Average Error: 0.2 → 0.2
Time: 4.4s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(m \cdot \frac{1 - m}{v} - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(m \cdot \frac{1 - m}{v} - 1\right) \cdot m
double f(double m, double v) {
        double r10800 = m;
        double r10801 = 1.0;
        double r10802 = r10801 - r10800;
        double r10803 = r10800 * r10802;
        double r10804 = v;
        double r10805 = r10803 / r10804;
        double r10806 = r10805 - r10801;
        double r10807 = r10806 * r10800;
        return r10807;
}
↓
double f(double m, double v) {
        double r10808 = m;
        double r10809 = 1.0;
        double r10810 = r10809 - r10808;
        double r10811 = v;
        double r10812 = r10810 / r10811;
        double r10813 = r10808 * r10812;
        double r10814 = r10813 - r10809;
        double r10815 = r10814 * r10808;
        return r10815;
}

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 0.2

    \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.2

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

  4. Applied times-frac0.2

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

  5. Simplified0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019352 +o rules:numerics
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))