Average Error: 0.0 → 0.0
Time: 4.9s
Precision: 64
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\left(x \cdot y + z \cdot t\right) + \left(a \cdot b + i \cdot c\right)\]
\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 code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((double) (((double) (((double) (((double) (x * y)) + ((double) (z * t)))) + ((double) (a * b)))) + ((double) (c * i))));
}
↓
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((double) (((double) (((double) (x * y)) + ((double) (z * t)))) + ((double) (((double) (a * b)) + ((double) (i * c))))));
}

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 2020121 
(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)))