Average Error: 0.1 → 0.1
Time: 15.9s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
double f(double e, double v) {
        double r25468 = e;
        double r25469 = v;
        double r25470 = sin(r25469);
        double r25471 = r25468 * r25470;
        double r25472 = 1.0;
        double r25473 = cos(r25469);
        double r25474 = r25468 * r25473;
        double r25475 = r25472 + r25474;
        double r25476 = r25471 / r25475;
        return r25476;
}
↓
double f(double e, double v) {
        double r25477 = e;
        double r25478 = v;
        double r25479 = sin(r25478);
        double r25480 = r25477 * r25479;
        double r25481 = 1.0;
        double r25482 = cos(r25478);
        double r25483 = r25477 * r25482;
        double r25484 = r25481 + r25483;
        double r25485 = r25480 / r25484;
        return r25485;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019235 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))