Average Error: 0.2 → 0.2
Time: 4.5m
Precision: 64
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[m \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)\]
double f(double m, double v) {
        double r19646551 = m;
        double r19646552 = 1.0;
        double r19646553 = r19646552 - r19646551;
        double r19646554 = r19646551 * r19646553;
        double r19646555 = v;
        double r19646556 = r19646554 / r19646555;
        double r19646557 = r19646556 - r19646552;
        double r19646558 = r19646557 * r19646551;
        return r19646558;
}
↓
double f(double m, double v) {
        double r19646559 = m;
        double r19646560 = 1.0;
        double r19646561 = r19646560 - r19646559;
        double r19646562 = r19646559 * r19646561;
        double r19646563 = v;
        double r19646564 = r19646562 / r19646563;
        double r19646565 = r19646564 - r19646560;
        double r19646566 = r19646559 * r19646565;
        return r19646566;
}


\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
m \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)

Error

Bits error versus m

Bits error versus v

Derivation

  1. Initial program 0.2

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

  2. Final simplification0.2

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

Reproduce

herbie shell --seed 2019102 +o rules:numerics
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))