(log (* (exp x) (exp y)))

Average Error: 56.5 → 0

Time: 3.9s

Precision: binary64

• could not determine a ground truth for program body

  1. x = 0.00015306162073024137
  2. y = 0.0001569110934647668

Math

\[\log \left(e^{x} \cdot e^{y}\right)\]

↓

\[x + y\]

C

double code(double x, double y) {
	return ((double) log(((double) (((double) exp(x)) * ((double) exp(y))))));
}

↓

double code(double x, double y) {
	return ((double) (x + y));
}

Error

Bits error versus x

Bits error versus y

Derivation

1. Initial program 56.5

   \[\log \left(e^{x} \cdot e^{y}\right)\]

2. Simplified 0

   \[\leadsto \color{blue}{x + y}\]

3. Final simplification 0

   \[\leadsto x + y\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x y)
  :name "(log (* (exp x) (exp y)))"
  :precision binary64
  (log (* (exp x) (exp y))))