Average Error: 0.1 → 0.1
Time: 4.1s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot 1 + \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(-m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot 1 + \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(-m\right)
double f(double m, double v) {
        double r14097 = m;
        double r14098 = 1.0;
        double r14099 = r14098 - r14097;
        double r14100 = r14097 * r14099;
        double r14101 = v;
        double r14102 = r14100 / r14101;
        double r14103 = r14102 - r14098;
        double r14104 = r14103 * r14099;
        return r14104;
}
↓
double f(double m, double v) {
        double r14105 = m;
        double r14106 = 1.0;
        double r14107 = r14106 - r14105;
        double r14108 = r14105 * r14107;
        double r14109 = v;
        double r14110 = r14108 / r14109;
        double r14111 = r14110 - r14106;
        double r14112 = r14111 * r14106;
        double r14113 = -r14105;
        double r14114 = r14111 * r14113;
        double r14115 = r14112 + r14114;
        return r14115;
}

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

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

  4. Applied distribute-lft-in0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020018 +o rules:numerics
(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)))