Average Error: 0.2 → 0.2
Time: 17.0s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m}{v} \cdot \frac{1}{\frac{1}{1 - m}} - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{m}{v} \cdot \frac{1}{\frac{1}{1 - m}} - 1\right) \cdot m
double f(double m, double v) {
        double r20991 = m;
        double r20992 = 1.0;
        double r20993 = r20992 - r20991;
        double r20994 = r20991 * r20993;
        double r20995 = v;
        double r20996 = r20994 / r20995;
        double r20997 = r20996 - r20992;
        double r20998 = r20997 * r20991;
        return r20998;
}
↓
double f(double m, double v) {
        double r20999 = m;
        double r21000 = v;
        double r21001 = r20999 / r21000;
        double r21002 = 1.0;
        double r21003 = 1.0;
        double r21004 = r21003 - r20999;
        double r21005 = r21002 / r21004;
        double r21006 = r21002 / r21005;
        double r21007 = r21001 * r21006;
        double r21008 = r21007 - r21003;
        double r21009 = r21008 * r20999;
        return r21009;
}

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

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

  4. Applied associate-*r*0.2

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

  5. Simplified0.2

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

  7. Applied div-inv0.2

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

  9. Applied div-inv0.3

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

  10. Applied *-un-lft-identity0.3

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

  11. Applied times-frac0.3

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

  12. Applied associate-*r*0.3

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

  13. Simplified0.2

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

  14. Final simplification0.2

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

Reproduce

herbie shell --seed 2019212 
(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))