Average Error: 0.2 → 0.2
Time: 3.7s
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 r11560 = m;
        double r11561 = 1.0;
        double r11562 = r11561 - r11560;
        double r11563 = r11560 * r11562;
        double r11564 = v;
        double r11565 = r11563 / r11564;
        double r11566 = r11565 - r11561;
        double r11567 = r11566 * r11560;
        return r11567;
}
↓
double f(double m, double v) {
        double r11568 = m;
        double r11569 = 1.0;
        double r11570 = r11569 - r11568;
        double r11571 = v;
        double r11572 = r11570 / r11571;
        double r11573 = r11568 * r11572;
        double r11574 = r11573 - r11569;
        double r11575 = r11574 * r11568;
        return r11575;
}

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 2020020 +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))