Average Error: 0.1 → 0.1
Time: 22.4s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\left(1 \cdot \frac{m}{v} - \frac{{m}^{2}}{v}\right) - 1\right) \cdot \left(1 - m\right)\]
\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 r22415 = m;
        double r22416 = 1.0;
        double r22417 = r22416 - r22415;
        double r22418 = r22415 * r22417;
        double r22419 = v;
        double r22420 = r22418 / r22419;
        double r22421 = r22420 - r22416;
        double r22422 = r22421 * r22417;
        return r22422;
}
↓
double f(double m, double v) {
        double r22423 = 1.0;
        double r22424 = m;
        double r22425 = v;
        double r22426 = r22424 / r22425;
        double r22427 = r22423 * r22426;
        double r22428 = 2.0;
        double r22429 = pow(r22424, r22428);
        double r22430 = r22429 / r22425;
        double r22431 = r22427 - r22430;
        double r22432 = r22431 - r22423;
        double r22433 = r22423 - r22424;
        double r22434 = r22432 * r22433;
        return r22434;
}

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 +o rules:numerics
(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)))