a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 3.8s

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r9490 = m;
        double r9491 = 1.0;
        double r9492 = r9491 - r9490;
        double r9493 = r9490 * r9492;
        double r9494 = v;
        double r9495 = r9493 / r9494;
        double r9496 = r9495 - r9491;
        double r9497 = r9496 * r9490;
        return r9497;
}

↓

double f(double m, double v) {
        double r9498 = m;
        double r9499 = 1.0;
        double r9500 = r9499 - r9498;
        double r9501 = r9498 * r9500;
        double r9502 = v;
        double r9503 = r9501 / r9502;
        double r9504 = r9503 - r9499;
        double r9505 = r9504 * r9498;
        return r9505;
}

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 *-un-lft-identity 0.2

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

4. Applied times-frac 0.2

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

5. Simplified 0.2

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

7. Applied associate-*r/ 0.2

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

8. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019354 
(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))