Average Error: 0.1 → 0.1
Time: 5.3s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{1 + m}}{v} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{1 + m}}{v} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r21411 = m;
        double r21412 = 1.0;
        double r21413 = r21412 - r21411;
        double r21414 = r21411 * r21413;
        double r21415 = v;
        double r21416 = r21414 / r21415;
        double r21417 = r21416 - r21412;
        double r21418 = r21417 * r21413;
        return r21418;
}
↓
double f(double m, double v) {
        double r21419 = m;
        double r21420 = 1.0;
        double r21421 = r21420 * r21420;
        double r21422 = r21419 * r21419;
        double r21423 = r21421 - r21422;
        double r21424 = r21419 * r21423;
        double r21425 = r21420 + r21419;
        double r21426 = r21424 / r21425;
        double r21427 = v;
        double r21428 = r21426 / r21427;
        double r21429 = r21428 - r21420;
        double r21430 = r21420 - r21419;
        double r21431 = r21429 * r21430;
        return r21431;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))