Average Error: 0.2 → 0.1
Time: 2.0s
Precision: binary64
\[\left(\left(\left(\left(\left(x + \frac{\frac{\frac{t}{16}}{16}}{16}\right) + \frac{\frac{\frac{t}{16}}{16}}{16}\right) + \frac{\frac{\frac{t}{16}}{16}}{16}\right) + \frac{\frac{\frac{t}{16}}{16}}{16}\right) + \frac{\frac{\frac{t}{16}}{16}}{16}\right) + \frac{\frac{\frac{t}{16}}{16}}{16}\]
↓
\[3 \cdot \frac{2 \cdot t}{{16}^{3}} + x\]
\left(\left(\left(\left(\left(x + \frac{\frac{\frac{t}{16}}{16}}{16}\right) + \frac{\frac{\frac{t}{16}}{16}}{16}\right) + \frac{\frac{\frac{t}{16}}{16}}{16}\right) + \frac{\frac{\frac{t}{16}}{16}}{16}\right) + \frac{\frac{\frac{t}{16}}{16}}{16}\right) + \frac{\frac{\frac{t}{16}}{16}}{16}
↓
3 \cdot \frac{2 \cdot t}{{16}^{3}} + x
double code(double x, double t) {
	return ((double) (((double) (((double) (((double) (((double) (((double) (x + ((double) (((double) (((double) (t / 16.0)) / 16.0)) / 16.0)))) + ((double) (((double) (((double) (t / 16.0)) / 16.0)) / 16.0)))) + ((double) (((double) (((double) (t / 16.0)) / 16.0)) / 16.0)))) + ((double) (((double) (((double) (t / 16.0)) / 16.0)) / 16.0)))) + ((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) (3.0 * ((double) (((double) (2.0 * t)) / ((double) pow(16.0, 3.0)))))) + 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 0.2

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

  2. Simplified0.1

    \[\leadsto \color{blue}{3 \cdot \frac{2 \cdot t}{{16}^{3}} + x}\]

  3. Final simplification0.1

    \[\leadsto 3 \cdot \frac{2 \cdot t}{{16}^{3}} + x\]

Reproduce

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