(- (/ 2 (- 1 (tanh (/ x 2)))) 1)

Average Error: 0.2 → 0.2

Time: 1.6s

Precision: binary64

• could not determine a ground truth for program body

  1. x = 2.7279434923395366e+116

Math

\[\frac{2}{1 - \tanh \left(\frac{x}{2}\right)} - 1\]

↓

\[\frac{2}{1 - \tanh \left(\frac{x}{2}\right)} - 1\]

C

double code(double x) {
	return ((double) (((double) (2.0 / ((double) (1.0 - ((double) tanh(((double) (x / 2.0)))))))) - 1.0));
}

↓

double code(double x) {
	return ((double) (((double) (2.0 / ((double) (1.0 - ((double) tanh(((double) (x / 2.0)))))))) - 1.0));
}

Error

Bits error versus x

Derivation

1. Initial program 0.2

   \[\frac{2}{1 - \tanh \left(\frac{x}{2}\right)} - 1\]

2. Final simplification 0.2

   \[\leadsto \frac{2}{1 - \tanh \left(\frac{x}{2}\right)} - 1\]

Reproduce

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