Average Error: 0.1 → 0.1
Time: 26.7s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\left(1 - m\right) \cdot \frac{m}{v} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\left(1 - m\right) \cdot \frac{m}{v} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r1305486 = m;
        double r1305487 = 1.0;
        double r1305488 = r1305487 - r1305486;
        double r1305489 = r1305486 * r1305488;
        double r1305490 = v;
        double r1305491 = r1305489 / r1305490;
        double r1305492 = r1305491 - r1305487;
        double r1305493 = r1305492 * r1305488;
        return r1305493;
}
↓
double f(double m, double v) {
        double r1305494 = 1.0;
        double r1305495 = m;
        double r1305496 = r1305494 - r1305495;
        double r1305497 = v;
        double r1305498 = r1305495 / r1305497;
        double r1305499 = r1305496 * r1305498;
        double r1305500 = r1305499 - r1305494;
        double r1305501 = r1305500 * r1305496;
        return r1305501;
}

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 *-un-lft-identity0.1

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

  4. Applied associate-*r*0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))