Average Error: 0.2 → 0.2
Time: 16.4s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m}{\frac{v}{m}} - \frac{m}{v} \cdot \left(m \cdot m\right)\right) - m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{m}{\frac{v}{m}} - \frac{m}{v} \cdot \left(m \cdot m\right)\right) - m
double f(double m, double v) {
        double r566389 = m;
        double r566390 = 1.0;
        double r566391 = r566390 - r566389;
        double r566392 = r566389 * r566391;
        double r566393 = v;
        double r566394 = r566392 / r566393;
        double r566395 = r566394 - r566390;
        double r566396 = r566395 * r566389;
        return r566396;
}
↓
double f(double m, double v) {
        double r566397 = m;
        double r566398 = v;
        double r566399 = r566398 / r566397;
        double r566400 = r566397 / r566399;
        double r566401 = r566397 / r566398;
        double r566402 = r566397 * r566397;
        double r566403 = r566401 * r566402;
        double r566404 = r566400 - r566403;
        double r566405 = r566404 - r566397;
        return r566405;
}

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 0.2

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

  2. Simplified0.2

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

  3. Taylor expanded around 0 0.2

    \[\leadsto \frac{m}{v} \cdot \color{blue}{\left(m - {m}^{2}\right)} - m\]

  4. Simplified0.2

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

  6. Applied div-inv0.2

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

  7. Applied associate-*l*0.2

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

  8. Simplified0.2

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

  9. Taylor expanded around -inf 0.2

    \[\leadsto m \cdot \color{blue}{\left(\frac{m}{v} - \frac{{m}^{2}}{v}\right)} - m\]

  10. Simplified0.2

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

  11. Taylor expanded around inf 6.7

    \[\leadsto \color{blue}{\left(\frac{{m}^{2}}{v} - \frac{{m}^{3}}{v}\right)} - m\]

  12. Simplified0.2

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

  13. Final simplification0.2

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

Reproduce

herbie shell --seed 2019129 
(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))