Average Error: 0.1 → 0.1
Time: 4.9s
Precision: binary64
\[0 \leq e \land e \leq 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\left(e \cdot \sin v\right) \cdot \frac{1}{1 + e \cdot \cos v}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\left(e \cdot \sin v\right) \cdot \frac{1}{1 + e \cdot \cos v}
(FPCore (e v) :precision binary64 (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))
↓
(FPCore (e v)
 :precision binary64
 (* (* e (sin v)) (/ 1.0 (+ 1.0 (* e (cos v))))))
double code(double e, double v) {
	return (((double) (e * ((double) sin(v)))) / ((double) (1.0 + ((double) (e * ((double) cos(v)))))));
}
↓
double code(double e, double v) {
	return ((double) (((double) (e * ((double) sin(v)))) * (1.0 / ((double) (1.0 + ((double) (e * ((double) cos(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 Error: 0.1 bits

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

  2. SimplifiedError: 0.1 bits

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

  4. Applied div-invError: 0.1 bits

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

  5. Applied associate-*r*Error: 0.1 bits

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

  6. Final simplificationError: 0.1 bits

    \[\leadsto \left(e \cdot \sin v\right) \cdot \frac{1}{1 + e \cdot \cos v}\]

Reproduce

herbie shell --seed 2020203 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1.0)
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))