Average Error: 0.1 → 0.1
Time: 4.3s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot 1 + \left(\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{v \cdot \left(1 + m\right)} - 1\right) \cdot \left(-m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot 1 + \left(\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{v \cdot \left(1 + m\right)} - 1\right) \cdot \left(-m\right)
double f(double m, double v) {
        double r12710 = m;
        double r12711 = 1.0;
        double r12712 = r12711 - r12710;
        double r12713 = r12710 * r12712;
        double r12714 = v;
        double r12715 = r12713 / r12714;
        double r12716 = r12715 - r12711;
        double r12717 = r12716 * r12712;
        return r12717;
}
↓
double f(double m, double v) {
        double r12718 = m;
        double r12719 = 1.0;
        double r12720 = r12719 - r12718;
        double r12721 = r12718 * r12720;
        double r12722 = v;
        double r12723 = r12721 / r12722;
        double r12724 = r12723 - r12719;
        double r12725 = r12724 * r12719;
        double r12726 = r12719 * r12719;
        double r12727 = r12718 * r12718;
        double r12728 = r12726 - r12727;
        double r12729 = r12718 * r12728;
        double r12730 = r12719 + r12718;
        double r12731 = r12722 * r12730;
        double r12732 = r12729 / r12731;
        double r12733 = r12732 - r12719;
        double r12734 = -r12718;
        double r12735 = r12733 * r12734;
        double r12736 = r12725 + r12735;
        return r12736;
}

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

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

  7. Applied associate-*r/0.1

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

  8. Applied associate-/l/0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019344 
(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)))