;
        return r3445800;
}
↓
double f(double __attribute__((unused)) a, double b, double c) {
        double r3445801 = c;
        double r3445802 = b;
        double r3445803 = r3445801 / r3445802;
        double r3445804 = -0.5;
        double r3445805 = r3445803 * r3445804;
        return r3445805;
}

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 52.2

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

  2. Simplified52.2

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

  3. Taylor expanded around inf 6.4

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

  4. Final simplification6.4

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

Reproduce

herbie shell --seed 2019144 
(FPCore (a b c)
  :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)))