Average Error: 0.1 → 0.1
Time: 15.6s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{\left(1 - m \cdot m\right) \cdot m}{\left(1 + m\right) \cdot v} - 1\right) \cdot \left(1 - m\right)\]
\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 r387068 = m;
        double r387069 = 1.0;
        double r387070 = r387069 - r387068;
        double r387071 = r387068 * r387070;
        double r387072 = v;
        double r387073 = r387071 / r387072;
        double r387074 = r387073 - r387069;
        double r387075 = r387074 * r387070;
        return r387075;
}
↓
double f(double m, double v) {
        double r387076 = 1.0;
        double r387077 = m;
        double r387078 = r387077 * r387077;
        double r387079 = r387076 - r387078;
        double r387080 = r387079 * r387077;
        double r387081 = r387076 + r387077;
        double r387082 = v;
        double r387083 = r387081 * r387082;
        double r387084 = r387080 / r387083;
        double r387085 = r387084 - r387076;
        double r387086 = r387076 - r387077;
        double r387087 = r387085 * r387086;
        return r387087;
}

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 2019151 +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)))