Average Error: 52.3 → 0.4
Time: 6.8s
Precision: 64
\[4.93038 \cdot 10^{-32} \lt a \lt 2.02824 \cdot 10^{31} \land 4.93038 \cdot 10^{-32} \lt b \lt 2.02824 \cdot 10^{31} \land 4.93038 \cdot 10^{-32} \lt c \lt 2.02824 \cdot 10^{31}\]
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
↓
\[\frac{\frac{0 + 4 \cdot \left(a \cdot c\right)}{\left(-b\right) - \sqrt{\frac{{b}^{4} - \left(4 \cdot \left(a \cdot c\right)\right) \cdot \left(4 \cdot \left(a \cdot c\right)\right)}{b \cdot b + \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a}\]
\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}
↓
\frac{\frac{0 + 4 \cdot \left(a \cdot c\right)}{\left(-b\right) - \sqrt{\frac{{b}^{4} - \left(4 \cdot \left(a \cdot c\right)\right) \cdot \left(4 \cdot \left(a \cdot c\right)\right)}{b \cdot b + \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a}
double f(double a, double b, double c) {
        double r36611 = b;
        double r36612 = -r36611;
        double r36613 = r36611 * r36611;
        double r36614 = 4.0;
        double r36615 = a;
        double r36616 = r36614 * r36615;
        double r36617 = c;
        double r36618 = r36616 * r36617;
        double r36619 = r36613 - r36618;
        double r36620 = sqrt(r36619);
        double r36621 = r36612 + r36620;
        double r36622 = 2.0;
        double r36623 = r36622 * r36615;
        double r36624 = r36621 / r36623;
        return r36624;
}
↓
double f(double a, double b, double c) {
        double r36625 = 0.0;
        double r36626 = 4.0;
        double r36627 = a;
        double r36628 = c;
        double r36629 = r36627 * r36628;
        double r36630 = r36626 * r36629;
        double r36631 = r36625 + r36630;
        double r36632 = b;
        double r36633 = -r36632;
        double r36634 = 4.0;
        double r36635 = pow(r36632, r36634);
        double r36636 = r36630 * r36630;
        double r36637 = r36635 - r36636;
        double r36638 = r36632 * r36632;
        double r36639 = r36626 * r36627;
        double r36640 = r36639 * r36628;
        double r36641 = r36638 + r36640;
        double r36642 = r36637 / r36641;
        double r36643 = sqrt(r36642);
        double r36644 = r36633 - r36643;
        double r36645 = r36631 / r36644;
        double r36646 = 2.0;
        double r36647 = r36646 * r36627;
        double r36648 = r36645 / r36647;
        return r36648;
}

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 52.3

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

  3. Applied flip-+52.3

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

  4. Simplified0.4

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

  6. Applied flip--0.4

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

  7. Simplified0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2020060 
(FPCore (a b c)
  :name "Quadratic roots, 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) (* (* 4 a) c)))) (* 2 a)))