Average Error: 0.2 → 0.2
Time: 46.4s
Precision: 64
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\frac{m - m \cdot m}{\frac{v}{m}} - m\]
double f(double m, double v) {
        double r1916500 = m;
        double r1916501 = 1.0;
        double r1916502 = r1916501 - r1916500;
        double r1916503 = r1916500 * r1916502;
        double r1916504 = v;
        double r1916505 = r1916503 / r1916504;
        double r1916506 = r1916505 - r1916501;
        double r1916507 = r1916506 * r1916500;
        return r1916507;
}
↓
double f(double m, double v) {
        double r1916508 = m;
        double r1916509 = r1916508 * r1916508;
        double r1916510 = r1916508 - r1916509;
        double r1916511 = v;
        double r1916512 = r1916511 / r1916508;
        double r1916513 = r1916510 / r1916512;
        double r1916514 = r1916513 - r1916508;
        return r1916514;
}


\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\frac{m - m \cdot m}{\frac{v}{m}} - m

Error

Bits error versus m

Bits error versus v

Derivation

  1. Initial program 0.2

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

  2. Simplified0.2

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

  4. Applied *-un-lft-identity0.2

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

  5. Applied add-sqr-sqrt0.4

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

  6. Applied times-frac0.3

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

  7. Applied associate-*l*0.3

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

  8. Simplified0.3

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

  10. Applied pow10.3

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

  11. Applied pow10.3

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

  12. Applied pow-prod-down0.3

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

  13. Applied pow10.3

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

  14. Applied pow-prod-down0.3

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

  15. Simplified0.2

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

  16. Final simplification0.2

    \[\leadsto \frac{m - m \cdot m}{\frac{v}{m}} - m\]

Reproduce

herbie shell --seed 2019102 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))