Average Error: 0.0 → 0.0
Time: 9.1s
Precision: 64
\[\left(\left(x - \left(y - 1.0\right) \cdot z\right) - \left(t - 1.0\right) \cdot a\right) + \left(\left(y + t\right) - 2.0\right) \cdot b\]
↓
\[\mathsf{fma}\left(\left(y + t\right) - 2.0, b, \mathsf{fma}\left(a, 1.0 - t, \mathsf{fma}\left(z, 1.0 - y, x\right)\right)\right)\]
\left(\left(x - \left(y - 1.0\right) \cdot z\right) - \left(t - 1.0\right) \cdot a\right) + \left(\left(y + t\right) - 2.0\right) \cdot b
↓
\mathsf{fma}\left(\left(y + t\right) - 2.0, b, \mathsf{fma}\left(a, 1.0 - t, \mathsf{fma}\left(z, 1.0 - y, x\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r959921 = x;
        double r959922 = y;
        double r959923 = 1.0;
        double r959924 = r959922 - r959923;
        double r959925 = z;
        double r959926 = r959924 * r959925;
        double r959927 = r959921 - r959926;
        double r959928 = t;
        double r959929 = r959928 - r959923;
        double r959930 = a;
        double r959931 = r959929 * r959930;
        double r959932 = r959927 - r959931;
        double r959933 = r959922 + r959928;
        double r959934 = 2.0;
        double r959935 = r959933 - r959934;
        double r959936 = b;
        double r959937 = r959935 * r959936;
        double r959938 = r959932 + r959937;
        return r959938;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r959939 = y;
        double r959940 = t;
        double r959941 = r959939 + r959940;
        double r959942 = 2.0;
        double r959943 = r959941 - r959942;
        double r959944 = b;
        double r959945 = a;
        double r959946 = 1.0;
        double r959947 = r959946 - r959940;
        double r959948 = z;
        double r959949 = r959946 - r959939;
        double r959950 = x;
        double r959951 = fma(r959948, r959949, r959950);
        double r959952 = fma(r959945, r959947, r959951);
        double r959953 = fma(r959943, r959944, r959952);
        return r959953;
}

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

    \[\left(\left(x - \left(y - 1.0\right) \cdot z\right) - \left(t - 1.0\right) \cdot a\right) + \left(\left(y + t\right) - 2.0\right) \cdot b\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2.0, b, \mathsf{fma}\left(a, 1.0 - t, \mathsf{fma}\left(z, 1.0 - y, x\right)\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(\left(y + t\right) - 2.0, b, \mathsf{fma}\left(a, 1.0 - t, \mathsf{fma}\left(z, 1.0 - y, x\right)\right)\right)\]

Reproduce

herbie shell --seed 2019163 +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)))