Average Error: 14.1 → 14.1
Time: 1.9s
Precision: binary64
\[\frac{a \cdot \left(1 - {e}^{2}\right)}{1 - e \cdot \cos b}\]
↓
\[\frac{a \cdot \left(1 - {e}^{2}\right)}{1 - e \cdot \cos b}\]
\frac{a \cdot \left(1 - {e}^{2}\right)}{1 - e \cdot \cos b}
↓
\frac{a \cdot \left(1 - {e}^{2}\right)}{1 - e \cdot \cos b}
double code(double a, double e, double b) {
	return ((double) (((double) (a * ((double) (1.0 - ((double) pow(e, 2.0)))))) / ((double) (1.0 - ((double) (e * ((double) cos(b))))))));
}
↓
double code(double a, double e, double b) {
	return ((double) (((double) (a * ((double) (1.0 - ((double) pow(e, 2.0)))))) / ((double) (1.0 - ((double) (e * ((double) cos(b))))))));
}

Error

Bits error versus a

Bits error versus e

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.1

    \[\frac{a \cdot \left(1 - {e}^{2}\right)}{1 - e \cdot \cos b}\]

  2. Final simplification14.1

    \[\leadsto \frac{a \cdot \left(1 - {e}^{2}\right)}{1 - e \cdot \cos b}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (a e b)
  :name "(/ (* a (- 1.0 (pow e 2))) (- 1.0 (* e (cos b))))"
  :precision binary64
  (/ (* a (- 1.0 (pow e 2.0))) (- 1.0 (* e (cos b)))))