Average Error: 0.0 → 0.0
Time: 5.6s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(b, \left(y + t\right) - 2, x\right) - \left(t - 1\right) \cdot a\right)\]
\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(1 - y, z, \mathsf{fma}\left(b, \left(y + t\right) - 2, x\right) - \left(t - 1\right) \cdot a\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r35655 = x;
        double r35656 = y;
        double r35657 = 1.0;
        double r35658 = r35656 - r35657;
        double r35659 = z;
        double r35660 = r35658 * r35659;
        double r35661 = r35655 - r35660;
        double r35662 = t;
        double r35663 = r35662 - r35657;
        double r35664 = a;
        double r35665 = r35663 * r35664;
        double r35666 = r35661 - r35665;
        double r35667 = r35656 + r35662;
        double r35668 = 2.0;
        double r35669 = r35667 - r35668;
        double r35670 = b;
        double r35671 = r35669 * r35670;
        double r35672 = r35666 + r35671;
        return r35672;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r35673 = 1.0;
        double r35674 = y;
        double r35675 = r35673 - r35674;
        double r35676 = z;
        double r35677 = b;
        double r35678 = t;
        double r35679 = r35674 + r35678;
        double r35680 = 2.0;
        double r35681 = r35679 - r35680;
        double r35682 = x;
        double r35683 = fma(r35677, r35681, r35682);
        double r35684 = r35678 - r35673;
        double r35685 = a;
        double r35686 = r35684 * r35685;
        double r35687 = r35683 - r35686;
        double r35688 = fma(r35675, r35676, r35687);
        return r35688;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 +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)))