a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 22.1s

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r1184954 = m;
        double r1184955 = 1.0;
        double r1184956 = r1184955 - r1184954;
        double r1184957 = r1184954 * r1184956;
        double r1184958 = v;
        double r1184959 = r1184957 / r1184958;
        double r1184960 = r1184959 - r1184955;
        double r1184961 = r1184960 * r1184954;
        return r1184961;
}

↓

double f(double m, double v) {
        double r1184962 = m;
        double r1184963 = v;
        double r1184964 = 1.0;
        double r1184965 = r1184963 / r1184964;
        double r1184966 = r1184962 / r1184965;
        double r1184967 = r1184962 * r1184962;
        double r1184968 = r1184967 / r1184963;
        double r1184969 = r1184966 - r1184968;
        double r1184970 = r1184969 - r1184964;
        double r1184971 = r1184962 * r1184970;
        return r1184971;
}

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. Taylor expanded around 0 0.2

   \[\leadsto \left(\color{blue}{\left(1 \cdot \frac{m}{v} - \frac{{m}^{2}}{v}\right)} - 1\right) \cdot m\]

3. Simplified 0.2

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

4. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019171 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) m))