Average Error: 0.2 → 0.2
Time: 47.3s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\left(\frac{1 \cdot m}{v} - \frac{m}{\frac{v}{m}}\right) - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\left(\frac{1 \cdot m}{v} - \frac{m}{\frac{v}{m}}\right) - 1\right) \cdot m
double f(double m, double v) {
        double r997042 = m;
        double r997043 = 1.0;
        double r997044 = r997043 - r997042;
        double r997045 = r997042 * r997044;
        double r997046 = v;
        double r997047 = r997045 / r997046;
        double r997048 = r997047 - r997043;
        double r997049 = r997048 * r997042;
        return r997049;
}
↓
double f(double m, double v) {
        double r997050 = 1.0;
        double r997051 = m;
        double r997052 = r997050 * r997051;
        double r997053 = v;
        double r997054 = r997052 / r997053;
        double r997055 = r997053 / r997051;
        double r997056 = r997051 / r997055;
        double r997057 = r997054 - r997056;
        double r997058 = r997057 - r997050;
        double r997059 = r997058 * r997051;
        return r997059;
}

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 0.2

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

  3. Applied clear-num0.2

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

  4. Taylor expanded around 0 0.2

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

  5. Simplified0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) m))