Average Error: 0.0 → 0.0
Time: 8.8s
Precision: 64
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\left(x \cdot y + z \cdot t\right) + \left(a \cdot b + i \cdot c\right)\]
\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i
↓
\left(x \cdot y + z \cdot t\right) + \left(a \cdot b + i \cdot c\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r388 = x;
        double r389 = y;
        double r390 = r388 * r389;
        double r391 = z;
        double r392 = t;
        double r393 = r391 * r392;
        double r394 = r390 + r393;
        double r395 = a;
        double r396 = b;
        double r397 = r395 * r396;
        double r398 = r394 + r397;
        double r399 = c;
        double r400 = i;
        double r401 = r399 * r400;
        double r402 = r398 + r401;
        return r402;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r403 = x;
        double r404 = y;
        double r405 = r403 * r404;
        double r406 = z;
        double r407 = t;
        double r408 = r406 * r407;
        double r409 = r405 + r408;
        double r410 = a;
        double r411 = b;
        double r412 = r410 * r411;
        double r413 = i;
        double r414 = c;
        double r415 = r413 * r414;
        double r416 = r412 + r415;
        double r417 = r409 + r416;
        return r417;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
  2. Using strategy rm

  3. Applied associate-+l+0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020025 
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3"
  :precision binary64
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))