Trigonometry A

Average Error: 0.1 → 0.1

Time: 12.4s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

\[0.0 \le e \le 1\]

Math

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

↓

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

C

double f(double e, double v) {
        double r16127 = e;
        double r16128 = v;
        double r16129 = sin(r16128);
        double r16130 = r16127 * r16129;
        double r16131 = 1.0;
        double r16132 = cos(r16128);
        double r16133 = r16127 * r16132;
        double r16134 = r16131 + r16133;
        double r16135 = r16130 / r16134;
        return r16135;
}

↓

double f(double e, double v) {
        double r16136 = e;
        double r16137 = v;
        double r16138 = sin(r16137);
        double r16139 = r16136 * r16138;
        double r16140 = 1.0;
        double r16141 = cos(r16137);
        double r16142 = r16136 * r16141;
        double r16143 = r16140 + r16142;
        double r16144 = r16139 / r16143;
        return r16144;
}

Error

Bits error versus e

Bits error versus v

Derivation

1. Initial program 0.1

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

2. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020043 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))