(fmod (pow 2 x) 1)

Average Error: 39.1 → 39.1

Time: 3.3s

Precision: binary64

• could not determine a ground truth for program body

  1. x = 2.7279434923395366e+116

Math

\[\left(\left({2}^{x}\right) \bmod 1\right)\]

↓

\[\left(\left({2}^{x}\right) \bmod 1\right)\]

C

double code(double x) {
	return ((double) fmod(((double) pow(2.0, x)), 1.0));
}

↓

double code(double x) {
	return ((double) fmod(((double) pow(2.0, x)), 1.0));
}

Error

Bits error versus x

Derivation

1. Initial program 39.1

   \[\left(\left({2}^{x}\right) \bmod 1\right)\]

2. Final simplification 39.1

   \[\leadsto \left(\left({2}^{x}\right) \bmod 1\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(fmod (pow 2 x) 1)"
  :precision binary64
  (fmod (pow 2.0 x) 1.0))