Average Error: 0.1 → 0.1
Time: 6.5s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e}{1 + e \cdot \cos v} \cdot \sin v\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e}{1 + e \cdot \cos v} \cdot \sin v
double f(double e, double v) {
        double r10364 = e;
        double r10365 = v;
        double r10366 = sin(r10365);
        double r10367 = r10364 * r10366;
        double r10368 = 1.0;
        double r10369 = cos(r10365);
        double r10370 = r10364 * r10369;
        double r10371 = r10368 + r10370;
        double r10372 = r10367 / r10371;
        return r10372;
}
↓
double f(double e, double v) {
        double r10373 = e;
        double r10374 = 1.0;
        double r10375 = v;
        double r10376 = cos(r10375);
        double r10377 = r10373 * r10376;
        double r10378 = r10374 + r10377;
        double r10379 = r10373 / r10378;
        double r10380 = sin(r10375);
        double r10381 = r10379 * r10380;
        return r10381;
}

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. Using strategy rm

  5. Applied associate-/r/0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020047 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))