Average Error: 0.0 → 0.0
Time: 6.7s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\mathsf{fma}\left(b, \left(y + t\right) - 2, \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)\]
\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 r15742 = x;
        double r15743 = y;
        double r15744 = 1.0;
        double r15745 = r15743 - r15744;
        double r15746 = z;
        double r15747 = r15745 * r15746;
        double r15748 = r15742 - r15747;
        double r15749 = t;
        double r15750 = r15749 - r15744;
        double r15751 = a;
        double r15752 = r15750 * r15751;
        double r15753 = r15748 - r15752;
        double r15754 = r15743 + r15749;
        double r15755 = 2.0;
        double r15756 = r15754 - r15755;
        double r15757 = b;
        double r15758 = r15756 * r15757;
        double r15759 = r15753 + r15758;
        return r15759;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r15760 = b;
        double r15761 = y;
        double r15762 = t;
        double r15763 = r15761 + r15762;
        double r15764 = 2.0;
        double r15765 = r15763 - r15764;
        double r15766 = 1.0;
        double r15767 = r15766 - r15761;
        double r15768 = z;
        double r15769 = a;
        double r15770 = r15766 - r15762;
        double r15771 = x;
        double r15772 = fma(r15769, r15770, r15771);
        double r15773 = fma(r15767, r15768, r15772);
        double r15774 = fma(r15760, r15765, r15773);
        return r15774;
}

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 2019306 +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)))