Average Error: 0.1 → 0.1
Time: 4.8s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{\frac{m}{v}}{\frac{1}{1 - m}} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{\frac{m}{v}}{\frac{1}{1 - m}} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r14901 = m;
        double r14902 = 1.0;
        double r14903 = r14902 - r14901;
        double r14904 = r14901 * r14903;
        double r14905 = v;
        double r14906 = r14904 / r14905;
        double r14907 = r14906 - r14902;
        double r14908 = r14907 * r14903;
        return r14908;
}
↓
double f(double m, double v) {
        double r14909 = m;
        double r14910 = v;
        double r14911 = r14909 / r14910;
        double r14912 = 1.0;
        double r14913 = 1.0;
        double r14914 = r14913 - r14909;
        double r14915 = r14912 / r14914;
        double r14916 = r14911 / r14915;
        double r14917 = r14916 - r14913;
        double r14918 = r14917 * r14914;
        return r14918;
}

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 0.1

    \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
  2. Using strategy rm

  3. Applied clear-num0.2

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

  5. Applied div-inv0.2

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

  6. Applied associate-/r*0.2

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

  8. Applied *-un-lft-identity0.2

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

  9. Applied times-frac0.3

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

  10. Applied associate-/r*0.3

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

  11. Simplified0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2020001 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))