Average Error: 0.2 → 0.2
Time: 4.2s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{v \cdot \left(1 + m\right)} - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{v \cdot \left(1 + m\right)} - 1\right) \cdot m
double f(double m, double v) {
        double r12139 = m;
        double r12140 = 1.0;
        double r12141 = r12140 - r12139;
        double r12142 = r12139 * r12141;
        double r12143 = v;
        double r12144 = r12142 / r12143;
        double r12145 = r12144 - r12140;
        double r12146 = r12145 * r12139;
        return r12146;
}
↓
double f(double m, double v) {
        double r12147 = m;
        double r12148 = 1.0;
        double r12149 = r12148 * r12148;
        double r12150 = r12147 * r12147;
        double r12151 = r12149 - r12150;
        double r12152 = r12147 * r12151;
        double r12153 = v;
        double r12154 = r12148 + r12147;
        double r12155 = r12153 * r12154;
        double r12156 = r12152 / r12155;
        double r12157 = r12156 - r12148;
        double r12158 = r12157 * r12147;
        return r12158;
}

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 flip--0.2

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

  4. Applied associate-*r/0.2

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

  5. Applied associate-/l/0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019344 +o rules:numerics
(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))