Average Error: 0.2 → 0.2
Time: 19.0s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[m \cdot \left(\frac{m - m \cdot m}{v} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
m \cdot \left(\frac{m - m \cdot m}{v} - 1\right)
double f(double m, double v) {
        double r494180 = m;
        double r494181 = 1.0;
        double r494182 = r494181 - r494180;
        double r494183 = r494180 * r494182;
        double r494184 = v;
        double r494185 = r494183 / r494184;
        double r494186 = r494185 - r494181;
        double r494187 = r494186 * r494180;
        return r494187;
}
↓
double f(double m, double v) {
        double r494188 = m;
        double r494189 = r494188 * r494188;
        double r494190 = r494188 - r494189;
        double r494191 = v;
        double r494192 = r494190 / r494191;
        double r494193 = 1.0;
        double r494194 = r494192 - r494193;
        double r494195 = r494188 * r494194;
        return r494195;
}

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. Simplified0.2

    \[\leadsto \color{blue}{\frac{m - m \cdot m}{\frac{v}{m}} - m}\]
  3. Using strategy rm

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

    \[\leadsto \frac{m - m \cdot m}{\frac{v}{m}} - \color{blue}{1 \cdot m}\]

  5. Applied associate-/r/0.2

    \[\leadsto \color{blue}{\frac{m - m \cdot m}{v} \cdot m} - 1 \cdot m\]

  6. Applied distribute-rgt-out--0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019139 
(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))