Average Error: 0.1 → 0.1
Time: 10.9s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e}{\cos v \cdot e + 1} \cdot \sin v\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e}{\cos v \cdot e + 1} \cdot \sin v
double f(double e, double v) {
        double r10240 = e;
        double r10241 = v;
        double r10242 = sin(r10241);
        double r10243 = r10240 * r10242;
        double r10244 = 1.0;
        double r10245 = cos(r10241);
        double r10246 = r10240 * r10245;
        double r10247 = r10244 + r10246;
        double r10248 = r10243 / r10247;
        return r10248;
}
↓
double f(double e, double v) {
        double r10249 = e;
        double r10250 = v;
        double r10251 = cos(r10250);
        double r10252 = r10251 * r10249;
        double r10253 = 1.0;
        double r10254 = r10252 + r10253;
        double r10255 = r10249 / r10254;
        double r10256 = sin(r10250);
        double r10257 = r10255 * r10256;
        return r10257;
}

Error

Bits error versus e

Bits error versus v

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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. Simplified0.3

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

  6. Applied associate-/r/0.1

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

  7. Final simplification0.1

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

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)))))