Average Error: 0.0 → 0.0
Time: 13.0s
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 r27661 = x;
        double r27662 = y;
        double r27663 = 1.0;
        double r27664 = r27662 - r27663;
        double r27665 = z;
        double r27666 = r27664 * r27665;
        double r27667 = r27661 - r27666;
        double r27668 = t;
        double r27669 = r27668 - r27663;
        double r27670 = a;
        double r27671 = r27669 * r27670;
        double r27672 = r27667 - r27671;
        double r27673 = r27662 + r27668;
        double r27674 = 2.0;
        double r27675 = r27673 - r27674;
        double r27676 = b;
        double r27677 = r27675 * r27676;
        double r27678 = r27672 + r27677;
        return r27678;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r27679 = b;
        double r27680 = y;
        double r27681 = t;
        double r27682 = r27680 + r27681;
        double r27683 = 2.0;
        double r27684 = r27682 - r27683;
        double r27685 = 1.0;
        double r27686 = r27685 - r27680;
        double r27687 = z;
        double r27688 = a;
        double r27689 = r27685 - r27681;
        double r27690 = x;
        double r27691 = fma(r27688, r27689, r27690);
        double r27692 = fma(r27686, r27687, r27691);
        double r27693 = fma(r27679, r27684, r27692);
        return r27693;
}

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 2019303 +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)))