Average Error: 0.2 → 0.2
Time: 17.4s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(m \cdot \frac{1 - m}{v} - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(m \cdot \frac{1 - m}{v} - 1\right) \cdot m
double f(double m, double v) {
        double r18510 = m;
        double r18511 = 1.0;
        double r18512 = r18511 - r18510;
        double r18513 = r18510 * r18512;
        double r18514 = v;
        double r18515 = r18513 / r18514;
        double r18516 = r18515 - r18511;
        double r18517 = r18516 * r18510;
        return r18517;
}
↓
double f(double m, double v) {
        double r18518 = m;
        double r18519 = 1.0;
        double r18520 = r18519 - r18518;
        double r18521 = v;
        double r18522 = r18520 / r18521;
        double r18523 = r18518 * r18522;
        double r18524 = r18523 - r18519;
        double r18525 = r18524 * r18518;
        return r18525;
}

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

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

  4. Applied times-frac0.2

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

  5. Simplified0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019195 +o rules:numerics
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) m))