Average Error: 29.6 → 29.6
Time: 1.7s
Precision: binary64
\[\frac{\left(3 \cdot a\right) \cdot c - b \cdot b}{\left(\left(3 \cdot a\right) \cdot a\right) \cdot a}\]
↓
\[\frac{\frac{\left(3 \cdot a\right) \cdot c - b \cdot b}{3}}{{a}^{3}}\]
\frac{\left(3 \cdot a\right) \cdot c - b \cdot b}{\left(\left(3 \cdot a\right) \cdot a\right) \cdot a}
↓
\frac{\frac{\left(3 \cdot a\right) \cdot c - b \cdot b}{3}}{{a}^{3}}
double code(double a, double c, double b) {
	return ((double) (((double) (((double) (((double) (3.0 * a)) * c)) - ((double) (b * b)))) / ((double) (((double) (((double) (3.0 * a)) * a)) * a))));
}
↓
double code(double a, double c, double b) {
	return ((double) (((double) (((double) (((double) (((double) (3.0 * a)) * c)) - ((double) (b * b)))) / 3.0)) / ((double) pow(a, 3.0))));
}

Error

Bits error versus a

Bits error versus c

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.6

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

  2. Simplified29.6

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

  3. Final simplification29.6

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

Reproduce

herbie shell --seed 2020153 
(FPCore (a c b)
  :name "(/ (- (* (* 3 a) c) (* b b)) (* (* (* 3 a) a) a))"
  :precision binary64
  (/ (- (* (* 3.0 a) c) (* b b)) (* (* (* 3.0 a) a) a)))