Average Error: 0.1 → 0.1
Time: 1.7m
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(1 - m\right) \cdot \left(\left(\frac{m}{v} - m \cdot \frac{m}{v}\right) - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(1 - m\right) \cdot \left(\left(\frac{m}{v} - m \cdot \frac{m}{v}\right) - 1\right)
double f(double m, double v) {
        double r7016387 = m;
        double r7016388 = 1.0;
        double r7016389 = r7016388 - r7016387;
        double r7016390 = r7016387 * r7016389;
        double r7016391 = v;
        double r7016392 = r7016390 / r7016391;
        double r7016393 = r7016392 - r7016388;
        double r7016394 = r7016393 * r7016389;
        return r7016394;
}
↓
double f(double m, double v) {
        double r7016395 = 1.0;
        double r7016396 = m;
        double r7016397 = r7016395 - r7016396;
        double r7016398 = v;
        double r7016399 = r7016396 / r7016398;
        double r7016400 = r7016396 * r7016399;
        double r7016401 = r7016399 - r7016400;
        double r7016402 = r7016401 - r7016395;
        double r7016403 = r7016397 * r7016402;
        return r7016403;
}

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 flip--0.1

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

  4. Applied associate-*r/0.1

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

  5. Applied associate-/l/0.1

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

  6. Taylor expanded around inf 0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019128 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))