Average Error: 0.2 → 0.2
Time: 28.4s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\frac{m}{\frac{v}{m}} - \left(\frac{m}{\frac{\frac{v}{m}}{m}} + m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\frac{m}{\frac{v}{m}} - \left(\frac{m}{\frac{\frac{v}{m}}{m}} + m\right)
double f(double m, double v) {
        double r712594 = m;
        double r712595 = 1.0;
        double r712596 = r712595 - r712594;
        double r712597 = r712594 * r712596;
        double r712598 = v;
        double r712599 = r712597 / r712598;
        double r712600 = r712599 - r712595;
        double r712601 = r712600 * r712594;
        return r712601;
}
↓
double f(double m, double v) {
        double r712602 = m;
        double r712603 = v;
        double r712604 = r712603 / r712602;
        double r712605 = r712602 / r712604;
        double r712606 = r712604 / r712602;
        double r712607 = r712602 / r712606;
        double r712608 = r712607 + r712602;
        double r712609 = r712605 - r712608;
        return r712609;
}

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 6.7

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

  5. Simplified0.2

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

  7. Applied associate-/l*0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019130 +o rules:numerics
(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))