Details

analyze15.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	1.6%	48.5%	9
50.4%	1.2%	48.5%	10
50.4%	1.2%	48.5%	11
50.4%	1.1%	48.6%	12
50.4%	1%	48.6%	13
50.5%	0.9%	48.6%	14

sample72.0ms (2.6%)

Algorithm

1×

intervals

Results

37.0ms	115×	body	1280	valid
21.0ms	75×	body	640	valid
5.0ms	40×	body	320	valid
1.0ms	12×	body	160	valid
1.0ms	14×	body	80	valid

simplify48.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4835	13
1	4835	13

prune5.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 57.9b

Counts

2 → 1

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+ (exp x) (exp (neg x)))
1.0b	(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
3.6b	(- (exp x) (exp (neg x)))

rewrite22.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity`
30×	`add-sqr-sqrt` `times-frac`
16×	`add-cube-cbrt`
8×	`cosh-undef` `distribute-lft-out`
7×	`sinh-undef` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
6×	`associate-/l*`
5×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
3×	`pow1`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `tanh-undef` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 86

Calls

3 calls:

10.0ms	(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
5.0ms	(- (exp x) (exp (neg x)))
4.0ms	(+ (exp x) (exp (neg x)))

series23.0ms (0.8%)

Counts

3 → 9

Calls

3 calls:

14.0ms	(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
6.0ms	(- (exp x) (exp (neg x)))
3.0ms	(+ (exp x) (exp (neg x)))

simplify61.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4863	1393
1	4863	1393

prune104.0ms (3.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	3	96

Merged error: 0b

Counts

96 → 3

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b

(tanh x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `tanh-def-c` `add-cbrt-cube` `tanh-def-b` `add-log-exp` `tanh-def-a`

Counts

1 → 10

Calls

1 calls:

1.0ms

(tanh x)

series17.0ms (0.6%)

Counts

1 → 3

Calls

1 calls:

17.0ms

(tanh x)

simplify34.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	6015	79

prune21.0ms (0.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	12	1	13
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	13	3	16

Merged error: 0b

Counts

16 → 3

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+ (exp x) (exp (neg x)))
0.0b	(sinh x)
1.0b	(/ (* 2 (sinh x)) (+ (exp x) (exp (neg x))))

rewrite14.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`add-exp-log` `add-cbrt-cube`
5×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac` `associate-/r*` `add-log-exp`
3×	`pow1` `cosh-undef` `distribute-lft-out`
2×	`cbrt-undiv` `sinh-def` `flip3-+` `div-exp` `associate-/r/` `flip-+`
1×	`+-commutative` `frac-2neg` `associate-r/` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `associate-/l/` `associate-/l`

Counts

3 → 49

Calls

3 calls:

8.0ms	(/ (* 2 (sinh x)) (+ (exp x) (exp (neg x))))
4.0ms	(+ (exp x) (exp (neg x)))
1.0ms	(sinh x)

series29.0ms (1.1%)

Counts

3 → 9

Calls

3 calls:

18.0ms	(/ (* 2 (sinh x)) (+ (exp x) (exp (neg x))))
7.0ms	(sinh x)
3.0ms	(+ (exp x) (exp (neg x)))

simplify47.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4915	454
1	4915	454

prune67.0ms (2.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	58	3	61

Merged error: 0b

Counts

61 → 3

localize4.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(tanh x)
0.0b	(tanh x)
0.2b	(* (sqrt (tanh x)) (sqrt (tanh x)))

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`sqrt-div`
23×	`add-sqr-sqrt`
18×	`pow1` `sqrt-prod`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`tanh-def-c` `tanh-def-b` `tanh-def-a`
9×	`frac-times`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`associate-r` `associate-l`
5×	`add-exp-log` `pow-prod-up` `add-cbrt-cube`
4×	`unswap-sqr`
3×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `add-log-exp`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

3 → 84

Calls

3 calls:

7.0ms	(* (sqrt (tanh x)) (sqrt (tanh x)))
1.0ms	(tanh x)
1.0ms	(tanh x)

series41.0ms (1.5%)

Counts

3 → 9

Calls

3 calls:

14.0ms	(tanh x)
14.0ms	(* (sqrt (tanh x)) (sqrt (tanh x)))
13.0ms	(tanh x)

simplify29.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5805	653

prune109.0ms (4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	93	3	96

Merged error: 0b

Counts

96 → 3

regimes29.0ms (1.1%)

Accuracy

Total 0.0b remaining (69.7%)

Threshold costs 0.0b (69.7%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2	2
1	2	2

end0.0ms (0%)

sample1.9s (69.8%)

Algorithm

1×

intervals

Results

1.1s	3270×	body	1280	valid
496.0ms	2478×	body	640	valid
164.0ms	1231×	body	320	valid
49.0ms	616×	body	160	valid
17.0ms	405×	body	80	valid
0.0ms	1×	body	80	overflowed

Details

analyze15.0ms (0.5%)

sample72.0ms (2.6%)

simplify48.0ms (1.7%)

prune5.0ms (0.2%)

localize7.0ms (0.3%)

rewrite22.0ms (0.8%)

series23.0ms (0.8%)

simplify61.0ms (2.3%)

prune104.0ms (3.8%)

localize2.0ms (0.1%)

rewrite1.0ms (0%)

series17.0ms (0.6%)

simplify34.0ms (1.2%)

prune21.0ms (0.8%)

localize8.0ms (0.3%)

rewrite14.0ms (0.5%)

series29.0ms (1.1%)

simplify47.0ms (1.7%)

prune67.0ms (2.4%)

localize4.0ms (0.2%)

rewrite12.0ms (0.4%)

series41.0ms (1.5%)

simplify29.0ms (1.1%)

prune109.0ms (4%)

regimes29.0ms (1.1%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample1.9s (69.8%)

Profiling