Average Error: 43.9 → 0.4
Time: 6.4s
Precision: 64
\[1.1102230246251565404236316680908203125 \cdot 10^{-16} \lt a \lt 9007199254740992 \land 1.1102230246251565404236316680908203125 \cdot 10^{-16} \lt b \lt 9007199254740992 \land 1.1102230246251565404236316680908203125 \cdot 10^{-16} \lt c \lt 9007199254740992\]
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]
↓
\[\frac{\frac{\left({b}^{2} - {b}^{2}\right) + \left(3 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}}{3 \cdot a}\]
\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 r121474 = b;
        double r121475 = -r121474;
        double r121476 = r121474 * r121474;
        double r121477 = 3.0;
        double r121478 = a;
        double r121479 = r121477 * r121478;
        double r121480 = c;
        double r121481 = r121479 * r121480;
        double r121482 = r121476 - r121481;
        double r121483 = sqrt(r121482);
        double r121484 = r121475 + r121483;
        double r121485 = r121484 / r121479;
        return r121485;
}
↓
double f(double a, double b, double c) {
        double r121486 = b;
        double r121487 = 2.0;
        double r121488 = pow(r121486, r121487);
        double r121489 = r121488 - r121488;
        double r121490 = 3.0;
        double r121491 = a;
        double r121492 = r121490 * r121491;
        double r121493 = c;
        double r121494 = r121492 * r121493;
        double r121495 = r121489 + r121494;
        double r121496 = -r121486;
        double r121497 = r121486 * r121486;
        double r121498 = r121497 - r121494;
        double r121499 = sqrt(r121498);
        double r121500 = r121496 - r121499;
        double r121501 = r121495 / r121500;
        double r121502 = r121501 / r121492;
        return r121502;
}

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 43.9

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

  3. Applied flip-+43.9

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

  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 2019353 
(FPCore (a b c)
  :name "Cubic critical, medium range"
  :precision binary64
  :pre (and (< 1.11022e-16 a 9.0072e+15) (< 1.11022e-16 b 9.0072e+15) (< 1.11022e-16 c 9.0072e+15))
  (/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a)))