Average Error: 0.2 → 0.2
Time: 15.7s
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 r12022 = m;
        double r12023 = 1.0;
        double r12024 = r12023 - r12022;
        double r12025 = r12022 * r12024;
        double r12026 = v;
        double r12027 = r12025 / r12026;
        double r12028 = r12027 - r12023;
        double r12029 = r12028 * r12022;
        return r12029;
}
↓
double f(double m, double v) {
        double r12030 = m;
        double r12031 = 1.0;
        double r12032 = r12031 - r12030;
        double r12033 = v;
        double r12034 = r12032 / r12033;
        double r12035 = r12030 * r12034;
        double r12036 = r12035 - r12031;
        double r12037 = r12036 * r12030;
        return r12037;
}

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 2019350 +o rules:numerics
(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))