Average Error: 0.0 → 0.0
Time: 3.4s
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 2018360 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))

Details

Time bar (total: 1.7s)Debug log

start44.0ms

Algorithm
intervals

setup45.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

Algorithm
rewrite-expression-head
Counts
1 → 16
Calls

1 calls. Slowest were:

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

series55.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

55.0ms
(/ 2 (+ (exp x) (exp (- x))))

simplify187.0ms

Counts
9 → 19
Calls

9 calls. Slowest were:

89.0ms
(+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x)))))
56.0ms
(- (+ (* 5/24 (pow x 4)) 1) (* 1/2 (pow x 2)))
11.0ms
(- (exp x) (exp (- x)))

prune184.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 3 expressions with local error:

12.4b
(- (+ (* 5/24 (pow x 4)) 1) (* 1/2 (pow x 2)))
0.1b
(* 5/24 (pow x 4))
0.0b
(* 1/2 (pow x 2))

rewrite27.0ms

Algorithm
rewrite-expression-head
Counts
3 → 36
Calls

3 calls. Slowest were:

22.0ms
(- (+ (* 5/24 (pow x 4)) 1) (* 1/2 (pow x 2)))
2.0ms
(* 5/24 (pow x 4))
2.0ms
(* 1/2 (pow x 2))

series70.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

32.0ms
(- (+ (* 5/24 (pow x 4)) 1) (* 1/2 (pow x 2)))
23.0ms
(* 5/24 (pow x 4))
15.0ms
(* 1/2 (pow x 2))

simplify256.0ms

Counts
17 → 45
Calls

17 calls. Slowest were:

81.0ms
(/ (exp (+ (* 5/24 (pow x 4)) 1)) (exp (* 1/2 (pow x 2))))
54.0ms
(- (+ (* 5/24 (pow x 4)) 1) (* 1/2 (pow x 2)))
47.0ms
(- (+ (* 5/24 (pow x 4)) 1) (* 1/2 (pow x 2)))

prune687.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes103.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch1.0ms