Average Error: 0.2 → 0.2
Time: 24.7s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{\frac{\left(m \cdot \left(1 - m\right)\right) \cdot \left(1 + m\right)}{v}}{1 + m} - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{\frac{\left(m \cdot \left(1 - m\right)\right) \cdot \left(1 + m\right)}{v}}{1 + m} - 1\right) \cdot m
double f(double m, double v) {
        double r1058464 = m;
        double r1058465 = 1.0;
        double r1058466 = r1058465 - r1058464;
        double r1058467 = r1058464 * r1058466;
        double r1058468 = v;
        double r1058469 = r1058467 / r1058468;
        double r1058470 = r1058469 - r1058465;
        double r1058471 = r1058470 * r1058464;
        return r1058471;
}
↓
double f(double m, double v) {
        double r1058472 = m;
        double r1058473 = 1.0;
        double r1058474 = r1058473 - r1058472;
        double r1058475 = r1058472 * r1058474;
        double r1058476 = r1058473 + r1058472;
        double r1058477 = r1058475 * r1058476;
        double r1058478 = v;
        double r1058479 = r1058477 / r1058478;
        double r1058480 = r1058479 / r1058476;
        double r1058481 = r1058480 - r1058473;
        double r1058482 = r1058481 * r1058472;
        return r1058482;
}

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 clear-num0.2

    \[\leadsto \left(\color{blue}{\frac{1}{\frac{v}{m \cdot \left(1 - m\right)}}} - 1\right) \cdot m\]
  4. Using strategy rm

  5. Applied flip--0.2

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

  6. Applied associate-*r/0.2

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

  7. Applied associate-/r/0.2

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

  8. Applied associate-/r*0.2

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

  9. Simplified0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2019169 +o rules:numerics
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) m))