Average Error: 0.0 → 0.0
Time: 7.4s
Precision: 64
\[\left(\left(x - \left(y - 1.0\right) \cdot z\right) - \left(t - 1.0\right) \cdot a\right) + \left(\left(y + t\right) - 2.0\right) \cdot b\]
↓
\[\mathsf{fma}\left(\left(y + t\right) - 2.0, b, \mathsf{fma}\left(a, 1.0 - t, \mathsf{fma}\left(z, 1.0 - y, x\right)\right)\right)\]
\left(\left(x - \left(y - 1.0\right) \cdot z\right) - \left(t - 1.0\right) \cdot a\right) + \left(\left(y + t\right) - 2.0\right) \cdot b
↓
\mathsf{fma}\left(\left(y + t\right) - 2.0, b, \mathsf{fma}\left(a, 1.0 - t, \mathsf{fma}\left(z, 1.0 - y, x\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r1106319 = x;
        double r1106320 = y;
        double r1106321 = 1.0;
        double r1106322 = r1106320 - r1106321;
        double r1106323 = z;
        double r1106324 = r1106322 * r1106323;
        double r1106325 = r1106319 - r1106324;
        double r1106326 = t;
        double r1106327 = r1106326 - r1106321;
        double r1106328 = a;
        double r1106329 = r1106327 * r1106328;
        double r1106330 = r1106325 - r1106329;
        double r1106331 = r1106320 + r1106326;
        double r1106332 = 2.0;
        double r1106333 = r1106331 - r1106332;
        double r1106334 = b;
        double r1106335 = r1106333 * r1106334;
        double r1106336 = r1106330 + r1106335;
        return r1106336;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r1106337 = y;
        double r1106338 = t;
        double r1106339 = r1106337 + r1106338;
        double r1106340 = 2.0;
        double r1106341 = r1106339 - r1106340;
        double r1106342 = b;
        double r1106343 = a;
        double r1106344 = 1.0;
        double r1106345 = r1106344 - r1106338;
        double r1106346 = z;
        double r1106347 = r1106344 - r1106337;
        double r1106348 = x;
        double r1106349 = fma(r1106346, r1106347, r1106348);
        double r1106350 = fma(r1106343, r1106345, r1106349);
        double r1106351 = fma(r1106341, r1106342, r1106350);
        return r1106351;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Derivation

  1. Initial program 0.0

    \[\left(\left(x - \left(y - 1.0\right) \cdot z\right) - \left(t - 1.0\right) \cdot a\right) + \left(\left(y + t\right) - 2.0\right) \cdot b\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2.0, b, \mathsf{fma}\left(a, 1.0 - t, \mathsf{fma}\left(z, 1.0 - y, x\right)\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(\left(y + t\right) - 2.0, b, \mathsf{fma}\left(a, 1.0 - t, \mathsf{fma}\left(z, 1.0 - y, x\right)\right)\right)\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))