Average Error: 0.0 → 0.0
Time: 23.3s
Precision: 64
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[(i \cdot c + \left((a \cdot b + \left((x \cdot y + \left(t \cdot z\right))_*\right))_*\right))_*\]
\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i
↓
(i \cdot c + \left((a \cdot b + \left((x \cdot y + \left(t \cdot z\right))_*\right))_*\right))_*
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r9497607 = x;
        double r9497608 = y;
        double r9497609 = r9497607 * r9497608;
        double r9497610 = z;
        double r9497611 = t;
        double r9497612 = r9497610 * r9497611;
        double r9497613 = r9497609 + r9497612;
        double r9497614 = a;
        double r9497615 = b;
        double r9497616 = r9497614 * r9497615;
        double r9497617 = r9497613 + r9497616;
        double r9497618 = c;
        double r9497619 = i;
        double r9497620 = r9497618 * r9497619;
        double r9497621 = r9497617 + r9497620;
        return r9497621;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r9497622 = i;
        double r9497623 = c;
        double r9497624 = a;
        double r9497625 = b;
        double r9497626 = x;
        double r9497627 = y;
        double r9497628 = t;
        double r9497629 = z;
        double r9497630 = r9497628 * r9497629;
        double r9497631 = fma(r9497626, r9497627, r9497630);
        double r9497632 = fma(r9497624, r9497625, r9497631);
        double r9497633 = fma(r9497622, r9497623, r9497632);
        return r9497633;
}

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

Bits error versus c

Bits error versus i

Derivation

  1. Initial program 0.0

    \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]

  2. Simplified0.0

    \[\leadsto \color{blue}{(i \cdot c + \left((a \cdot b + \left((x \cdot y + \left(z \cdot t\right))_*\right))_*\right))_*}\]

  3. Final simplification0.0

    \[\leadsto (i \cdot c + \left((a \cdot b + \left((x \cdot y + \left(t \cdot z\right))_*\right))_*\right))_*\]

Reproduce

herbie shell --seed 2019104 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3"
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))