Average Error: 0.2 → 0.2
Time: 21.2s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\left(1 - m\right) \cdot \frac{m}{v} - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\left(1 - m\right) \cdot \frac{m}{v} - 1\right) \cdot m
double f(double m, double v) {
        double r17324 = m;
        double r17325 = 1.0;
        double r17326 = r17325 - r17324;
        double r17327 = r17324 * r17326;
        double r17328 = v;
        double r17329 = r17327 / r17328;
        double r17330 = r17329 - r17325;
        double r17331 = r17330 * r17324;
        return r17331;
}
↓
double f(double m, double v) {
        double r17332 = 1.0;
        double r17333 = m;
        double r17334 = r17332 - r17333;
        double r17335 = v;
        double r17336 = r17333 / r17335;
        double r17337 = r17334 * r17336;
        double r17338 = r17337 - r17332;
        double r17339 = r17338 * r17333;
        return r17339;
}

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 pow10.2

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

  4. Taylor expanded around 0 0.2

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

  5. Simplified0.2

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

  7. Applied div-inv0.2

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

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2019326 
(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))