Average Error: 0.1 → 0.1
Time: 13.3s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(1 - m\right) \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(1 - m\right) \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)
double f(double m, double v) {
        double r24871 = m;
        double r24872 = 1.0;
        double r24873 = r24872 - r24871;
        double r24874 = r24871 * r24873;
        double r24875 = v;
        double r24876 = r24874 / r24875;
        double r24877 = r24876 - r24872;
        double r24878 = r24877 * r24873;
        return r24878;
}
↓
double f(double m, double v) {
        double r24879 = 1.0;
        double r24880 = m;
        double r24881 = r24879 - r24880;
        double r24882 = r24880 * r24881;
        double r24883 = v;
        double r24884 = r24882 / r24883;
        double r24885 = r24884 - r24879;
        double r24886 = r24881 * r24885;
        return r24886;
}

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

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

  11. Final simplification0.1

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

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)))