Average Error: 0.1 → 0.1
Time: 1.6m
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\frac{m}{v} \cdot \left(\left(1 - m\right) \cdot \left(1 - m\right)\right) - \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\frac{m}{v} \cdot \left(\left(1 - m\right) \cdot \left(1 - m\right)\right) - \left(1 - m\right)
double f(double m, double v) {
        double r5917876 = m;
        double r5917877 = 1.0;
        double r5917878 = r5917877 - r5917876;
        double r5917879 = r5917876 * r5917878;
        double r5917880 = v;
        double r5917881 = r5917879 / r5917880;
        double r5917882 = r5917881 - r5917877;
        double r5917883 = r5917882 * r5917878;
        return r5917883;
}
↓
double f(double m, double v) {
        double r5917884 = m;
        double r5917885 = v;
        double r5917886 = r5917884 / r5917885;
        double r5917887 = 1.0;
        double r5917888 = r5917887 - r5917884;
        double r5917889 = r5917888 * r5917888;
        double r5917890 = r5917886 * r5917889;
        double r5917891 = r5917890 - r5917888;
        return r5917891;
}

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

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

  3. Simplified0.1

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

  5. Applied pow10.1

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

  6. Applied pow10.1

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

  7. Applied pow-prod-down0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019104 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))