Average Error: 0.1 → 0.3
Time: 4.8s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e}{\frac{1 + e \cdot \cos v}{\sin v}}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e}{\frac{1 + e \cdot \cos v}{\sin v}}
double code(double e, double v) {
	return ((e * sin(v)) / (1.0 + (e * cos(v))));
}
↓
double code(double e, double v) {
	return (e / ((1.0 + (e * cos(v))) / sin(v)));
}

Error

Bits error versus e

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
  2. Using strategy rm

  3. Applied associate-/l*0.3

    \[\leadsto \color{blue}{\frac{e}{\frac{1 + e \cdot \cos v}{\sin v}}}\]

  4. Final simplification0.3

    \[\leadsto \frac{e}{\frac{1 + e \cdot \cos v}{\sin v}}\]

Reproduce

herbie shell --seed 2020091 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))