Average Error: 0.1 → 0.1
Time: 3.8s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m}{\frac{v}{1 - m}} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m}{\frac{v}{1 - m}} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r11275 = m;
        double r11276 = 1.0;
        double r11277 = r11276 - r11275;
        double r11278 = r11275 * r11277;
        double r11279 = v;
        double r11280 = r11278 / r11279;
        double r11281 = r11280 - r11276;
        double r11282 = r11281 * r11277;
        return r11282;
}
↓
double f(double m, double v) {
        double r11283 = m;
        double r11284 = v;
        double r11285 = 1.0;
        double r11286 = r11285 - r11283;
        double r11287 = r11284 / r11286;
        double r11288 = r11283 / r11287;
        double r11289 = r11288 - r11285;
        double r11290 = r11289 * r11286;
        return r11290;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020059 +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)))