Average Error: 0.2 → 0.2
Time: 4.8s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\left(1 \cdot \frac{m}{v} - \frac{{m}^{2}}{v}\right) - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\left(1 \cdot \frac{m}{v} - \frac{{m}^{2}}{v}\right) - 1\right) \cdot m
double f(double m, double v) {
        double r12043 = m;
        double r12044 = 1.0;
        double r12045 = r12044 - r12043;
        double r12046 = r12043 * r12045;
        double r12047 = v;
        double r12048 = r12046 / r12047;
        double r12049 = r12048 - r12044;
        double r12050 = r12049 * r12043;
        return r12050;
}
↓
double f(double m, double v) {
        double r12051 = 1.0;
        double r12052 = m;
        double r12053 = v;
        double r12054 = r12052 / r12053;
        double r12055 = r12051 * r12054;
        double r12056 = 2.0;
        double r12057 = pow(r12052, r12056);
        double r12058 = r12057 / r12053;
        double r12059 = r12055 - r12058;
        double r12060 = r12059 - r12051;
        double r12061 = r12060 * r12052;
        return r12061;
}

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 associate-/l*0.2

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

  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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020018 +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))