Average Error: 0.1 → 0.1
Time: 14.3s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{\left(1 - m \cdot m\right) \cdot m}{\left(1 + m\right) \cdot v} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{\left(1 - m \cdot m\right) \cdot m}{\left(1 + m\right) \cdot v} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r542197 = m;
        double r542198 = 1.0;
        double r542199 = r542198 - r542197;
        double r542200 = r542197 * r542199;
        double r542201 = v;
        double r542202 = r542200 / r542201;
        double r542203 = r542202 - r542198;
        double r542204 = r542203 * r542199;
        return r542204;
}
↓
double f(double m, double v) {
        double r542205 = 1.0;
        double r542206 = m;
        double r542207 = r542206 * r542206;
        double r542208 = r542205 - r542207;
        double r542209 = r542208 * r542206;
        double r542210 = r542205 + r542206;
        double r542211 = v;
        double r542212 = r542210 * r542211;
        double r542213 = r542209 / r542212;
        double r542214 = r542213 - r542205;
        double r542215 = r542205 - r542206;
        double r542216 = r542214 * r542215;
        return r542216;
}

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 flip--0.1

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

  4. Applied associate-*r/0.1

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

  5. Applied associate-/l/0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019128 
(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)))