Average Error: 0.2 → 0.2
Time: 3.5s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
double f(double m, double v) {
        double r7051 = m;
        double r7052 = 1.0;
        double r7053 = r7052 - r7051;
        double r7054 = r7051 * r7053;
        double r7055 = v;
        double r7056 = r7054 / r7055;
        double r7057 = r7056 - r7052;
        double r7058 = r7057 * r7051;
        return r7058;
}
↓
double f(double m, double v) {
        double r7059 = m;
        double r7060 = 1.0;
        double r7061 = r7060 - r7059;
        double r7062 = r7059 * r7061;
        double r7063 = v;
        double r7064 = r7062 / r7063;
        double r7065 = r7064 - r7060;
        double r7066 = r7065 * r7059;
        return r7066;
}

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 clear-num0.2

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

  4. Taylor expanded around 0 0.2

    \[\leadsto \left(\color{blue}{\left(1 \cdot \frac{m}{v} - \frac{{m}^{2}}{v}\right)} - 1\right) \cdot m\]

  5. Simplified0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020034 
(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))