Average Error: 0.2 → 0.2
Time: 12.5s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m}{v} \cdot \left(1 - m\right) - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{m}{v} \cdot \left(1 - m\right) - 1\right) \cdot m
double f(double m, double v) {
        double r8409 = m;
        double r8410 = 1.0;
        double r8411 = r8410 - r8409;
        double r8412 = r8409 * r8411;
        double r8413 = v;
        double r8414 = r8412 / r8413;
        double r8415 = r8414 - r8410;
        double r8416 = r8415 * r8409;
        return r8416;
}
↓
double f(double m, double v) {
        double r8417 = m;
        double r8418 = v;
        double r8419 = r8417 / r8418;
        double r8420 = 1.0;
        double r8421 = r8420 - r8417;
        double r8422 = r8419 * r8421;
        double r8423 = r8422 - r8420;
        double r8424 = r8423 * r8417;
        return r8424;
}

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. Simplified0.2

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

  5. Applied *-commutative0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020042 
(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))