Average Error: 0.2 → 0.2
Time: 16.9s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\left(\frac{m}{v} \cdot 1 - \frac{1}{\frac{v}{m \cdot m}}\right) - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\left(\frac{m}{v} \cdot 1 - \frac{1}{\frac{v}{m \cdot m}}\right) - 1\right) \cdot m
double f(double m, double v) {
        double r1108715 = m;
        double r1108716 = 1.0;
        double r1108717 = r1108716 - r1108715;
        double r1108718 = r1108715 * r1108717;
        double r1108719 = v;
        double r1108720 = r1108718 / r1108719;
        double r1108721 = r1108720 - r1108716;
        double r1108722 = r1108721 * r1108715;
        return r1108722;
}
↓
double f(double m, double v) {
        double r1108723 = m;
        double r1108724 = v;
        double r1108725 = r1108723 / r1108724;
        double r1108726 = 1.0;
        double r1108727 = r1108725 * r1108726;
        double r1108728 = 1.0;
        double r1108729 = r1108723 * r1108723;
        double r1108730 = r1108724 / r1108729;
        double r1108731 = r1108728 / r1108730;
        double r1108732 = r1108727 - r1108731;
        double r1108733 = r1108732 - r1108726;
        double r1108734 = r1108733 * r1108723;
        return r1108734;
}

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. Taylor expanded around 0 0.2

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

  3. Simplified0.2

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

  5. Applied clear-num0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019179 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) m))