Average Error: 0.2 → 0.2
Time: 11.4s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\left(1 \cdot \frac{m}{v} - {m}^{2} \cdot \frac{1}{v}\right) - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\left(1 \cdot \frac{m}{v} - {m}^{2} \cdot \frac{1}{v}\right) - 1\right) \cdot m
double f(double m, double v) {
        double r9166 = m;
        double r9167 = 1.0;
        double r9168 = r9167 - r9166;
        double r9169 = r9166 * r9168;
        double r9170 = v;
        double r9171 = r9169 / r9170;
        double r9172 = r9171 - r9167;
        double r9173 = r9172 * r9166;
        return r9173;
}
↓
double f(double m, double v) {
        double r9174 = 1.0;
        double r9175 = m;
        double r9176 = v;
        double r9177 = r9175 / r9176;
        double r9178 = r9174 * r9177;
        double r9179 = 2.0;
        double r9180 = pow(r9175, r9179);
        double r9181 = 1.0;
        double r9182 = r9181 / r9176;
        double r9183 = r9180 * r9182;
        double r9184 = r9178 - r9183;
        double r9185 = r9184 - r9174;
        double r9186 = r9185 * r9175;
        return r9186;
}

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. Taylor expanded around 0 0.2

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

  4. Applied div-inv0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(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))