Average Error: 0.0 → 0.0
Time: 22.7s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(b, \left(t + y\right) - 2, x\right)\right)\right)\]
\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(a, 1 - t, \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(b, \left(t + y\right) - 2, x\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r1737853 = x;
        double r1737854 = y;
        double r1737855 = 1.0;
        double r1737856 = r1737854 - r1737855;
        double r1737857 = z;
        double r1737858 = r1737856 * r1737857;
        double r1737859 = r1737853 - r1737858;
        double r1737860 = t;
        double r1737861 = r1737860 - r1737855;
        double r1737862 = a;
        double r1737863 = r1737861 * r1737862;
        double r1737864 = r1737859 - r1737863;
        double r1737865 = r1737854 + r1737860;
        double r1737866 = 2.0;
        double r1737867 = r1737865 - r1737866;
        double r1737868 = b;
        double r1737869 = r1737867 * r1737868;
        double r1737870 = r1737864 + r1737869;
        return r1737870;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r1737871 = a;
        double r1737872 = 1.0;
        double r1737873 = t;
        double r1737874 = r1737872 - r1737873;
        double r1737875 = y;
        double r1737876 = r1737872 - r1737875;
        double r1737877 = z;
        double r1737878 = b;
        double r1737879 = r1737873 + r1737875;
        double r1737880 = 2.0;
        double r1737881 = r1737879 - r1737880;
        double r1737882 = x;
        double r1737883 = fma(r1737878, r1737881, r1737882);
        double r1737884 = fma(r1737876, r1737877, r1737883);
        double r1737885 = fma(r1737871, r1737874, r1737884);
        return r1737885;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 +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)))