Average Error: 0.1 → 0.1
Time: 18.6s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(1 - m\right) \cdot \left(\frac{m}{\frac{v}{1 - m}} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(1 - m\right) \cdot \left(\frac{m}{\frac{v}{1 - m}} - 1\right)
double f(double m, double v) {
        double r715204 = m;
        double r715205 = 1.0;
        double r715206 = r715205 - r715204;
        double r715207 = r715204 * r715206;
        double r715208 = v;
        double r715209 = r715207 / r715208;
        double r715210 = r715209 - r715205;
        double r715211 = r715210 * r715206;
        return r715211;
}
↓
double f(double m, double v) {
        double r715212 = 1.0;
        double r715213 = m;
        double r715214 = r715212 - r715213;
        double r715215 = v;
        double r715216 = r715215 / r715214;
        double r715217 = r715213 / r715216;
        double r715218 = r715217 - r715212;
        double r715219 = r715214 * r715218;
        return r715219;
}

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 associate-/l*0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019130 +o rules:numerics
(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)))