Average Error: 0.0 → 0
Time: 790.0ms
Precision: binary64
\[\left(x + \frac{\frac{\frac{t}{16}}{16}}{16}\right) + \frac{\frac{\frac{t}{16}}{16}}{16}\]
↓
\[2 \cdot \frac{\frac{\frac{t}{16}}{16}}{16} + x\]
\left(x + \frac{\frac{\frac{t}{16}}{16}}{16}\right) + \frac{\frac{\frac{t}{16}}{16}}{16}
↓
2 \cdot \frac{\frac{\frac{t}{16}}{16}}{16} + x
double code(double x, double t) {
	return ((double) (((double) (x + ((double) (((double) (((double) (t / 16.0)) / 16.0)) / 16.0)))) + ((double) (((double) (((double) (t / 16.0)) / 16.0)) / 16.0))));
}
↓
double code(double x, double t) {
	return ((double) (((double) (2.0 * ((double) (((double) (((double) (t / 16.0)) / 16.0)) / 16.0)))) + x));
}

Error

Bits error versus x

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(x + \frac{\frac{\frac{t}{16}}{16}}{16}\right) + \frac{\frac{\frac{t}{16}}{16}}{16}\]

  2. Simplified0

    \[\leadsto \color{blue}{2 \cdot \frac{\frac{\frac{t}{16}}{16}}{16} + x}\]

  3. Final simplification0

    \[\leadsto 2 \cdot \frac{\frac{\frac{t}{16}}{16}}{16} + x\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x t)
  :name "(+ (+ x (/ (/ (/ t 16) 16) 16)) (/ (/ (/ t 16) 16) 16))"
  :precision binary64
  (+ (+ x (/ (/ (/ t 16.0) 16.0) 16.0)) (/ (/ (/ t 16.0) 16.0) 16.0)))