Average Error: 0.1 → 0.1
Time: 5.2s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot 1 + \left(\left(1 \cdot m + \frac{{m}^{3}}{v}\right) - 1 \cdot \frac{{m}^{2}}{v}\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot 1 + \left(\left(1 \cdot m + \frac{{m}^{3}}{v}\right) - 1 \cdot \frac{{m}^{2}}{v}\right)
double f(double m, double v) {
        double r16597 = m;
        double r16598 = 1.0;
        double r16599 = r16598 - r16597;
        double r16600 = r16597 * r16599;
        double r16601 = v;
        double r16602 = r16600 / r16601;
        double r16603 = r16602 - r16598;
        double r16604 = r16603 * r16599;
        return r16604;
}
↓
double f(double m, double v) {
        double r16605 = m;
        double r16606 = 1.0;
        double r16607 = r16606 - r16605;
        double r16608 = r16605 * r16607;
        double r16609 = v;
        double r16610 = r16608 / r16609;
        double r16611 = r16610 - r16606;
        double r16612 = r16611 * r16606;
        double r16613 = r16606 * r16605;
        double r16614 = 3.0;
        double r16615 = pow(r16605, r16614);
        double r16616 = r16615 / r16609;
        double r16617 = r16613 + r16616;
        double r16618 = 2.0;
        double r16619 = pow(r16605, r16618);
        double r16620 = r16619 / r16609;
        double r16621 = r16606 * r16620;
        double r16622 = r16617 - r16621;
        double r16623 = r16612 + r16622;
        return r16623;
}

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. Using strategy rm

  3. Applied sub-neg0.1

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

  4. Applied distribute-lft-in0.1

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

  5. Taylor expanded around 0 0.1

    \[\leadsto \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot 1 + \color{blue}{\left(\left(1 \cdot m + \frac{{m}^{3}}{v}\right) - 1 \cdot \frac{{m}^{2}}{v}\right)}\]

  6. Final simplification0.1

    \[\leadsto \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot 1 + \left(\left(1 \cdot m + \frac{{m}^{3}}{v}\right) - 1 \cdot \frac{{m}^{2}}{v}\right)\]

Reproduce

herbie shell --seed 2020027 
(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)))