Average Error: 0.1 → 0.6
Time: 16.3s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{\frac{m \cdot \left({1}^{3} - {m}^{3}\right)}{1 \cdot 1 + \left(m \cdot m + 1 \cdot m\right)}}{v} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{\frac{m \cdot \left({1}^{3} - {m}^{3}\right)}{1 \cdot 1 + \left(m \cdot m + 1 \cdot m\right)}}{v} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r23356 = m;
        double r23357 = 1.0;
        double r23358 = r23357 - r23356;
        double r23359 = r23356 * r23358;
        double r23360 = v;
        double r23361 = r23359 / r23360;
        double r23362 = r23361 - r23357;
        double r23363 = r23362 * r23358;
        return r23363;
}
↓
double f(double m, double v) {
        double r23364 = m;
        double r23365 = 1.0;
        double r23366 = 3.0;
        double r23367 = pow(r23365, r23366);
        double r23368 = pow(r23364, r23366);
        double r23369 = r23367 - r23368;
        double r23370 = r23364 * r23369;
        double r23371 = r23365 * r23365;
        double r23372 = r23364 * r23364;
        double r23373 = r23365 * r23364;
        double r23374 = r23372 + r23373;
        double r23375 = r23371 + r23374;
        double r23376 = r23370 / r23375;
        double r23377 = v;
        double r23378 = r23376 / r23377;
        double r23379 = r23378 - r23365;
        double r23380 = r23365 - r23364;
        double r23381 = r23379 * r23380;
        return r23381;
}

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 flip3--0.1

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

  4. Applied associate-*r/0.6

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

  5. Final simplification0.6

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

Reproduce

herbie shell --seed 2019298 
(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)))