Average Error: 0.2 → 0.2
Time: 3.3s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m}{v} \cdot \left(1 - m\right) - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{m}{v} \cdot \left(1 - m\right) - 1\right) \cdot m
double f(double m, double v) {
        double r9639 = m;
        double r9640 = 1.0;
        double r9641 = r9640 - r9639;
        double r9642 = r9639 * r9641;
        double r9643 = v;
        double r9644 = r9642 / r9643;
        double r9645 = r9644 - r9640;
        double r9646 = r9645 * r9639;
        return r9646;
}
↓
double f(double m, double v) {
        double r9647 = m;
        double r9648 = v;
        double r9649 = r9647 / r9648;
        double r9650 = 1.0;
        double r9651 = r9650 - r9647;
        double r9652 = r9649 * r9651;
        double r9653 = r9652 - r9650;
        double r9654 = r9653 * r9647;
        return r9654;
}

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 sub-neg0.2

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

  4. Applied distribute-lft-in0.2

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

  5. Simplified0.2

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

  6. Simplified0.2

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

  7. Taylor expanded around 0 0.2

    \[\leadsto \left(\color{blue}{\left(1 \cdot \frac{m}{v} - \frac{{m}^{2}}{v}\right)} - 1\right) \cdot m\]

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020056 +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))