Average Error: 0.0 → 0.0
Time: 8.5s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\mathsf{fma}\left(\left(y + t\right) - 2, b, \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)\]
\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(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r1348803 = x;
        double r1348804 = y;
        double r1348805 = 1.0;
        double r1348806 = r1348804 - r1348805;
        double r1348807 = z;
        double r1348808 = r1348806 * r1348807;
        double r1348809 = r1348803 - r1348808;
        double r1348810 = t;
        double r1348811 = r1348810 - r1348805;
        double r1348812 = a;
        double r1348813 = r1348811 * r1348812;
        double r1348814 = r1348809 - r1348813;
        double r1348815 = r1348804 + r1348810;
        double r1348816 = 2.0;
        double r1348817 = r1348815 - r1348816;
        double r1348818 = b;
        double r1348819 = r1348817 * r1348818;
        double r1348820 = r1348814 + r1348819;
        return r1348820;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r1348821 = y;
        double r1348822 = t;
        double r1348823 = r1348821 + r1348822;
        double r1348824 = 2.0;
        double r1348825 = r1348823 - r1348824;
        double r1348826 = b;
        double r1348827 = a;
        double r1348828 = 1.0;
        double r1348829 = r1348828 - r1348822;
        double r1348830 = z;
        double r1348831 = r1348828 - r1348821;
        double r1348832 = x;
        double r1348833 = fma(r1348830, r1348831, r1348832);
        double r1348834 = fma(r1348827, r1348829, r1348833);
        double r1348835 = fma(r1348825, r1348826, r1348834);
        return r1348835;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019169 +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)))