Details

Time bar (total: 5.2s)

sample21.0ms

Algorithm
intervals
Results
14.0ms256×body80valid

simplify214.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1125
2145
3155
4205
5415
6665
71655
811235
950015

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b
(/ 2.0 (+ (exp x) (exp (- x))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
12×times-frac
10×add-sqr-sqrt add-cube-cbrt
4×associate-/r* distribute-lft-out
3×add-exp-log add-cbrt-cube associate-/l*
2×associate-/r/
1×pow1 cbrt-undiv expm1-log1p-u frac-2neg flip3-+ div-exp clear-num flip-+ log1p-expm1-u div-inv add-log-exp
Counts
1 → 35
Calls
1 calls:
10.0ms
(/ 2.0 (+ (exp x) (exp (- x))))

series43.0ms

Counts
1 → 3
Calls
1 calls:
42.0ms
(/ 2.0 (+ (exp x) (exp (- x))))

simplify71.0ms

Algorithm
egg-herbie
Counts
38 → 38
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0167323
1568300
22220299
35001299

prune84.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (sqrt 2.0) (sqrt (+ (exp x) (exp (- x)))))
0.0b
(/ (sqrt 2.0) (sqrt (+ (exp x) (exp (- x)))))
0.0b
(* (/ (sqrt 2.0) (sqrt (+ (exp x) (exp (- x))))) (/ (sqrt 2.0) (sqrt (+ (exp x) (exp (- x))))))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
434×sqrt-prod
384×times-frac
361×add-sqr-sqrt
327×*-un-lft-identity
195×add-cube-cbrt
94×swap-sqr
58×distribute-lft-out
48×associate-*r* associate-*l*
25×unswap-sqr
19×add-exp-log add-cbrt-cube
14×associate-/r*
12×sqrt-div associate-/r/ associate-/l*
10×pow1
6×cbrt-undiv sqrt-undiv flip3-+ div-exp flip-+ div-inv
4×prod-exp cbrt-unprod
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×pow2 frac-times pow-plus sqrt-unprod associate-*r/ pow-prod-down associate-*l/ rem-square-sqrt pow-sqr *-commutative pow-prod-up
Counts
3 → 387
Calls
3 calls:
15.0ms
(/ (sqrt 2.0) (sqrt (+ (exp x) (exp (- x)))))
13.0ms
(/ (sqrt 2.0) (sqrt (+ (exp x) (exp (- x)))))
93.0ms
(* (/ (sqrt 2.0) (sqrt (+ (exp x) (exp (- x))))) (/ (sqrt 2.0) (sqrt (+ (exp x) (exp (- x))))))

series321.0ms

Counts
3 → 9
Calls
3 calls:
107.0ms
(/ (sqrt 2.0) (sqrt (+ (exp x) (exp (- x)))))
113.0ms
(/ (sqrt 2.0) (sqrt (+ (exp x) (exp (- x)))))
101.0ms
(* (/ (sqrt 2.0) (sqrt (+ (exp x) (exp (- x))))) (/ (sqrt 2.0) (sqrt (+ (exp x) (exp (- x))))))

simplify127.0ms

Algorithm
egg-herbie
Counts
396 → 396
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
08197847
142926769
250016695

prune612.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ (sqrt 1) (sqrt (sqrt (+ (exp x) (exp (- x)))))) (/ (/ 2.0 (sqrt (+ (exp x) (exp (- x))))) (sqrt (sqrt (+ (exp x) (exp (- x)))))))
0.5b
(/ (sqrt 1) (sqrt (sqrt (+ (exp x) (exp (- x))))))
0.5b
(/ (/ 2.0 (sqrt (+ (exp x) (exp (- x))))) (sqrt (sqrt (+ (exp x) (exp (- x))))))
0.5b
(/ 2.0 (sqrt (+ (exp x) (exp (- x)))))

rewrite485.0ms

Algorithm
rewrite-expression-head
Rules
1362×times-frac
1349×sqrt-prod
972×add-sqr-sqrt
862×*-un-lft-identity
562×add-cube-cbrt
276×associate-*r*
135×distribute-lft-out
100×unswap-sqr
66×associate-*l*
60×sqrt-div
52×associate-/r/
36×associate-/l*
34×add-exp-log add-cbrt-cube
27×associate-/r*
26×flip3-+ flip-+ div-inv
14×cbrt-undiv div-exp
6×pow1 prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
1×frac-times sqrt-undiv associate-*r/ pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
4 → 934
Calls
4 calls:
334.0ms
(* (/ (sqrt 1) (sqrt (sqrt (+ (exp x) (exp (- x)))))) (/ (/ 2.0 (sqrt (+ (exp x) (exp (- x))))) (sqrt (sqrt (+ (exp x) (exp (- x)))))))
14.0ms
(/ (sqrt 1) (sqrt (sqrt (+ (exp x) (exp (- x))))))
36.0ms
(/ (/ 2.0 (sqrt (+ (exp x) (exp (- x))))) (sqrt (sqrt (+ (exp x) (exp (- x))))))
15.0ms
(/ 2.0 (sqrt (+ (exp x) (exp (- x)))))

series474.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* (/ (sqrt 1) (sqrt (sqrt (+ (exp x) (exp (- x)))))) (/ (/ 2.0 (sqrt (+ (exp x) (exp (- x))))) (sqrt (sqrt (+ (exp x) (exp (- x)))))))
145.0ms
(/ (sqrt 1) (sqrt (sqrt (+ (exp x) (exp (- x))))))
201.0ms
(/ (/ 2.0 (sqrt (+ (exp x) (exp (- x))))) (sqrt (sqrt (+ (exp x) (exp (- x))))))
89.0ms
(/ 2.0 (sqrt (+ (exp x) (exp (- x)))))

simplify194.0ms

Algorithm
egg-herbie
Counts
946 → 946
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
0210224324
1500122364

prune1.8s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01822
11822

end0.0ms

sample558.0ms

Algorithm
intervals
Results
464.0ms8000×body80valid