a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 4.2s

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 r10235 = m;
        double r10236 = 1.0;
        double r10237 = r10236 - r10235;
        double r10238 = r10235 * r10237;
        double r10239 = v;
        double r10240 = r10238 / r10239;
        double r10241 = r10240 - r10236;
        double r10242 = r10241 * r10235;
        return r10242;
}

↓

double f(double m, double v) {
        double r10243 = 1.0;
        double r10244 = v;
        double r10245 = m;
        double r10246 = 1.0;
        double r10247 = r10246 - r10245;
        double r10248 = r10245 * r10247;
        double r10249 = r10244 / r10248;
        double r10250 = r10243 / r10249;
        double r10251 = r10250 - r10246;
        double r10252 = r10251 * r10245;
        return r10252;
}

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 2020083 
(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))