Average Error: 0.1 → 0.1
Time: 3.9s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m}{\frac{v}{1 \cdot 1 - m \cdot m} \cdot \left(1 + m\right)} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m}{\frac{v}{1 \cdot 1 - m \cdot m} \cdot \left(1 + m\right)} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r11606 = m;
        double r11607 = 1.0;
        double r11608 = r11607 - r11606;
        double r11609 = r11606 * r11608;
        double r11610 = v;
        double r11611 = r11609 / r11610;
        double r11612 = r11611 - r11607;
        double r11613 = r11612 * r11608;
        return r11613;
}
↓
double f(double m, double v) {
        double r11614 = m;
        double r11615 = v;
        double r11616 = 1.0;
        double r11617 = r11616 * r11616;
        double r11618 = r11614 * r11614;
        double r11619 = r11617 - r11618;
        double r11620 = r11615 / r11619;
        double r11621 = r11616 + r11614;
        double r11622 = r11620 * r11621;
        double r11623 = r11614 / r11622;
        double r11624 = r11623 - r11616;
        double r11625 = r11616 - r11614;
        double r11626 = r11624 * r11625;
        return r11626;
}

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 flip--0.1

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

  6. Applied associate-/r/0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(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)))