Average Error: 0.1 → 0.1
Time: 19.2s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m}{\frac{v}{1 - m \cdot m} \cdot \left(m + 1\right)} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m}{\frac{v}{1 - m \cdot m} \cdot \left(m + 1\right)} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r832203 = m;
        double r832204 = 1.0;
        double r832205 = r832204 - r832203;
        double r832206 = r832203 * r832205;
        double r832207 = v;
        double r832208 = r832206 / r832207;
        double r832209 = r832208 - r832204;
        double r832210 = r832209 * r832205;
        return r832210;
}
↓
double f(double m, double v) {
        double r832211 = m;
        double r832212 = v;
        double r832213 = 1.0;
        double r832214 = r832211 * r832211;
        double r832215 = r832213 - r832214;
        double r832216 = r832212 / r832215;
        double r832217 = r832211 + r832213;
        double r832218 = r832216 * r832217;
        double r832219 = r832211 / r832218;
        double r832220 = r832219 - r832213;
        double r832221 = r832213 - r832211;
        double r832222 = r832220 * r832221;
        return r832222;
}

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. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019141 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))