Average Error: 0.1 → 0.1
Time: 5.2s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \sqrt{1} + \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \sqrt{m}\right) \cdot \left(\sqrt{1} - \sqrt{m}\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \sqrt{1} + \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \sqrt{m}\right) \cdot \left(\sqrt{1} - \sqrt{m}\right)
double f(double m, double v) {
        double r17972 = m;
        double r17973 = 1.0;
        double r17974 = r17973 - r17972;
        double r17975 = r17972 * r17974;
        double r17976 = v;
        double r17977 = r17975 / r17976;
        double r17978 = r17977 - r17973;
        double r17979 = r17978 * r17974;
        return r17979;
}
↓
double f(double m, double v) {
        double r17980 = m;
        double r17981 = 1.0;
        double r17982 = r17981 - r17980;
        double r17983 = r17980 * r17982;
        double r17984 = v;
        double r17985 = r17983 / r17984;
        double r17986 = r17985 - r17981;
        double r17987 = sqrt(r17981);
        double r17988 = r17986 * r17987;
        double r17989 = sqrt(r17980);
        double r17990 = r17986 * r17989;
        double r17991 = r17988 + r17990;
        double r17992 = r17987 - r17989;
        double r17993 = r17991 * r17992;
        return r17993;
}

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 add-sqr-sqrt0.1

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

  4. Applied add-sqr-sqrt0.1

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

  5. Applied difference-of-squares0.1

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

  6. Applied associate-*r*0.1

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

  8. Applied distribute-lft-in0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020089 +o rules:numerics
(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)))