Average Error: 43.1 → 0.4
Time: 17.9s
Precision: 64
\[1.1102230246251565404236316680908203125 \cdot 10^{-16} \lt a \lt 9007199254740992 \land 1.1102230246251565404236316680908203125 \cdot 10^{-16} \lt b \lt 9007199254740992 \land 1.1102230246251565404236316680908203125 \cdot 10^{-16} \lt c \lt 9007199254740992\]
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
↓
\[\frac{\frac{4 \cdot \left(c \cdot a\right)}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)}}}{a \cdot 2}\]
\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}
↓
\frac{\frac{4 \cdot \left(c \cdot a\right)}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)}}}{a \cdot 2}
double f(double a, double b, double c) {
        double r44427 = b;
        double r44428 = -r44427;
        double r44429 = r44427 * r44427;
        double r44430 = 4.0;
        double r44431 = a;
        double r44432 = r44430 * r44431;
        double r44433 = c;
        double r44434 = r44432 * r44433;
        double r44435 = r44429 - r44434;
        double r44436 = sqrt(r44435);
        double r44437 = r44428 + r44436;
        double r44438 = 2.0;
        double r44439 = r44438 * r44431;
        double r44440 = r44437 / r44439;
        return r44440;
}
↓
double f(double a, double b, double c) {
        double r44441 = 4.0;
        double r44442 = c;
        double r44443 = a;
        double r44444 = r44442 * r44443;
        double r44445 = r44441 * r44444;
        double r44446 = b;
        double r44447 = -r44446;
        double r44448 = r44446 * r44446;
        double r44449 = r44448 - r44445;
        double r44450 = sqrt(r44449);
        double r44451 = r44447 - r44450;
        double r44452 = r44445 / r44451;
        double r44453 = 2.0;
        double r44454 = r44443 * r44453;
        double r44455 = r44452 / r44454;
        return r44455;
}

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 43.1

    \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
  2. Using strategy rm

  3. Applied flip-+43.1

    \[\leadsto \frac{\color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a}\]

  4. Simplified0.4

    \[\leadsto \frac{\frac{\color{blue}{0 + 4 \cdot \left(c \cdot a\right)}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\]

  5. Simplified0.4

    \[\leadsto \frac{\frac{0 + 4 \cdot \left(c \cdot a\right)}{\color{blue}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)}}}}{2 \cdot a}\]
  6. Using strategy rm

  7. Applied pow10.4

    \[\leadsto \frac{\frac{0 + 4 \cdot \left(c \cdot a\right)}{\color{blue}{{\left(\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)}\right)}^{1}}}}{2 \cdot a}\]

  8. Final simplification0.4

    \[\leadsto \frac{\frac{4 \cdot \left(c \cdot a\right)}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)}}}{a \cdot 2}\]

Reproduce

herbie shell --seed 2019194 
(FPCore (a b c)
  :name "Quadratic roots, medium range"
  :pre (and (< 1.1102230246251565e-16 a 9007199254740992.0) (< 1.1102230246251565e-16 b 9007199254740992.0) (< 1.1102230246251565e-16 c 9007199254740992.0))
  (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)))