Average Error: 0.0 → 0.0
Time: 39.3s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\mathsf{fma}\left(\left(y + t\right) - 2, b, \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)\]
\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(\left(y + t\right) - 2, b, \mathsf{fma}\left(1 - y, z, \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 r2350822 = x;
        double r2350823 = y;
        double r2350824 = 1.0;
        double r2350825 = r2350823 - r2350824;
        double r2350826 = z;
        double r2350827 = r2350825 * r2350826;
        double r2350828 = r2350822 - r2350827;
        double r2350829 = t;
        double r2350830 = r2350829 - r2350824;
        double r2350831 = a;
        double r2350832 = r2350830 * r2350831;
        double r2350833 = r2350828 - r2350832;
        double r2350834 = r2350823 + r2350829;
        double r2350835 = 2.0;
        double r2350836 = r2350834 - r2350835;
        double r2350837 = b;
        double r2350838 = r2350836 * r2350837;
        double r2350839 = r2350833 + r2350838;
        return r2350839;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r2350840 = y;
        double r2350841 = t;
        double r2350842 = r2350840 + r2350841;
        double r2350843 = 2.0;
        double r2350844 = r2350842 - r2350843;
        double r2350845 = b;
        double r2350846 = 1.0;
        double r2350847 = r2350846 - r2350840;
        double r2350848 = z;
        double r2350849 = a;
        double r2350850 = r2350846 - r2350841;
        double r2350851 = x;
        double r2350852 = fma(r2350849, r2350850, r2350851);
        double r2350853 = fma(r2350847, r2350848, r2350852);
        double r2350854 = fma(r2350844, r2350845, r2350853);
        return r2350854;
}

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

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

  3. Final simplification0.0

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

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)))