Average Error: 0.0 → 0.0
Time: 1.4m
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\mathsf{fma}\left(b, \left(y + t\right) - 2, \mathsf{fma}\left(z, 1 - y, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)\]
\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(z, 1 - y, \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 r89905 = x;
        double r89906 = y;
        double r89907 = 1.0;
        double r89908 = r89906 - r89907;
        double r89909 = z;
        double r89910 = r89908 * r89909;
        double r89911 = r89905 - r89910;
        double r89912 = t;
        double r89913 = r89912 - r89907;
        double r89914 = a;
        double r89915 = r89913 * r89914;
        double r89916 = r89911 - r89915;
        double r89917 = r89906 + r89912;
        double r89918 = 2.0;
        double r89919 = r89917 - r89918;
        double r89920 = b;
        double r89921 = r89919 * r89920;
        double r89922 = r89916 + r89921;
        return r89922;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r89923 = b;
        double r89924 = y;
        double r89925 = t;
        double r89926 = r89924 + r89925;
        double r89927 = 2.0;
        double r89928 = r89926 - r89927;
        double r89929 = z;
        double r89930 = 1.0;
        double r89931 = r89930 - r89924;
        double r89932 = a;
        double r89933 = r89930 - r89925;
        double r89934 = x;
        double r89935 = fma(r89932, r89933, r89934);
        double r89936 = fma(r89929, r89931, r89935);
        double r89937 = fma(r89923, r89928, r89936);
        return r89937;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019212 +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)))