Average Error: 0.1 → 0.1
Time: 23.0s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r1254748 = m;
        double r1254749 = 1.0;
        double r1254750 = r1254749 - r1254748;
        double r1254751 = r1254748 * r1254750;
        double r1254752 = v;
        double r1254753 = r1254751 / r1254752;
        double r1254754 = r1254753 - r1254749;
        double r1254755 = r1254754 * r1254750;
        return r1254755;
}
↓
double f(double m, double v) {
        double r1254756 = 1.0;
        double r1254757 = m;
        double r1254758 = r1254756 - r1254757;
        double r1254759 = r1254758 * r1254757;
        double r1254760 = v;
        double r1254761 = r1254759 / r1254760;
        double r1254762 = r1254761 - r1254756;
        double r1254763 = r1254762 * r1254758;
        return r1254763;
}

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 *-un-lft-identity0.1

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

  4. Applied associate-/r*0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(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)))