Average Error: 0.1 → 0.1
Time: 19.6s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{\frac{m}{v} - \frac{\left(m \cdot m\right) \cdot m}{v}}{m + 1} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{\frac{m}{v} - \frac{\left(m \cdot m\right) \cdot m}{v}}{m + 1} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r646024 = m;
        double r646025 = 1.0;
        double r646026 = r646025 - r646024;
        double r646027 = r646024 * r646026;
        double r646028 = v;
        double r646029 = r646027 / r646028;
        double r646030 = r646029 - r646025;
        double r646031 = r646030 * r646026;
        return r646031;
}
↓
double f(double m, double v) {
        double r646032 = m;
        double r646033 = v;
        double r646034 = r646032 / r646033;
        double r646035 = r646032 * r646032;
        double r646036 = r646035 * r646032;
        double r646037 = r646036 / r646033;
        double r646038 = r646034 - r646037;
        double r646039 = 1.0;
        double r646040 = r646032 + r646039;
        double r646041 = r646038 / r646040;
        double r646042 = r646041 - r646039;
        double r646043 = r646039 - r646032;
        double r646044 = r646042 * r646043;
        return r646044;
}

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 flip--0.1

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

  4. Applied associate-*r/0.1

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

  5. Applied associate-/l/0.1

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

  7. Applied associate-/r*0.1

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

  8. Simplified0.1

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

  9. Taylor expanded around 0 0.1

    \[\leadsto \left(\frac{\color{blue}{\frac{m}{v} - \frac{{m}^{3}}{v}}}{1 + m} - 1\right) \cdot \left(1 - m\right)\]

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019155 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))