Average Error: 0.0 → 0.0
Time: 29.0s
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 r9173826 = x;
        double r9173827 = y;
        double r9173828 = r9173826 * r9173827;
        double r9173829 = z;
        double r9173830 = t;
        double r9173831 = r9173829 * r9173830;
        double r9173832 = r9173828 + r9173831;
        double r9173833 = a;
        double r9173834 = b;
        double r9173835 = r9173833 * r9173834;
        double r9173836 = r9173832 + r9173835;
        double r9173837 = c;
        double r9173838 = i;
        double r9173839 = r9173837 * r9173838;
        double r9173840 = r9173836 + r9173839;
        return r9173840;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r9173841 = i;
        double r9173842 = c;
        double r9173843 = a;
        double r9173844 = b;
        double r9173845 = x;
        double r9173846 = y;
        double r9173847 = t;
        double r9173848 = z;
        double r9173849 = r9173847 * r9173848;
        double r9173850 = fma(r9173845, r9173846, r9173849);
        double r9173851 = fma(r9173843, r9173844, r9173850);
        double r9173852 = fma(r9173841, r9173842, r9173851);
        return r9173852;
}

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 2019112 +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)))