b parameter of renormalized beta distribution

Average Error: 0.1 → 0.1

Time: 5.2s

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r15348 = m;
        double r15349 = 1.0;
        double r15350 = r15349 - r15348;
        double r15351 = r15348 * r15350;
        double r15352 = v;
        double r15353 = r15351 / r15352;
        double r15354 = r15353 - r15349;
        double r15355 = r15354 * r15350;
        return r15355;
}

↓

double f(double m, double v) {
        double r15356 = m;
        double r15357 = v;
        double r15358 = r15356 / r15357;
        double r15359 = 1.0;
        double r15360 = r15359 - r15356;
        double r15361 = r15358 * r15360;
        double r15362 = r15361 - r15359;
        double r15363 = r15362 * r15360;
        return r15363;
}

Error

Bits error versus m

Bits error versus v

Derivation

1. Initial program 0.1

   \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
2. Using strategy rm

3. Applied associate-/l* 0.1

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

5. Applied associate-/r/ 0.1

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

6. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020033 +o rules:numerics
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))