Average Error: 0.2 → 0.2
Time: 5.3s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{1}{\frac{\frac{v}{m}}{1 - m}} - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{1}{\frac{\frac{v}{m}}{1 - m}} - 1\right) \cdot m
double f(double m, double v) {
        double r16625 = m;
        double r16626 = 1.0;
        double r16627 = r16626 - r16625;
        double r16628 = r16625 * r16627;
        double r16629 = v;
        double r16630 = r16628 / r16629;
        double r16631 = r16630 - r16626;
        double r16632 = r16631 * r16625;
        return r16632;
}
↓
double f(double m, double v) {
        double r16633 = 1.0;
        double r16634 = v;
        double r16635 = m;
        double r16636 = r16634 / r16635;
        double r16637 = 1.0;
        double r16638 = r16637 - r16635;
        double r16639 = r16636 / r16638;
        double r16640 = r16633 / r16639;
        double r16641 = r16640 - r16637;
        double r16642 = r16641 * r16635;
        return r16642;
}

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 sub-neg0.2

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

  4. Applied distribute-lft-in0.2

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

  5. Simplified0.2

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

  6. Simplified0.2

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

  8. Applied clear-num0.2

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

  9. Simplified0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(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))