Average Error: 0.2 → 0.2
Time: 22.9s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m}{\frac{v}{m}} - m\right) \cdot 1 - {m}^{3} \cdot \frac{1}{v}\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{m}{\frac{v}{m}} - m\right) \cdot 1 - {m}^{3} \cdot \frac{1}{v}
double f(double m, double v) {
        double r38002 = m;
        double r38003 = 1.0;
        double r38004 = r38003 - r38002;
        double r38005 = r38002 * r38004;
        double r38006 = v;
        double r38007 = r38005 / r38006;
        double r38008 = r38007 - r38003;
        double r38009 = r38008 * r38002;
        return r38009;
}
↓
double f(double m, double v) {
        double r38010 = m;
        double r38011 = v;
        double r38012 = r38011 / r38010;
        double r38013 = r38010 / r38012;
        double r38014 = r38013 - r38010;
        double r38015 = 1.0;
        double r38016 = r38014 * r38015;
        double r38017 = 3.0;
        double r38018 = pow(r38010, r38017);
        double r38019 = 1.0;
        double r38020 = r38019 / r38011;
        double r38021 = r38018 * r38020;
        double r38022 = r38016 - r38021;
        return r38022;
}

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 0 6.8

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

  5. Simplified0.2

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

  7. Applied div-inv0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) m))