Average Error: 0.2 → 0.2
Time: 1.3m
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[m \cdot \frac{m}{v} + m \cdot \left(-1 - \sqrt{m} \cdot \left(\frac{m}{v} \cdot \sqrt{m}\right)\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
m \cdot \frac{m}{v} + m \cdot \left(-1 - \sqrt{m} \cdot \left(\frac{m}{v} \cdot \sqrt{m}\right)\right)
double f(double m, double v) {
        double r1939040 = m;
        double r1939041 = 1.0;
        double r1939042 = r1939041 - r1939040;
        double r1939043 = r1939040 * r1939042;
        double r1939044 = v;
        double r1939045 = r1939043 / r1939044;
        double r1939046 = r1939045 - r1939041;
        double r1939047 = r1939046 * r1939040;
        return r1939047;
}
↓
double f(double m, double v) {
        double r1939048 = m;
        double r1939049 = v;
        double r1939050 = r1939048 / r1939049;
        double r1939051 = r1939048 * r1939050;
        double r1939052 = -1.0;
        double r1939053 = sqrt(r1939048);
        double r1939054 = r1939050 * r1939053;
        double r1939055 = r1939053 * r1939054;
        double r1939056 = r1939052 - r1939055;
        double r1939057 = r1939048 * r1939056;
        double r1939058 = r1939051 + r1939057;
        return r1939058;
}

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. Simplified0.2

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

  4. Applied sub-neg0.2

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

  5. Applied distribute-lft-in0.2

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

  6. Simplified0.2

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

  8. Applied add-sqr-sqrt0.2

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

  9. Applied associate-*l*0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2019107 +o rules:numerics
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))