Average Error: 0.0 → 0.0
Time: 11.1s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\mathsf{fma}\left(b, \left(y + t\right) - 2, \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)\]
\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b
↓
\mathsf{fma}\left(b, \left(y + t\right) - 2, \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r24515 = x;
        double r24516 = y;
        double r24517 = 1.0;
        double r24518 = r24516 - r24517;
        double r24519 = z;
        double r24520 = r24518 * r24519;
        double r24521 = r24515 - r24520;
        double r24522 = t;
        double r24523 = r24522 - r24517;
        double r24524 = a;
        double r24525 = r24523 * r24524;
        double r24526 = r24521 - r24525;
        double r24527 = r24516 + r24522;
        double r24528 = 2.0;
        double r24529 = r24527 - r24528;
        double r24530 = b;
        double r24531 = r24529 * r24530;
        double r24532 = r24526 + r24531;
        return r24532;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r24533 = b;
        double r24534 = y;
        double r24535 = t;
        double r24536 = r24534 + r24535;
        double r24537 = 2.0;
        double r24538 = r24536 - r24537;
        double r24539 = 1.0;
        double r24540 = r24539 - r24534;
        double r24541 = z;
        double r24542 = a;
        double r24543 = r24539 - r24535;
        double r24544 = x;
        double r24545 = fma(r24542, r24543, r24544);
        double r24546 = fma(r24540, r24541, r24545);
        double r24547 = fma(r24533, r24538, r24546);
        return r24547;
}

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

    \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(b, \left(y + t\right) - 2, \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(b, \left(y + t\right) - 2, \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)\]

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1) z)) (* (- t 1) a)) (* (- (+ y t) 2) b)))