Average Error: 0.1 → 0.1
Time: 10.6s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[1 \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) + \left(\left(1 \cdot m + \frac{{m}^{3}}{v}\right) - 1 \cdot \left(\sqrt{\frac{{m}^{2}}{v}} \cdot \sqrt{\frac{{m}^{2}}{v}}\right)\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
1 \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) + \left(\left(1 \cdot m + \frac{{m}^{3}}{v}\right) - 1 \cdot \left(\sqrt{\frac{{m}^{2}}{v}} \cdot \sqrt{\frac{{m}^{2}}{v}}\right)\right)
double f(double m, double v) {
        double r13553 = m;
        double r13554 = 1.0;
        double r13555 = r13554 - r13553;
        double r13556 = r13553 * r13555;
        double r13557 = v;
        double r13558 = r13556 / r13557;
        double r13559 = r13558 - r13554;
        double r13560 = r13559 * r13555;
        return r13560;
}
↓
double f(double m, double v) {
        double r13561 = 1.0;
        double r13562 = m;
        double r13563 = r13561 - r13562;
        double r13564 = r13562 * r13563;
        double r13565 = v;
        double r13566 = r13564 / r13565;
        double r13567 = r13566 - r13561;
        double r13568 = r13561 * r13567;
        double r13569 = r13561 * r13562;
        double r13570 = 3.0;
        double r13571 = pow(r13562, r13570);
        double r13572 = r13571 / r13565;
        double r13573 = r13569 + r13572;
        double r13574 = 2.0;
        double r13575 = pow(r13562, r13574);
        double r13576 = r13575 / r13565;
        double r13577 = sqrt(r13576);
        double r13578 = r13577 * r13577;
        double r13579 = r13561 * r13578;
        double r13580 = r13573 - r13579;
        double r13581 = r13568 + r13580;
        return r13581;
}

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 sub-neg0.1

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

  4. Applied distribute-lft-in0.1

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

  5. Simplified0.1

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

  6. Simplified0.1

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

  7. Taylor expanded around 0 0.1

    \[\leadsto 1 \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) + \color{blue}{\left(\left(1 \cdot m + \frac{{m}^{3}}{v}\right) - 1 \cdot \frac{{m}^{2}}{v}\right)}\]
  8. Using strategy rm

  9. Applied add-sqr-sqrt0.1

    \[\leadsto 1 \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) + \left(\left(1 \cdot m + \frac{{m}^{3}}{v}\right) - 1 \cdot \color{blue}{\left(\sqrt{\frac{{m}^{2}}{v}} \cdot \sqrt{\frac{{m}^{2}}{v}}\right)}\right)\]

  10. Final simplification0.1

    \[\leadsto 1 \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) + \left(\left(1 \cdot m + \frac{{m}^{3}}{v}\right) - 1 \cdot \left(\sqrt{\frac{{m}^{2}}{v}} \cdot \sqrt{\frac{{m}^{2}}{v}}\right)\right)\]

Reproduce

herbie shell --seed 2020047 
(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)))