(sqrt (- (pow PI x) (pow E X)))

Average Error: 28.1 → 28.1

Time: 10.4s

Precision: binary64

• could not determine a ground truth for program body

  1. x = -4.701282719128794e+112
  2. X = -5.864158910711846e+129

Math

\[\sqrt{{\pi}^{x} - {e}^{X}}\]

↓

\[\sqrt{{\pi}^{x} - {e}^{X}}\]

C

double code(double x, double X) {
	return ((double) sqrt(((double) (((double) pow(((double) M_PI), x)) - ((double) pow(((double) M_E), X))))));
}

↓

double code(double x, double X) {
	return ((double) sqrt(((double) (((double) pow(((double) M_PI), x)) - ((double) pow(((double) M_E), X))))));
}

Error

Bits error versus x

Bits error versus X

Derivation

1. Initial program 28.1

   \[\sqrt{{\pi}^{x} - {e}^{X}}\]

2. Final simplification 28.1

   \[\leadsto \sqrt{{\pi}^{x} - {e}^{X}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x X)
  :name "(sqrt (- (pow PI x) (pow E X)))"
  :precision binary64
  (sqrt (- (pow PI x) (pow E X))))