a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 3.7s

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 r15209 = m;
        double r15210 = 1.0;
        double r15211 = r15210 - r15209;
        double r15212 = r15209 * r15211;
        double r15213 = v;
        double r15214 = r15212 / r15213;
        double r15215 = r15214 - r15210;
        double r15216 = r15215 * r15209;
        return r15216;
}

↓

double f(double m, double v) {
        double r15217 = 1.0;
        double r15218 = v;
        double r15219 = m;
        double r15220 = 1.0;
        double r15221 = r15220 - r15219;
        double r15222 = r15219 * r15221;
        double r15223 = r15218 / r15222;
        double r15224 = r15217 / r15223;
        double r15225 = r15224 - r15220;
        double r15226 = r15225 * r15219;
        return r15226;
}

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. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020062 
(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))