Average Error: 0.2 → 0.2
Time: 22.4s
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 r20656 = m;
        double r20657 = 1.0;
        double r20658 = r20657 - r20656;
        double r20659 = r20656 * r20658;
        double r20660 = v;
        double r20661 = r20659 / r20660;
        double r20662 = r20661 - r20657;
        double r20663 = r20662 * r20656;
        return r20663;
}
↓
double f(double m, double v) {
        double r20664 = m;
        double r20665 = 1.0;
        double r20666 = r20665 * r20665;
        double r20667 = r20664 * r20664;
        double r20668 = r20666 - r20667;
        double r20669 = r20664 * r20668;
        double r20670 = v;
        double r20671 = r20665 + r20664;
        double r20672 = r20670 * r20671;
        double r20673 = r20669 / r20672;
        double r20674 = r20673 - r20665;
        double r20675 = r20674 * r20664;
        return r20675;
}

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 2019323 +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))