Average Error: 0.1 → 0.1
Time: 20.0s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\frac{\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)}{\sqrt{1} - \sqrt{m}} \cdot \left(\sqrt{1} - \sqrt{m}\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\frac{\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)}{\sqrt{1} - \sqrt{m}} \cdot \left(\sqrt{1} - \sqrt{m}\right)
double f(double m, double v) {
        double r24978 = m;
        double r24979 = 1.0;
        double r24980 = r24979 - r24978;
        double r24981 = r24978 * r24980;
        double r24982 = v;
        double r24983 = r24981 / r24982;
        double r24984 = r24983 - r24979;
        double r24985 = r24984 * r24980;
        return r24985;
}
↓
double f(double m, double v) {
        double r24986 = m;
        double r24987 = 1.0;
        double r24988 = r24987 - r24986;
        double r24989 = r24986 * r24988;
        double r24990 = v;
        double r24991 = r24989 / r24990;
        double r24992 = r24991 - r24987;
        double r24993 = r24992 * r24988;
        double r24994 = sqrt(r24987);
        double r24995 = sqrt(r24986);
        double r24996 = r24994 - r24995;
        double r24997 = r24993 / r24996;
        double r24998 = r24997 * r24996;
        return r24998;
}

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 flip-+0.1

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

  9. Applied associate-*r/0.1

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019303 
(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)))