Average Error: 0.1 → 0.1
Time: 19.0s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right) \cdot \left(-m\right) + \left(\frac{\left(1 - m \cdot m\right) \cdot m}{\left(1 + m\right) \cdot v} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right) \cdot \left(-m\right) + \left(\frac{\left(1 - m \cdot m\right) \cdot m}{\left(1 + m\right) \cdot v} - 1\right)
double f(double m, double v) {
        double r774548 = m;
        double r774549 = 1.0;
        double r774550 = r774549 - r774548;
        double r774551 = r774548 * r774550;
        double r774552 = v;
        double r774553 = r774551 / r774552;
        double r774554 = r774553 - r774549;
        double r774555 = r774554 * r774550;
        return r774555;
}
↓
double f(double m, double v) {
        double r774556 = 1.0;
        double r774557 = m;
        double r774558 = r774556 - r774557;
        double r774559 = r774558 * r774557;
        double r774560 = v;
        double r774561 = r774559 / r774560;
        double r774562 = r774561 - r774556;
        double r774563 = -r774557;
        double r774564 = r774562 * r774563;
        double r774565 = r774557 * r774557;
        double r774566 = r774556 - r774565;
        double r774567 = r774566 * r774557;
        double r774568 = r774556 + r774557;
        double r774569 = r774568 * r774560;
        double r774570 = r774567 / r774569;
        double r774571 = r774570 - r774556;
        double r774572 = r774564 + r774571;
        return r774572;
}

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 sub-neg0.1

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

  4. Applied distribute-lft-in0.1

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

  6. Applied flip--0.1

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

  7. Applied associate-*r/0.1

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

  8. Applied associate-/l/0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019133 +o rules:numerics
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))