Average Error: 43.8 → 0.3
Time: 5.1s
Precision: binary64
\[1.1102230246251565 \cdot 10^{-16} \lt a \lt 9007199254740992 \land 1.1102230246251565 \cdot 10^{-16} \lt b \lt 9007199254740992 \land 1.1102230246251565 \cdot 10^{-16} \lt c \lt 9007199254740992\]
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]
↓
\[\frac{1}{\frac{\left(-b\right) - \sqrt{b \cdot b - 3 \cdot \left(a \cdot c\right)}}{c}}\]
\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}
↓
\frac{1}{\frac{\left(-b\right) - \sqrt{b \cdot b - 3 \cdot \left(a \cdot c\right)}}{c}}
double code(double a, double b, double c) {
	return ((double) (((double) (((double) -(b)) + ((double) sqrt(((double) (((double) (b * b)) - ((double) (((double) (3.0 * a)) * c)))))))) / ((double) (3.0 * a))));
}
↓
double code(double a, double b, double c) {
	return ((double) (1.0 / ((double) (((double) (((double) -(b)) - ((double) sqrt(((double) (((double) (b * b)) - ((double) (3.0 * ((double) (a * c)))))))))) / c))));
}

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 43.8

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

  3. Applied flip-+43.8

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

  4. Simplified0.5

    \[\leadsto \frac{\frac{\color{blue}{3 \cdot \left(a \cdot c\right) + 0}}{\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}}{3 \cdot a}\]

  5. Simplified0.5

    \[\leadsto \frac{\frac{3 \cdot \left(a \cdot c\right) + 0}{\color{blue}{\left(-b\right) - \sqrt{b \cdot b - 3 \cdot \left(a \cdot c\right)}}}}{3 \cdot a}\]
  6. Using strategy rm

  7. Applied clear-num0.6

    \[\leadsto \color{blue}{\frac{1}{\frac{3 \cdot a}{\frac{3 \cdot \left(a \cdot c\right) + 0}{\left(-b\right) - \sqrt{b \cdot b - 3 \cdot \left(a \cdot c\right)}}}}}\]

  8. Simplified0.3

    \[\leadsto \frac{1}{\color{blue}{\frac{\left(-b\right) - \sqrt{b \cdot b - 3 \cdot \left(a \cdot c\right)}}{c}}}\]

  9. Final simplification0.3

    \[\leadsto \frac{1}{\frac{\left(-b\right) - \sqrt{b \cdot b - 3 \cdot \left(a \cdot c\right)}}{c}}\]

Reproduce

herbie shell --seed 2020184 
(FPCore (a b c)
  :name "Cubic critical, medium range"
  :precision binary64
  :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)))