(/ (pow x n) (+ (pow t n) (pow x n)))

Average Error: 0.5 → 0.5

Time: 3.7s

Precision: binary64

• could not determine a ground truth for program body

  1. x = 6.08545063198846e-126
  2. n = -7056042156807565.0
  3. t = -1.038344523943695e-88

Math

\[\frac{{x}^{n}}{{t}^{n} + {x}^{n}}\]

↓

\[\frac{{x}^{n}}{{t}^{n} + {x}^{n}}\]

C

double code(double x, double n, double t) {
	return ((double) (((double) pow(x, n)) / ((double) (((double) pow(t, n)) + ((double) pow(x, n))))));
}

↓

double code(double x, double n, double t) {
	return ((double) (((double) pow(x, n)) / ((double) (((double) pow(t, n)) + ((double) pow(x, n))))));
}

Error

Bits error versus x

Bits error versus n

Bits error versus t

Derivation

1. Initial program 0.5

   \[\frac{{x}^{n}}{{t}^{n} + {x}^{n}}\]

2. Final simplification 0.5

   \[\leadsto \frac{{x}^{n}}{{t}^{n} + {x}^{n}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x n t)
  :name "(/ (pow x n) (+ (pow t n) (pow x n)))"
  :precision binary64
  (/ (pow x n) (+ (pow t n) (pow x n))))