Average Error: 0.1 → 0.1
Time: 26.3s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\left(\frac{m}{v} - \frac{m}{\frac{v}{m}}\right) - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\left(\frac{m}{v} - \frac{m}{\frac{v}{m}}\right) - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r771116 = m;
        double r771117 = 1.0;
        double r771118 = r771117 - r771116;
        double r771119 = r771116 * r771118;
        double r771120 = v;
        double r771121 = r771119 / r771120;
        double r771122 = r771121 - r771117;
        double r771123 = r771122 * r771118;
        return r771123;
}
↓
double f(double m, double v) {
        double r771124 = m;
        double r771125 = v;
        double r771126 = r771124 / r771125;
        double r771127 = r771125 / r771124;
        double r771128 = r771124 / r771127;
        double r771129 = r771126 - r771128;
        double r771130 = 1.0;
        double r771131 = r771129 - r771130;
        double r771132 = r771130 - r771124;
        double r771133 = r771131 * r771132;
        return r771133;
}

Error

Bits error versus m

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  2. Taylor expanded around -inf 0.1

    \[\leadsto \left(\color{blue}{\left(\frac{m}{v} - \frac{{m}^{2}}{v}\right)} - 1\right) \cdot \left(1 - m\right)\]

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))