a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 5.2s

Precision: 64

\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]

Math

\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]

↓

\[\left(\frac{m}{\frac{v}{1 - m}} - 1\right) \cdot m\]

C

double f(double m, double v) {
        double r23278 = m;
        double r23279 = 1.0;
        double r23280 = r23279 - r23278;
        double r23281 = r23278 * r23280;
        double r23282 = v;
        double r23283 = r23281 / r23282;
        double r23284 = r23283 - r23279;
        double r23285 = r23284 * r23278;
        return r23285;
}

↓

double f(double m, double v) {
        double r23286 = m;
        double r23287 = v;
        double r23288 = 1.0;
        double r23289 = r23288 - r23286;
        double r23290 = r23287 / r23289;
        double r23291 = r23286 / r23290;
        double r23292 = r23291 - r23288;
        double r23293 = r23292 * r23286;
        return r23293;
}

Error

Bits error versus m

Bits error versus v

Derivation

1. Initial program 0.2

   \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
2. Using strategy rm

3. Applied associate-/l* 0.2

   \[\leadsto \left(\color{blue}{\frac{m}{\frac{v}{1 - m}}} - 1\right) \cdot m\]

4. Final simplification 0.2

   \[\leadsto \left(\frac{m}{\frac{v}{1 - m}} - 1\right) \cdot m\]

Reproduce

herbie shell --seed 2020057 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))