Average Error: 52.5 → 0.4
Time: 6.2s
Precision: 64
\[4.93038 \cdot 10^{-32} \lt a \lt 2.02824 \cdot 10^{31} \land 4.93038 \cdot 10^{-32} \lt b \lt 2.02824 \cdot 10^{31} \land 4.93038 \cdot 10^{-32} \lt c \lt 2.02824 \cdot 10^{31}\]
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]
↓
\[\frac{\frac{\left({b}^{2} - {b}^{2}\right) + \left(3 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}}{3 \cdot a}\]
\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}
↓
\frac{\frac{\left({b}^{2} - {b}^{2}\right) + \left(3 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}}{3 \cdot a}
double f(double a, double b, double c) {
        double r73074 = b;
        double r73075 = -r73074;
        double r73076 = r73074 * r73074;
        double r73077 = 3.0;
        double r73078 = a;
        double r73079 = r73077 * r73078;
        double r73080 = c;
        double r73081 = r73079 * r73080;
        double r73082 = r73076 - r73081;
        double r73083 = sqrt(r73082);
        double r73084 = r73075 + r73083;
        double r73085 = r73084 / r73079;
        return r73085;
}
↓
double f(double a, double b, double c) {
        double r73086 = b;
        double r73087 = 2.0;
        double r73088 = pow(r73086, r73087);
        double r73089 = r73088 - r73088;
        double r73090 = 3.0;
        double r73091 = a;
        double r73092 = r73090 * r73091;
        double r73093 = c;
        double r73094 = r73092 * r73093;
        double r73095 = r73089 + r73094;
        double r73096 = -r73086;
        double r73097 = r73086 * r73086;
        double r73098 = r73097 - r73094;
        double r73099 = sqrt(r73098);
        double r73100 = r73096 - r73099;
        double r73101 = r73095 / r73100;
        double r73102 = r73101 / r73092;
        return r73102;
}

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

    \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]
  2. Using strategy rm

  3. Applied flip-+52.5

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

  4. Simplified0.5

    \[\leadsto \frac{\frac{\color{blue}{\left({b}^{2} - {b}^{2}\right) + 3 \cdot \left(a \cdot c\right)}}{\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}}{3 \cdot a}\]
  5. Using strategy rm

  6. Applied associate-*r*0.4

    \[\leadsto \frac{\frac{\left({b}^{2} - {b}^{2}\right) + \color{blue}{\left(3 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}}{3 \cdot a}\]

  7. Final simplification0.4

    \[\leadsto \frac{\frac{\left({b}^{2} - {b}^{2}\right) + \left(3 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}}{3 \cdot a}\]

Reproduce

herbie shell --seed 2020018 
(FPCore (a b c)
  :name "Cubic critical, wide range"
  :precision binary64
  :pre (and (< 4.9303800000000003e-32 a 2.02824e+31) (< 4.9303800000000003e-32 b 2.02824e+31) (< 4.9303800000000003e-32 c 2.02824e+31))
  (/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a)))