Average Error: 43.9 → 0.4
Time: 19.5s
Precision: 64
\[1.1102230246251565404236316680908203125 \cdot 10^{-16} \lt a \lt 9007199254740992 \land 1.1102230246251565404236316680908203125 \cdot 10^{-16} \lt b \lt 9007199254740992 \land 1.1102230246251565404236316680908203125 \cdot 10^{-16} \lt c \lt 9007199254740992\]
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]
↓
\[\frac{\frac{c \cdot \left(a \cdot 3\right) + \left(b \cdot b - b \cdot b\right)}{\left(-b\right) - \sqrt{b \cdot b - c \cdot \left(a \cdot 3\right)}}}{a \cdot 3}\]
\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}
↓
\frac{\frac{c \cdot \left(a \cdot 3\right) + \left(b \cdot b - b \cdot b\right)}{\left(-b\right) - \sqrt{b \cdot b - c \cdot \left(a \cdot 3\right)}}}{a \cdot 3}
double f(double a, double b, double c) {
        double r60398 = b;
        double r60399 = -r60398;
        double r60400 = r60398 * r60398;
        double r60401 = 3.0;
        double r60402 = a;
        double r60403 = r60401 * r60402;
        double r60404 = c;
        double r60405 = r60403 * r60404;
        double r60406 = r60400 - r60405;
        double r60407 = sqrt(r60406);
        double r60408 = r60399 + r60407;
        double r60409 = r60408 / r60403;
        return r60409;
}
↓
double f(double a, double b, double c) {
        double r60410 = c;
        double r60411 = a;
        double r60412 = 3.0;
        double r60413 = r60411 * r60412;
        double r60414 = r60410 * r60413;
        double r60415 = b;
        double r60416 = r60415 * r60415;
        double r60417 = r60416 - r60416;
        double r60418 = r60414 + r60417;
        double r60419 = -r60415;
        double r60420 = r60416 - r60414;
        double r60421 = sqrt(r60420);
        double r60422 = r60419 - r60421;
        double r60423 = r60418 / r60422;
        double r60424 = r60423 / r60413;
        return r60424;
}

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. Simplified0.4

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

  5. Simplified0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019179 
(FPCore (a b c)
  :name "Cubic critical, 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) (* (* 3.0 a) c)))) (* 3.0 a)))