Average Error: 0.2 → 0.3
Time: 7.1s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{\frac{m \cdot \left(1 - m\right)}{\sqrt{v}}}{\sqrt{v}} - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{\frac{m \cdot \left(1 - m\right)}{\sqrt{v}}}{\sqrt{v}} - 1\right) \cdot m
double f(double m, double v) {
        double r16657 = m;
        double r16658 = 1.0;
        double r16659 = r16658 - r16657;
        double r16660 = r16657 * r16659;
        double r16661 = v;
        double r16662 = r16660 / r16661;
        double r16663 = r16662 - r16658;
        double r16664 = r16663 * r16657;
        return r16664;
}
↓
double f(double m, double v) {
        double r16665 = m;
        double r16666 = 1.0;
        double r16667 = r16666 - r16665;
        double r16668 = r16665 * r16667;
        double r16669 = v;
        double r16670 = sqrt(r16669);
        double r16671 = r16668 / r16670;
        double r16672 = r16671 / r16670;
        double r16673 = r16672 - r16666;
        double r16674 = r16673 * r16665;
        return r16674;
}

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 add-sqr-sqrt0.4

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

  4. Applied associate-/r*0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2020003 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))