Average Error: 0.0 → 0.0
Time: 32.4s
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 r62990 = x;
        double r62991 = y;
        double r62992 = 1.0;
        double r62993 = r62991 - r62992;
        double r62994 = z;
        double r62995 = r62993 * r62994;
        double r62996 = r62990 - r62995;
        double r62997 = t;
        double r62998 = r62997 - r62992;
        double r62999 = a;
        double r63000 = r62998 * r62999;
        double r63001 = r62996 - r63000;
        double r63002 = r62991 + r62997;
        double r63003 = 2.0;
        double r63004 = r63002 - r63003;
        double r63005 = b;
        double r63006 = r63004 * r63005;
        double r63007 = r63001 + r63006;
        return r63007;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r63008 = b;
        double r63009 = y;
        double r63010 = t;
        double r63011 = r63009 + r63010;
        double r63012 = 2.0;
        double r63013 = r63011 - r63012;
        double r63014 = z;
        double r63015 = 1.0;
        double r63016 = r63015 - r63009;
        double r63017 = a;
        double r63018 = r63015 - r63010;
        double r63019 = x;
        double r63020 = fma(r63017, r63018, r63019);
        double r63021 = fma(r63014, r63016, r63020);
        double r63022 = fma(r63008, r63013, r63021);
        return r63022;
}

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 2019199 +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)))