(log (+ (pow p a) (pow p b)))

Average Error: 29.2 → 29.2

Time: 5.8s

Precision: binary64

• could not determine a ground truth for program body

  1. p = -2.335674277657988e-156
  2. a = 6.299112701246367e+131
  3. b = 8657020140556561.0

Math

\[\log \left({p}^{a} + {p}^{b}\right)\]

↓

\[\log \left({p}^{a} + {p}^{b}\right)\]

C

double code(double p, double a, double b) {
	return ((double) log(((double) (((double) pow(p, a)) + ((double) pow(p, b))))));
}

↓

double code(double p, double a, double b) {
	return ((double) log(((double) (((double) pow(p, a)) + ((double) pow(p, b))))));
}

Error

Bits error versus p

Bits error versus a

Bits error versus b

Derivation

1. Initial program 29.2

   \[\log \left({p}^{a} + {p}^{b}\right)\]

2. Final simplification 29.2

   \[\leadsto \log \left({p}^{a} + {p}^{b}\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (p a b)
  :name "(log (+ (pow p a) (pow p b)))"
  :precision binary64
  (log (+ (pow p a) (pow p b))))