Average Error: 0.1 → 0.1
Time: 15.3s
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 r18098 = m;
        double r18099 = 1.0;
        double r18100 = r18099 - r18098;
        double r18101 = r18098 * r18100;
        double r18102 = v;
        double r18103 = r18101 / r18102;
        double r18104 = r18103 - r18099;
        double r18105 = r18104 * r18100;
        return r18105;
}
↓
double f(double m, double v) {
        double r18106 = m;
        double r18107 = v;
        double r18108 = r18106 / r18107;
        double r18109 = 1.0;
        double r18110 = r18109 - r18106;
        double r18111 = r18108 * r18110;
        double r18112 = r18111 - r18109;
        double r18113 = r18112 * r18110;
        return r18113;
}

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 2019325 
(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)))