Average Error: 0.2 → 0.2
Time: 1.3m
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\frac{m}{v} \cdot \left(m - m \cdot m\right) - m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\frac{m}{v} \cdot \left(m - m \cdot m\right) - m
double f(double m, double v) {
        double r3454479 = m;
        double r3454480 = 1.0;
        double r3454481 = r3454480 - r3454479;
        double r3454482 = r3454479 * r3454481;
        double r3454483 = v;
        double r3454484 = r3454482 / r3454483;
        double r3454485 = r3454484 - r3454480;
        double r3454486 = r3454485 * r3454479;
        return r3454486;
}
↓
double f(double m, double v) {
        double r3454487 = m;
        double r3454488 = v;
        double r3454489 = r3454487 / r3454488;
        double r3454490 = r3454487 * r3454487;
        double r3454491 = r3454487 - r3454490;
        double r3454492 = r3454489 * r3454491;
        double r3454493 = r3454492 - r3454487;
        return r3454493;
}

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. Using strategy rm

  3. Applied associate-/l*0.2

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

  4. Taylor expanded around inf 6.9

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

  5. Simplified0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019125 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))