a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 20.3s

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r20192 = m;
        double r20193 = 1.0;
        double r20194 = r20193 - r20192;
        double r20195 = r20192 * r20194;
        double r20196 = v;
        double r20197 = r20195 / r20196;
        double r20198 = r20197 - r20193;
        double r20199 = r20198 * r20192;
        return r20199;
}

↓

double f(double m, double v) {
        double r20200 = 1.0;
        double r20201 = v;
        double r20202 = m;
        double r20203 = 1.0;
        double r20204 = r20203 - r20202;
        double r20205 = r20202 * r20204;
        double r20206 = r20201 / r20205;
        double r20207 = r20200 / r20206;
        double r20208 = r20207 - r20203;
        double r20209 = r20208 * r20202;
        return r20209;
}

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 clear-num 0.2

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

5. Applied *-un-lft-identity 0.2

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

6. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019347 
(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))