Average Error: 0.2 → 0.2
Time: 4.1s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(1 \cdot \frac{m}{v} - \left(1 + \frac{{m}^{2}}{v}\right)\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(1 \cdot \frac{m}{v} - \left(1 + \frac{{m}^{2}}{v}\right)\right) \cdot m
double f(double m, double v) {
        double r9975 = m;
        double r9976 = 1.0;
        double r9977 = r9976 - r9975;
        double r9978 = r9975 * r9977;
        double r9979 = v;
        double r9980 = r9978 / r9979;
        double r9981 = r9980 - r9976;
        double r9982 = r9981 * r9975;
        return r9982;
}
↓
double f(double m, double v) {
        double r9983 = 1.0;
        double r9984 = m;
        double r9985 = v;
        double r9986 = r9984 / r9985;
        double r9987 = r9983 * r9986;
        double r9988 = 2.0;
        double r9989 = pow(r9984, r9988);
        double r9990 = r9989 / r9985;
        double r9991 = r9983 + r9990;
        double r9992 = r9987 - r9991;
        double r9993 = r9992 * r9984;
        return r9993;
}

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 *-un-lft-identity0.2

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

  4. Applied times-frac0.2

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

  5. Applied fma-neg0.2

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

  6. Taylor expanded around 0 0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019347 +o rules:numerics
(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))