Average Error: 0.0 → 0.0
Time: 20.9s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(b, \left(t + y\right) - 2, x\right)\right)\right)\]
\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(a, 1 - t, \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(b, \left(t + y\right) - 2, x\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r1937695 = x;
        double r1937696 = y;
        double r1937697 = 1.0;
        double r1937698 = r1937696 - r1937697;
        double r1937699 = z;
        double r1937700 = r1937698 * r1937699;
        double r1937701 = r1937695 - r1937700;
        double r1937702 = t;
        double r1937703 = r1937702 - r1937697;
        double r1937704 = a;
        double r1937705 = r1937703 * r1937704;
        double r1937706 = r1937701 - r1937705;
        double r1937707 = r1937696 + r1937702;
        double r1937708 = 2.0;
        double r1937709 = r1937707 - r1937708;
        double r1937710 = b;
        double r1937711 = r1937709 * r1937710;
        double r1937712 = r1937706 + r1937711;
        return r1937712;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r1937713 = a;
        double r1937714 = 1.0;
        double r1937715 = t;
        double r1937716 = r1937714 - r1937715;
        double r1937717 = y;
        double r1937718 = r1937714 - r1937717;
        double r1937719 = z;
        double r1937720 = b;
        double r1937721 = r1937715 + r1937717;
        double r1937722 = 2.0;
        double r1937723 = r1937721 - r1937722;
        double r1937724 = x;
        double r1937725 = fma(r1937720, r1937723, r1937724);
        double r1937726 = fma(r1937718, r1937719, r1937725);
        double r1937727 = fma(r1937713, r1937716, r1937726);
        return r1937727;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 +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)))