Average Error: 0.1 → 0.1
Time: 11.5s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m \cdot 1 + \left(-m\right) \cdot m}{v} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m \cdot 1 + \left(-m\right) \cdot m}{v} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r14323 = m;
        double r14324 = 1.0;
        double r14325 = r14324 - r14323;
        double r14326 = r14323 * r14325;
        double r14327 = v;
        double r14328 = r14326 / r14327;
        double r14329 = r14328 - r14324;
        double r14330 = r14329 * r14325;
        return r14330;
}
↓
double f(double m, double v) {
        double r14331 = m;
        double r14332 = 1.0;
        double r14333 = r14331 * r14332;
        double r14334 = -r14331;
        double r14335 = r14334 * r14331;
        double r14336 = r14333 + r14335;
        double r14337 = v;
        double r14338 = r14336 / r14337;
        double r14339 = r14338 - r14332;
        double r14340 = r14332 - r14331;
        double r14341 = r14339 * r14340;
        return r14341;
}

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 sub-neg0.1

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

  4. Applied distribute-lft-in0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))