b parameter of renormalized beta distribution

Average Error: 0.1 → 0.1

Time: 4.6s

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r16274 = m;
        double r16275 = 1.0;
        double r16276 = r16275 - r16274;
        double r16277 = r16274 * r16276;
        double r16278 = v;
        double r16279 = r16277 / r16278;
        double r16280 = r16279 - r16275;
        double r16281 = r16280 * r16276;
        return r16281;
}

↓

double f(double m, double v) {
        double r16282 = m;
        double r16283 = v;
        double r16284 = 1.0;
        double r16285 = 1.0;
        double r16286 = r16285 - r16282;
        double r16287 = r16284 / r16286;
        double r16288 = r16283 * r16287;
        double r16289 = r16282 / r16288;
        double r16290 = r16289 - r16285;
        double r16291 = r16290 * r16286;
        return r16291;
}

Error

Bits error versus m

Bits error versus v

Derivation

1. Initial program 0.1

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

3. Applied associate-/l* 0.1

   \[\leadsto \left(\color{blue}{\frac{m}{\frac{v}{1 - m}}} - 1\right) \cdot \left(1 - m\right)\]
4. Using strategy rm

5. Applied div-inv 0.1

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

6. Final simplification 0.1

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

Reproduce

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