Average Error: 0.1 → 0.1
Time: 33.4s
Precision: 64
\[0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{1 + {\left(\cos v \cdot e\right)}^{3}} \cdot \left(\left(\cos v \cdot e + -1\right) \cdot \left(\cos v \cdot e\right) - -1\right)\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e \cdot \sin v}{1 + {\left(\cos v \cdot e\right)}^{3}} \cdot \left(\left(\cos v \cdot e + -1\right) \cdot \left(\cos v \cdot e\right) - -1\right)
double f(double e, double v) {
        double r1188410 = e;
        double r1188411 = v;
        double r1188412 = sin(r1188411);
        double r1188413 = r1188410 * r1188412;
        double r1188414 = 1.0;
        double r1188415 = cos(r1188411);
        double r1188416 = r1188410 * r1188415;
        double r1188417 = r1188414 + r1188416;
        double r1188418 = r1188413 / r1188417;
        return r1188418;
}
↓
double f(double e, double v) {
        double r1188419 = e;
        double r1188420 = v;
        double r1188421 = sin(r1188420);
        double r1188422 = r1188419 * r1188421;
        double r1188423 = 1.0;
        double r1188424 = cos(r1188420);
        double r1188425 = r1188424 * r1188419;
        double r1188426 = 3.0;
        double r1188427 = pow(r1188425, r1188426);
        double r1188428 = r1188423 + r1188427;
        double r1188429 = r1188422 / r1188428;
        double r1188430 = -1.0;
        double r1188431 = r1188425 + r1188430;
        double r1188432 = r1188431 * r1188425;
        double r1188433 = r1188432 - r1188430;
        double r1188434 = r1188429 * r1188433;
        return r1188434;
}

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 flip3-+0.1

    \[\leadsto \frac{e \cdot \sin v}{\color{blue}{\frac{{1}^{3} + {\left(e \cdot \cos v\right)}^{3}}{1 \cdot 1 + \left(\left(e \cdot \cos v\right) \cdot \left(e \cdot \cos v\right) - 1 \cdot \left(e \cdot \cos v\right)\right)}}}\]

  4. Applied associate-/r/0.1

    \[\leadsto \color{blue}{\frac{e \cdot \sin v}{{1}^{3} + {\left(e \cdot \cos v\right)}^{3}} \cdot \left(1 \cdot 1 + \left(\left(e \cdot \cos v\right) \cdot \left(e \cdot \cos v\right) - 1 \cdot \left(e \cdot \cos v\right)\right)\right)}\]

  5. Simplified0.1

    \[\leadsto \frac{e \cdot \sin v}{{1}^{3} + {\left(e \cdot \cos v\right)}^{3}} \cdot \color{blue}{\left(\left(\cos v \cdot e + -1\right) \cdot \left(\cos v \cdot e\right) - -1\right)}\]

  6. Final simplification0.1

    \[\leadsto \frac{e \cdot \sin v}{1 + {\left(\cos v \cdot e\right)}^{3}} \cdot \left(\left(\cos v \cdot e + -1\right) \cdot \left(\cos v \cdot e\right) - -1\right)\]

Reproduce

herbie shell --seed 2019112 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))