Average Error: 0.1 → 0.1
Time: 4.9s
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 r13268 = m;
        double r13269 = 1.0;
        double r13270 = r13269 - r13268;
        double r13271 = r13268 * r13270;
        double r13272 = v;
        double r13273 = r13271 / r13272;
        double r13274 = r13273 - r13269;
        double r13275 = r13274 * r13270;
        return r13275;
}
↓
double f(double m, double v) {
        double r13276 = m;
        double r13277 = v;
        double r13278 = 1.0;
        double r13279 = r13278 - r13276;
        double r13280 = r13277 / r13279;
        double r13281 = r13276 / r13280;
        double r13282 = r13281 - r13278;
        double r13283 = r13282 * r13279;
        return r13283;
}

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 2020020 +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)))