Average Error: 0.1 → 0.1
Time: 17.0s
Precision: 64
\[0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{\cos v \cdot e + 1}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e \cdot \sin v}{\cos v \cdot e + 1}
double f(double e, double v) {
        double r318141 = e;
        double r318142 = v;
        double r318143 = sin(r318142);
        double r318144 = r318141 * r318143;
        double r318145 = 1.0;
        double r318146 = cos(r318142);
        double r318147 = r318141 * r318146;
        double r318148 = r318145 + r318147;
        double r318149 = r318144 / r318148;
        return r318149;
}
↓
double f(double e, double v) {
        double r318150 = e;
        double r318151 = v;
        double r318152 = sin(r318151);
        double r318153 = r318150 * r318152;
        double r318154 = cos(r318151);
        double r318155 = r318154 * r318150;
        double r318156 = 1.0;
        double r318157 = r318155 + r318156;
        double r318158 = r318153 / r318157;
        return r318158;
}

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

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

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))