Average Error: 0.0 → 0.0
Time: 53.5s
Precision: 64
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, \mathsf{fma}\left(z, t, x \cdot y\right)\right)\right)\]
\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i
↓
\mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, \mathsf{fma}\left(z, t, x \cdot y\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r6762401 = x;
        double r6762402 = y;
        double r6762403 = r6762401 * r6762402;
        double r6762404 = z;
        double r6762405 = t;
        double r6762406 = r6762404 * r6762405;
        double r6762407 = r6762403 + r6762406;
        double r6762408 = a;
        double r6762409 = b;
        double r6762410 = r6762408 * r6762409;
        double r6762411 = r6762407 + r6762410;
        double r6762412 = c;
        double r6762413 = i;
        double r6762414 = r6762412 * r6762413;
        double r6762415 = r6762411 + r6762414;
        return r6762415;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r6762416 = c;
        double r6762417 = i;
        double r6762418 = a;
        double r6762419 = b;
        double r6762420 = z;
        double r6762421 = t;
        double r6762422 = x;
        double r6762423 = y;
        double r6762424 = r6762422 * r6762423;
        double r6762425 = fma(r6762420, r6762421, r6762424);
        double r6762426 = fma(r6762418, r6762419, r6762425);
        double r6762427 = fma(r6762416, r6762417, r6762426);
        return r6762427;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 +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)))