Average Error: 0.2 → 0.2
Time: 31.7s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[1 \cdot \left(\frac{m}{\frac{v}{m}} - m\right) - \frac{{m}^{3}}{v}\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
1 \cdot \left(\frac{m}{\frac{v}{m}} - m\right) - \frac{{m}^{3}}{v}
double f(double m, double v) {
        double r31276 = m;
        double r31277 = 1.0;
        double r31278 = r31277 - r31276;
        double r31279 = r31276 * r31278;
        double r31280 = v;
        double r31281 = r31279 / r31280;
        double r31282 = r31281 - r31277;
        double r31283 = r31282 * r31276;
        return r31283;
}
↓
double f(double m, double v) {
        double r31284 = 1.0;
        double r31285 = m;
        double r31286 = v;
        double r31287 = r31286 / r31285;
        double r31288 = r31285 / r31287;
        double r31289 = r31288 - r31285;
        double r31290 = r31284 * r31289;
        double r31291 = 3.0;
        double r31292 = pow(r31285, r31291);
        double r31293 = r31292 / r31286;
        double r31294 = r31290 - r31293;
        return r31294;
}

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 6.8

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

  3. Simplified6.8

    \[\leadsto \color{blue}{1 \cdot \left(\frac{{m}^{2}}{v} - m\right) - \frac{{m}^{3}}{v}}\]
  4. Using strategy rm

  5. Applied sqr-pow6.8

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

  6. Applied associate-/l*0.2

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

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019304 +o rules:numerics
(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))