Average Error: 0.1 → 0.1
Time: 6.2s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m}{\frac{v}{1 - m}} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m}{\frac{v}{1 - m}} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r21213 = m;
        double r21214 = 1.0;
        double r21215 = r21214 - r21213;
        double r21216 = r21213 * r21215;
        double r21217 = v;
        double r21218 = r21216 / r21217;
        double r21219 = r21218 - r21214;
        double r21220 = r21219 * r21215;
        return r21220;
}
↓
double f(double m, double v) {
        double r21221 = m;
        double r21222 = v;
        double r21223 = 1.0;
        double r21224 = r21223 - r21221;
        double r21225 = r21222 / r21224;
        double r21226 = r21221 / r21225;
        double r21227 = r21226 - r21223;
        double r21228 = r21227 * r21224;
        return r21228;
}

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

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

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))