Average Error: 0.0 → 0.0
Time: 9.1s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\mathsf{fma}\left(\left(y + t\right) - 2, b, \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)\]
\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 r1200779 = x;
        double r1200780 = y;
        double r1200781 = 1.0;
        double r1200782 = r1200780 - r1200781;
        double r1200783 = z;
        double r1200784 = r1200782 * r1200783;
        double r1200785 = r1200779 - r1200784;
        double r1200786 = t;
        double r1200787 = r1200786 - r1200781;
        double r1200788 = a;
        double r1200789 = r1200787 * r1200788;
        double r1200790 = r1200785 - r1200789;
        double r1200791 = r1200780 + r1200786;
        double r1200792 = 2.0;
        double r1200793 = r1200791 - r1200792;
        double r1200794 = b;
        double r1200795 = r1200793 * r1200794;
        double r1200796 = r1200790 + r1200795;
        return r1200796;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r1200797 = y;
        double r1200798 = t;
        double r1200799 = r1200797 + r1200798;
        double r1200800 = 2.0;
        double r1200801 = r1200799 - r1200800;
        double r1200802 = b;
        double r1200803 = a;
        double r1200804 = 1.0;
        double r1200805 = r1200804 - r1200798;
        double r1200806 = z;
        double r1200807 = r1200804 - r1200797;
        double r1200808 = x;
        double r1200809 = fma(r1200806, r1200807, r1200808);
        double r1200810 = fma(r1200803, r1200805, r1200809);
        double r1200811 = fma(r1200801, r1200802, r1200810);
        return r1200811;
}

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)))