Average Error: 0.1 → 0.1
Time: 16.2s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(-m\right) \cdot \left(\left(1 - m\right) \cdot \frac{m}{v} - 1\right) + 1 \cdot \left(\left(1 - m\right) \cdot \frac{m}{v} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(-m\right) \cdot \left(\left(1 - m\right) \cdot \frac{m}{v} - 1\right) + 1 \cdot \left(\left(1 - m\right) \cdot \frac{m}{v} - 1\right)
double f(double m, double v) {
        double r21627 = m;
        double r21628 = 1.0;
        double r21629 = r21628 - r21627;
        double r21630 = r21627 * r21629;
        double r21631 = v;
        double r21632 = r21630 / r21631;
        double r21633 = r21632 - r21628;
        double r21634 = r21633 * r21629;
        return r21634;
}
↓
double f(double m, double v) {
        double r21635 = m;
        double r21636 = -r21635;
        double r21637 = 1.0;
        double r21638 = r21637 - r21635;
        double r21639 = v;
        double r21640 = r21635 / r21639;
        double r21641 = r21638 * r21640;
        double r21642 = r21641 - r21637;
        double r21643 = r21636 * r21642;
        double r21644 = r21637 * r21642;
        double r21645 = r21643 + r21644;
        return r21645;
}

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 associate-/l*0.1

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

  5. Applied sub-neg0.1

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

  6. Applied distribute-lft-in0.1

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

  7. Simplified0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))