Average Error: 0.1 → 0.1
Time: 17.3s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m}{v} \cdot \left(1 - m\right) - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m}{v} \cdot \left(1 - m\right) - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r24064 = m;
        double r24065 = 1.0;
        double r24066 = r24065 - r24064;
        double r24067 = r24064 * r24066;
        double r24068 = v;
        double r24069 = r24067 / r24068;
        double r24070 = r24069 - r24065;
        double r24071 = r24070 * r24066;
        return r24071;
}
↓
double f(double m, double v) {
        double r24072 = m;
        double r24073 = v;
        double r24074 = r24072 / r24073;
        double r24075 = 1.0;
        double r24076 = r24075 - r24072;
        double r24077 = r24074 * r24076;
        double r24078 = r24077 - r24075;
        double r24079 = r24078 * r24076;
        return r24079;
}

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 0 0.1

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

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019304 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))