Average Error: 19.4 → 19.4
Time: 1.8s
Precision: binary64
\[\frac{9 \cdot ac - 3 \cdot {b}^{2}}{9 \cdot {a}^{2}}\]
↓
\[\frac{9 \cdot ac - 3 \cdot {b}^{2}}{9 \cdot {a}^{2}}\]
\frac{9 \cdot ac - 3 \cdot {b}^{2}}{9 \cdot {a}^{2}}
↓
\frac{9 \cdot ac - 3 \cdot {b}^{2}}{9 \cdot {a}^{2}}
double code(double ac, double b, double a) {
	return ((double) (((double) (((double) (9.0 * ac)) - ((double) (3.0 * ((double) pow(b, 2.0)))))) / ((double) (9.0 * ((double) pow(a, 2.0))))));
}
↓
double code(double ac, double b, double a) {
	return ((double) (((double) (((double) (9.0 * ac)) - ((double) (3.0 * ((double) pow(b, 2.0)))))) / ((double) (9.0 * ((double) pow(a, 2.0))))));
}

Error

Bits error versus ac

Bits error versus b

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 19.4

    \[\frac{9 \cdot ac - 3 \cdot {b}^{2}}{9 \cdot {a}^{2}}\]

  2. Final simplification19.4

    \[\leadsto \frac{9 \cdot ac - 3 \cdot {b}^{2}}{9 \cdot {a}^{2}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (ac b a)
  :name "(/ (- (* 9 ac) (* 3 (pow b 2))) (* 9 (pow a 2)))"
  :precision binary64
  (/ (- (* 9.0 ac) (* 3.0 (pow b 2.0))) (* 9.0 (pow a 2.0))))