Average Error: 43.9 → 0.4
Time: 18.3s
Precision: 64
\[1.1102230246251565404236316680908203125 \cdot 10^{-16} \lt a \lt 9007199254740992 \land 1.1102230246251565404236316680908203125 \cdot 10^{-16} \lt b \lt 9007199254740992 \land 1.1102230246251565404236316680908203125 \cdot 10^{-16} \lt c \lt 9007199254740992\]
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
↓
\[\frac{\left(a \cdot 4\right) \cdot c}{\left(a \cdot \left(\left(-b\right) - \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}\right)\right) \cdot 2}\]
\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}
↓
\frac{\left(a \cdot 4\right) \cdot c}{\left(a \cdot \left(\left(-b\right) - \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}\right)\right) \cdot 2}
double f(double a, double b, double c) {
        double r40045 = b;
        double r40046 = -r40045;
        double r40047 = r40045 * r40045;
        double r40048 = 4.0;
        double r40049 = a;
        double r40050 = r40048 * r40049;
        double r40051 = c;
        double r40052 = r40050 * r40051;
        double r40053 = r40047 - r40052;
        double r40054 = sqrt(r40053);
        double r40055 = r40046 + r40054;
        double r40056 = 2.0;
        double r40057 = r40056 * r40049;
        double r40058 = r40055 / r40057;
        return r40058;
}
↓
double f(double a, double b, double c) {
        double r40059 = a;
        double r40060 = 4.0;
        double r40061 = r40059 * r40060;
        double r40062 = c;
        double r40063 = r40061 * r40062;
        double r40064 = b;
        double r40065 = -r40064;
        double r40066 = r40064 * r40064;
        double r40067 = r40062 * r40059;
        double r40068 = r40067 * r40060;
        double r40069 = r40066 - r40068;
        double r40070 = sqrt(r40069);
        double r40071 = r40065 - r40070;
        double r40072 = r40059 * r40071;
        double r40073 = 2.0;
        double r40074 = r40072 * r40073;
        double r40075 = r40063 / r40074;
        return r40075;
}

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

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

  3. Applied flip-+43.9

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

  4. Simplified0.4

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

  6. Applied div-inv0.5

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

  7. Applied associate-/l*0.5

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

  8. Simplified0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019196 
(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)))