Average Error: 0.1 → 0.1
Time: 3.5m
Precision: 64
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right) \cdot \left(-m\right) + \left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right)\]
double f(double m, double v) {
        double r10849382 = m;
        double r10849383 = 1.0;
        double r10849384 = r10849383 - r10849382;
        double r10849385 = r10849382 * r10849384;
        double r10849386 = v;
        double r10849387 = r10849385 / r10849386;
        double r10849388 = r10849387 - r10849383;
        double r10849389 = r10849388 * r10849384;
        return r10849389;
}
↓
double f(double m, double v) {
        double r10849390 = 1.0;
        double r10849391 = m;
        double r10849392 = r10849390 - r10849391;
        double r10849393 = r10849392 * r10849391;
        double r10849394 = v;
        double r10849395 = r10849393 / r10849394;
        double r10849396 = r10849395 - r10849390;
        double r10849397 = -r10849391;
        double r10849398 = r10849396 * r10849397;
        double r10849399 = r10849398 + r10849396;
        return r10849399;
}


\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right) \cdot \left(-m\right) + \left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right)

Error

Bits error versus m

Bits error versus v

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019102 +o rules:numerics
(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)))