Average Error: 0.0 → 0.0
Time: 16.1s
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 r1931931 = x;
        double r1931932 = y;
        double r1931933 = 1.0;
        double r1931934 = r1931932 - r1931933;
        double r1931935 = z;
        double r1931936 = r1931934 * r1931935;
        double r1931937 = r1931931 - r1931936;
        double r1931938 = t;
        double r1931939 = r1931938 - r1931933;
        double r1931940 = a;
        double r1931941 = r1931939 * r1931940;
        double r1931942 = r1931937 - r1931941;
        double r1931943 = r1931932 + r1931938;
        double r1931944 = 2.0;
        double r1931945 = r1931943 - r1931944;
        double r1931946 = b;
        double r1931947 = r1931945 * r1931946;
        double r1931948 = r1931942 + r1931947;
        return r1931948;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r1931949 = y;
        double r1931950 = t;
        double r1931951 = r1931949 + r1931950;
        double r1931952 = 2.0;
        double r1931953 = r1931951 - r1931952;
        double r1931954 = b;
        double r1931955 = a;
        double r1931956 = 1.0;
        double r1931957 = r1931956 - r1931950;
        double r1931958 = z;
        double r1931959 = r1931956 - r1931949;
        double r1931960 = x;
        double r1931961 = fma(r1931958, r1931959, r1931960);
        double r1931962 = fma(r1931955, r1931957, r1931961);
        double r1931963 = fma(r1931953, r1931954, r1931962);
        return r1931963;
}

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 2019162 +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)))