Average Error: 0.2 → 0.2
Time: 16.0s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\left(\frac{m}{v} - \frac{m \cdot m}{v}\right) - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\left(\frac{m}{v} - \frac{m \cdot m}{v}\right) - 1\right) \cdot m
double f(double m, double v) {
        double r391574 = m;
        double r391575 = 1.0;
        double r391576 = r391575 - r391574;
        double r391577 = r391574 * r391576;
        double r391578 = v;
        double r391579 = r391577 / r391578;
        double r391580 = r391579 - r391575;
        double r391581 = r391580 * r391574;
        return r391581;
}
↓
double f(double m, double v) {
        double r391582 = m;
        double r391583 = v;
        double r391584 = r391582 / r391583;
        double r391585 = r391582 * r391582;
        double r391586 = r391585 / r391583;
        double r391587 = r391584 - r391586;
        double r391588 = 1.0;
        double r391589 = r391587 - r391588;
        double r391590 = r391589 * r391582;
        return r391590;
}

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. Using strategy rm

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

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

  4. Applied times-frac0.2

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

  5. Simplified0.2

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

  6. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{\left(\frac{m}{v} - \left(\frac{{m}^{2}}{v} + 1\right)\right)} \cdot m\]

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019153 
(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))