Average Error: 0.1 → 0.3
Time: 5.0s
Precision: binary64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e}{\frac{e \cdot \cos v + 1}{\sin v}}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e}{\frac{e \cdot \cos v + 1}{\sin v}}
double code(double e, double v) {
	return ((double) (((double) (e * ((double) sin(v)))) / ((double) (1.0 + ((double) (e * ((double) cos(v))))))));
}
↓
double code(double e, double v) {
	return ((double) (e / ((double) (((double) (((double) (e * ((double) cos(v)))) + 1.0)) / ((double) 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. Simplified0.1

    \[\leadsto \color{blue}{e \cdot \frac{\sin v}{1 + e \cdot \cos v}}\]
  3. Using strategy rm

  4. Applied clear-num0.2

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

  5. Simplified0.2

    \[\leadsto e \cdot \frac{1}{\color{blue}{\frac{e \cdot \cos v + 1}{\sin v}}}\]
  6. Using strategy rm

  7. Applied un-div-inv0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2020179 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1.0)
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))