Average Error: 0.2 → 0.2
Time: 9.9s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[1 \cdot \left(\frac{{m}^{\left(\frac{2}{2}\right)}}{\frac{v}{m}} - m\right) - \frac{{m}^{3}}{v}\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
1 \cdot \left(\frac{{m}^{\left(\frac{2}{2}\right)}}{\frac{v}{m}} - m\right) - \frac{{m}^{3}}{v}
double f(double m, double v) {
        double r12176 = m;
        double r12177 = 1.0;
        double r12178 = r12177 - r12176;
        double r12179 = r12176 * r12178;
        double r12180 = v;
        double r12181 = r12179 / r12180;
        double r12182 = r12181 - r12177;
        double r12183 = r12182 * r12176;
        return r12183;
}
↓
double f(double m, double v) {
        double r12184 = 1.0;
        double r12185 = m;
        double r12186 = 2.0;
        double r12187 = r12186 / r12186;
        double r12188 = pow(r12185, r12187);
        double r12189 = v;
        double r12190 = r12189 / r12185;
        double r12191 = r12188 / r12190;
        double r12192 = r12191 - r12185;
        double r12193 = r12184 * r12192;
        double r12194 = 3.0;
        double r12195 = pow(r12185, r12194);
        double r12196 = r12195 / r12189;
        double r12197 = r12193 - r12196;
        return r12197;
}

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 6.6

    \[\leadsto \color{blue}{1 \cdot \frac{{m}^{2}}{v} - \left(1 \cdot m + \frac{{m}^{3}}{v}\right)}\]

  3. Simplified6.6

    \[\leadsto \color{blue}{1 \cdot \left(\frac{{m}^{2}}{v} - m\right) - \frac{{m}^{3}}{v}}\]
  4. Using strategy rm

  5. Applied sqr-pow6.6

    \[\leadsto 1 \cdot \left(\frac{\color{blue}{{m}^{\left(\frac{2}{2}\right)} \cdot {m}^{\left(\frac{2}{2}\right)}}}{v} - m\right) - \frac{{m}^{3}}{v}\]

  6. Applied associate-/l*0.2

    \[\leadsto 1 \cdot \left(\color{blue}{\frac{{m}^{\left(\frac{2}{2}\right)}}{\frac{v}{{m}^{\left(\frac{2}{2}\right)}}}} - m\right) - \frac{{m}^{3}}{v}\]

  7. Simplified0.2

    \[\leadsto 1 \cdot \left(\frac{{m}^{\left(\frac{2}{2}\right)}}{\color{blue}{\frac{v}{m}}} - m\right) - \frac{{m}^{3}}{v}\]

  8. Final simplification0.2

    \[\leadsto 1 \cdot \left(\frac{{m}^{\left(\frac{2}{2}\right)}}{\frac{v}{m}} - m\right) - \frac{{m}^{3}}{v}\]

Reproduce

herbie shell --seed 2020045 
(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))