Average Error: 0.1 → 0.1
Time: 21.1s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\left(1 \cdot \frac{m}{v} - \frac{{m}^{2}}{v}\right) - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\left(1 \cdot \frac{m}{v} - \frac{{m}^{2}}{v}\right) - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r22401 = m;
        double r22402 = 1.0;
        double r22403 = r22402 - r22401;
        double r22404 = r22401 * r22403;
        double r22405 = v;
        double r22406 = r22404 / r22405;
        double r22407 = r22406 - r22402;
        double r22408 = r22407 * r22403;
        return r22408;
}
↓
double f(double m, double v) {
        double r22409 = 1.0;
        double r22410 = m;
        double r22411 = v;
        double r22412 = r22410 / r22411;
        double r22413 = r22409 * r22412;
        double r22414 = 2.0;
        double r22415 = pow(r22410, r22414);
        double r22416 = r22415 / r22411;
        double r22417 = r22413 - r22416;
        double r22418 = r22417 - r22409;
        double r22419 = r22409 - r22410;
        double r22420 = r22418 * r22419;
        return r22420;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019199 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))