Average Error: 0.2 → 0.2
Time: 11.4s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(1 \cdot \frac{m}{v} - \left(1 + \frac{{m}^{2}}{v}\right)\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(1 \cdot \frac{m}{v} - \left(1 + \frac{{m}^{2}}{v}\right)\right) \cdot m
double f(double m, double v) {
        double r13120 = m;
        double r13121 = 1.0;
        double r13122 = r13121 - r13120;
        double r13123 = r13120 * r13122;
        double r13124 = v;
        double r13125 = r13123 / r13124;
        double r13126 = r13125 - r13121;
        double r13127 = r13126 * r13120;
        return r13127;
}
↓
double f(double m, double v) {
        double r13128 = 1.0;
        double r13129 = m;
        double r13130 = v;
        double r13131 = r13129 / r13130;
        double r13132 = r13128 * r13131;
        double r13133 = 2.0;
        double r13134 = pow(r13129, r13133);
        double r13135 = r13134 / r13130;
        double r13136 = r13128 + r13135;
        double r13137 = r13132 - r13136;
        double r13138 = r13137 * r13129;
        return r13138;
}

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

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2020047 
(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))