b parameter of renormalized beta distribution

Average Error: 0.1 → 0.1

Time: 17.0s

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r24122 = m;
        double r24123 = 1.0;
        double r24124 = r24123 - r24122;
        double r24125 = r24122 * r24124;
        double r24126 = v;
        double r24127 = r24125 / r24126;
        double r24128 = r24127 - r24123;
        double r24129 = r24128 * r24124;
        return r24129;
}

↓

double f(double m, double v) {
        double r24130 = m;
        double r24131 = 1.0;
        double r24132 = r24130 * r24131;
        double r24133 = -r24130;
        double r24134 = r24130 * r24133;
        double r24135 = r24132 + r24134;
        double r24136 = v;
        double r24137 = r24135 / r24136;
        double r24138 = r24137 - r24131;
        double r24139 = r24131 - r24130;
        double r24140 = r24138 * r24139;
        return r24140;
}

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 sub-neg 0.1

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

4. Applied distribute-lft-in 0.1

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

5. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019305 +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)))