Average Error: 0.2 → 0.2
Time: 13.4s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[m \cdot \left(\frac{m}{v} \cdot \left(\left(-m\right) + 1\right) - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
m \cdot \left(\frac{m}{v} \cdot \left(\left(-m\right) + 1\right) - 1\right)
double f(double m, double v) {
        double r29893 = m;
        double r29894 = 1.0;
        double r29895 = r29894 - r29893;
        double r29896 = r29893 * r29895;
        double r29897 = v;
        double r29898 = r29896 / r29897;
        double r29899 = r29898 - r29894;
        double r29900 = r29899 * r29893;
        return r29900;
}
↓
double f(double m, double v) {
        double r29901 = m;
        double r29902 = v;
        double r29903 = r29901 / r29902;
        double r29904 = -r29901;
        double r29905 = 1.0;
        double r29906 = r29904 + r29905;
        double r29907 = r29903 * r29906;
        double r29908 = r29907 - r29905;
        double r29909 = r29901 * r29908;
        return r29909;
}

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. Using strategy rm

  4. Applied sqr-pow6.8

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

  5. Applied associate-/l*0.2

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

  6. Simplified0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019304 
(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))