Average Error: 0.2 → 0.2
Time: 23.1s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m}{\frac{v}{m}} - m\right) \cdot 1 - \frac{m \cdot m}{\frac{v}{m}}\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{m}{\frac{v}{m}} - m\right) \cdot 1 - \frac{m \cdot m}{\frac{v}{m}}
double f(double m, double v) {
        double r1117202 = m;
        double r1117203 = 1.0;
        double r1117204 = r1117203 - r1117202;
        double r1117205 = r1117202 * r1117204;
        double r1117206 = v;
        double r1117207 = r1117205 / r1117206;
        double r1117208 = r1117207 - r1117203;
        double r1117209 = r1117208 * r1117202;
        return r1117209;
}
↓
double f(double m, double v) {
        double r1117210 = m;
        double r1117211 = v;
        double r1117212 = r1117211 / r1117210;
        double r1117213 = r1117210 / r1117212;
        double r1117214 = r1117213 - r1117210;
        double r1117215 = 1.0;
        double r1117216 = r1117214 * r1117215;
        double r1117217 = r1117210 * r1117210;
        double r1117218 = r1117217 / r1117212;
        double r1117219 = r1117216 - r1117218;
        return r1117219;
}

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 associate-/l*0.2

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

  4. Taylor expanded around 0 6.7

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

  5. Simplified0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) m))