Average Error: 0.1 → 0.1
Time: 19.1s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[1 \cdot \left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right) + \left(\frac{m}{\frac{v}{1 - m}} - 1\right) \cdot \left(-m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
1 \cdot \left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right) + \left(\frac{m}{\frac{v}{1 - m}} - 1\right) \cdot \left(-m\right)
double f(double m, double v) {
        double r1202397 = m;
        double r1202398 = 1.0;
        double r1202399 = r1202398 - r1202397;
        double r1202400 = r1202397 * r1202399;
        double r1202401 = v;
        double r1202402 = r1202400 / r1202401;
        double r1202403 = r1202402 - r1202398;
        double r1202404 = r1202403 * r1202399;
        return r1202404;
}
↓
double f(double m, double v) {
        double r1202405 = 1.0;
        double r1202406 = m;
        double r1202407 = r1202405 - r1202406;
        double r1202408 = r1202407 * r1202406;
        double r1202409 = v;
        double r1202410 = r1202408 / r1202409;
        double r1202411 = r1202410 - r1202405;
        double r1202412 = r1202405 * r1202411;
        double r1202413 = r1202409 / r1202407;
        double r1202414 = r1202406 / r1202413;
        double r1202415 = r1202414 - r1202405;
        double r1202416 = -r1202406;
        double r1202417 = r1202415 * r1202416;
        double r1202418 = r1202412 + r1202417;
        return r1202418;
}

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 sub-neg0.1

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

  4. Applied distribute-rgt-in0.1

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

  6. Applied associate-/l*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))