Average Error: 0.1 → 0.1
Time: 38.4s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{\left(\left(1 + m\right) \cdot \frac{m}{v}\right) \cdot \left(1 - m\right)}{1 + m} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{\left(\left(1 + m\right) \cdot \frac{m}{v}\right) \cdot \left(1 - m\right)}{1 + m} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r1354489 = m;
        double r1354490 = 1.0;
        double r1354491 = r1354490 - r1354489;
        double r1354492 = r1354489 * r1354491;
        double r1354493 = v;
        double r1354494 = r1354492 / r1354493;
        double r1354495 = r1354494 - r1354490;
        double r1354496 = r1354495 * r1354491;
        return r1354496;
}
↓
double f(double m, double v) {
        double r1354497 = 1.0;
        double r1354498 = m;
        double r1354499 = r1354497 + r1354498;
        double r1354500 = v;
        double r1354501 = r1354498 / r1354500;
        double r1354502 = r1354499 * r1354501;
        double r1354503 = r1354497 - r1354498;
        double r1354504 = r1354502 * r1354503;
        double r1354505 = r1354504 / r1354499;
        double r1354506 = r1354505 - r1354497;
        double r1354507 = r1354506 * r1354503;
        return r1354507;
}

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. Applied associate-/r*0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019200 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))