Average Error: 0.0 → 0.0
Time: 1.6s
Precision: 64
Internal Precision: 128
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\frac{2}{e^{x} + e^{-x}}\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{2}{e^{x} + e^{-x}}\]

  2. Final simplification0.0

    \[\leadsto \frac{2}{e^{x} + e^{-x}}\]

Reproduce

herbie shell --seed 2019002 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))

Details

Time bar (total: 1.4s)Debug log

sample30.0ms

Algorithm
intervals

simplify7.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

7.0ms
(/ 2 (+ (exp x) (exp (- x))))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 2 (+ (exp x) (exp (- x))))
0.0b
(+ (exp x) (exp (- x)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Counts
2 → 35
Calls

2 calls. Slowest were:

7.0ms
(+ (exp x) (exp (- x)))
5.0ms
(/ 2 (+ (exp x) (exp (- x))))

series91.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

52.0ms
(/ 2 (+ (exp x) (exp (- x))))
39.0ms
(+ (exp x) (exp (- x)))

simplify306.0ms

Counts
16 → 41
Calls

16 calls. Slowest were:

186.0ms
(+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x)))))
47.0ms
(- (+ (* 5/24 (pow x 4)) 1) (* 1/2 (pow x 2)))
11.0ms
(+ (pow x 2) (+ (* 1/12 (pow x 4)) 2))

prune324.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample585.0ms

Algorithm
intervals