Average Error: 0.0 → 0.0
Time: 9.0s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\mathsf{fma}\left(b, \left(y + t\right) - 2, \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)\]
\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(b, \left(y + t\right) - 2, \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 r25797 = x;
        double r25798 = y;
        double r25799 = 1.0;
        double r25800 = r25798 - r25799;
        double r25801 = z;
        double r25802 = r25800 * r25801;
        double r25803 = r25797 - r25802;
        double r25804 = t;
        double r25805 = r25804 - r25799;
        double r25806 = a;
        double r25807 = r25805 * r25806;
        double r25808 = r25803 - r25807;
        double r25809 = r25798 + r25804;
        double r25810 = 2.0;
        double r25811 = r25809 - r25810;
        double r25812 = b;
        double r25813 = r25811 * r25812;
        double r25814 = r25808 + r25813;
        return r25814;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r25815 = b;
        double r25816 = y;
        double r25817 = t;
        double r25818 = r25816 + r25817;
        double r25819 = 2.0;
        double r25820 = r25818 - r25819;
        double r25821 = 1.0;
        double r25822 = r25821 - r25816;
        double r25823 = z;
        double r25824 = a;
        double r25825 = r25821 - r25817;
        double r25826 = x;
        double r25827 = fma(r25824, r25825, r25826);
        double r25828 = fma(r25822, r25823, r25827);
        double r25829 = fma(r25815, r25820, r25828);
        return r25829;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019347 +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)))