Average Error: 0.2 → 0.2
Time: 2.5m
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\frac{m - m \cdot m}{\frac{v}{m}} - m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\frac{m - m \cdot m}{\frac{v}{m}} - m
double f(double m, double v) {
        double r4128186 = m;
        double r4128187 = 1.0;
        double r4128188 = r4128187 - r4128186;
        double r4128189 = r4128186 * r4128188;
        double r4128190 = v;
        double r4128191 = r4128189 / r4128190;
        double r4128192 = r4128191 - r4128187;
        double r4128193 = r4128192 * r4128186;
        return r4128193;
}
↓
double f(double m, double v) {
        double r4128194 = m;
        double r4128195 = r4128194 * r4128194;
        double r4128196 = r4128194 - r4128195;
        double r4128197 = v;
        double r4128198 = r4128197 / r4128194;
        double r4128199 = r4128196 / r4128198;
        double r4128200 = r4128199 - r4128194;
        return r4128200;
}

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. Using strategy rm

  5. Applied clear-num0.2

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

  7. Applied pow10.2

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

  8. Applied pow10.2

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

  9. Applied pow-prod-down0.2

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

  10. Simplified0.2

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

  11. Final simplification0.2

    \[\leadsto \frac{m - m \cdot m}{\frac{v}{m}} - m\]

Reproduce

herbie shell --seed 2019121 
(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))