Average Error: 0.0 → 0.0
Time: 4.9s
Precision: 64
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, \mathsf{fma}\left(c, i, b \cdot a\right)\right)\right)\]
\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i
↓
\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, \mathsf{fma}\left(c, i, b \cdot a\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4377274 = x;
        double r4377275 = y;
        double r4377276 = r4377274 * r4377275;
        double r4377277 = z;
        double r4377278 = t;
        double r4377279 = r4377277 * r4377278;
        double r4377280 = r4377276 + r4377279;
        double r4377281 = a;
        double r4377282 = b;
        double r4377283 = r4377281 * r4377282;
        double r4377284 = r4377280 + r4377283;
        double r4377285 = c;
        double r4377286 = i;
        double r4377287 = r4377285 * r4377286;
        double r4377288 = r4377284 + r4377287;
        return r4377288;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4377289 = z;
        double r4377290 = t;
        double r4377291 = x;
        double r4377292 = y;
        double r4377293 = c;
        double r4377294 = i;
        double r4377295 = b;
        double r4377296 = a;
        double r4377297 = r4377295 * r4377296;
        double r4377298 = fma(r4377293, r4377294, r4377297);
        double r4377299 = fma(r4377291, r4377292, r4377298);
        double r4377300 = fma(r4377289, r4377290, r4377299);
        return r4377300;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, \mathsf{fma}\left(c, i, a \cdot b\right)\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, \mathsf{fma}\left(c, i, b \cdot a\right)\right)\right)\]

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3, C"
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))