Average Error: 0.0 → 0.0
Time: 9.7s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\mathsf{fma}\left(\left(y + t\right) - 2, b, \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)\]
\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(\left(y + t\right) - 2, b, \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r1353605 = x;
        double r1353606 = y;
        double r1353607 = 1.0;
        double r1353608 = r1353606 - r1353607;
        double r1353609 = z;
        double r1353610 = r1353608 * r1353609;
        double r1353611 = r1353605 - r1353610;
        double r1353612 = t;
        double r1353613 = r1353612 - r1353607;
        double r1353614 = a;
        double r1353615 = r1353613 * r1353614;
        double r1353616 = r1353611 - r1353615;
        double r1353617 = r1353606 + r1353612;
        double r1353618 = 2.0;
        double r1353619 = r1353617 - r1353618;
        double r1353620 = b;
        double r1353621 = r1353619 * r1353620;
        double r1353622 = r1353616 + r1353621;
        return r1353622;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r1353623 = y;
        double r1353624 = t;
        double r1353625 = r1353623 + r1353624;
        double r1353626 = 2.0;
        double r1353627 = r1353625 - r1353626;
        double r1353628 = b;
        double r1353629 = a;
        double r1353630 = 1.0;
        double r1353631 = r1353630 - r1353624;
        double r1353632 = z;
        double r1353633 = r1353630 - r1353623;
        double r1353634 = x;
        double r1353635 = fma(r1353632, r1353633, r1353634);
        double r1353636 = fma(r1353629, r1353631, r1353635);
        double r1353637 = fma(r1353627, r1353628, r1353636);
        return r1353637;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 +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)))