Average Error: 0.1 → 0.1
Time: 23.7s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\left(\frac{m \cdot \left(m \cdot m\right)}{v} - \frac{m \cdot m}{v}\right) + m\right) + \left(\frac{m}{\frac{v}{1 - m}} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\left(\frac{m \cdot \left(m \cdot m\right)}{v} - \frac{m \cdot m}{v}\right) + m\right) + \left(\frac{m}{\frac{v}{1 - m}} - 1\right)
double f(double m, double v) {
        double r736238 = m;
        double r736239 = 1.0;
        double r736240 = r736239 - r736238;
        double r736241 = r736238 * r736240;
        double r736242 = v;
        double r736243 = r736241 / r736242;
        double r736244 = r736243 - r736239;
        double r736245 = r736244 * r736240;
        return r736245;
}
↓
double f(double m, double v) {
        double r736246 = m;
        double r736247 = r736246 * r736246;
        double r736248 = r736246 * r736247;
        double r736249 = v;
        double r736250 = r736248 / r736249;
        double r736251 = r736247 / r736249;
        double r736252 = r736250 - r736251;
        double r736253 = r736252 + r736246;
        double r736254 = 1.0;
        double r736255 = r736254 - r736246;
        double r736256 = r736249 / r736255;
        double r736257 = r736246 / r736256;
        double r736258 = r736257 - r736254;
        double r736259 = r736253 + r736258;
        return r736259;
}

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 associate-/l*0.1

    \[\leadsto \left(\color{blue}{\frac{m}{\frac{v}{1 - m}}} - 1\right) \cdot \left(1 - m\right)\]
  4. Using strategy rm

  5. Applied sub-neg0.1

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

  6. Applied distribute-lft-in0.1

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

  7. Taylor expanded around -inf 0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019134 +o rules:numerics
(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)))