Average Error: 0.1 → 0.1
Time: 7.0s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(1 - m\right) \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(1 - m\right) \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)
double f(double m, double v) {
        double r19478 = m;
        double r19479 = 1.0;
        double r19480 = r19479 - r19478;
        double r19481 = r19478 * r19480;
        double r19482 = v;
        double r19483 = r19481 / r19482;
        double r19484 = r19483 - r19479;
        double r19485 = r19484 * r19480;
        return r19485;
}
↓
double f(double m, double v) {
        double r19486 = 1.0;
        double r19487 = m;
        double r19488 = r19486 - r19487;
        double r19489 = r19487 * r19488;
        double r19490 = v;
        double r19491 = r19489 / r19490;
        double r19492 = r19491 - r19486;
        double r19493 = r19488 * r19492;
        return r19493;
}

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 flip--0.1

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

  4. Applied associate-*r/0.1

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

  5. Applied associate-/l/0.1

    \[\leadsto \left(\color{blue}{\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{v \cdot \left(1 + m\right)}} - 1\right) \cdot \left(1 - m\right)\]
  6. Using strategy rm

  7. Applied flip-+0.1

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

  8. Applied associate-*r/0.1

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

  9. Applied associate-/r/0.1

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019304 
(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)))