Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.6%	25.4%	0
0%	74.6%	25.4%	1
37.3%	37.3%	25.4%	2
37.3%	18.7%	44%	3
46.7%	9.3%	44%	4
46.7%	4.7%	48.7%	5
49%	2.3%	48.7%	6
49%	1.2%	49.8%	7
49.6%	0.6%	49.8%	8
49.9%	0.3%	49.8%	9
49.9%	0.1%	50%	10
49.9%	0.1%	50.1%	11
49.9%	0%	50.1%	12
49.9%	0%	50.1%	13
49.9%	0%	50.1%	14

sample39.0ms (1.7%)

Algorithm

1×

intervals

Results

19.0ms	103×	body	1280	valid
8.0ms	80×	body	640	valid
3.0ms	44×	body	320	valid
3.0ms	256×	pre	80	true
1.0ms	19×	body	160	valid
0.0ms	10×	body	80	valid

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	68	4
1	68	4

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: 58.0b

Counts

2 → 1

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

5.1b	(- (exp x) 1.0)

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 13

Calls

1 calls:

4.0ms

(- (exp x) 1.0)

series2.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

2.0ms

(- (exp x) 1.0)

simplify65.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4883	115
1	4883	115

prune35.0ms (1.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	15	1	16
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	15	2	17

Merged error: 0.1b

Counts

17 → 2

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(* x (+ 1/2 (* x 1/6)))
0.0b	(* x (* x (+ 1/2 (* x 1/6))))
0.3b	(* x 1/6)

rewrite17.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`associate-l`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r`
6×	`associate-*r/`
5×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`*-commutative` `add-log-exp`
2×	`flip3-+` `flip-+` `unswap-sqr`

Counts

3 → 64

Calls

3 calls:

6.0ms	(* x (* x (+ 1/2 (* x 1/6))))
5.0ms	(* x (+ 1/2 (* x 1/6)))
3.0ms	(* x 1/6)

series14.0ms (0.6%)

Counts

3 → 9

Calls

3 calls:

6.0ms	(* x (* x (+ 1/2 (* x 1/6))))
6.0ms	(* x (+ 1/2 (* x 1/6)))
2.0ms	(* x 1/6)

simplify47.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4918	560
1	4918	560

prune98.0ms (4.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	72	3	75

Merged error: 0.1b

Counts

75 → 3

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) (+ (* x 1/6) 1/2))
0.0b	(* x (log (pow (exp x) (+ (* x 1/6) 1/2))))
0.3b	(* x 1/6)
5.4b	(log (pow (exp x) (+ (* x 1/6) 1/2)))

rewrite20.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`log-prod`
21×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
9×	`pow1` `add-exp-log`
8×	`distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
7×	`associate-r`
6×	`associate-l`
4×	`unpow-prod-up` `pow-pow` `add-log-exp` `sqr-pow`
3×	`pow-unpow` `exp-prod` `rem-log-exp`
2×	`pow-to-exp` `pow-prod-down` `pow-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 93

Calls

4 calls:

6.0ms	(* x (log (pow (exp x) (+ (* x 1/6) 1/2))))
5.0ms	(pow (exp x) (+ (* x 1/6) 1/2))
3.0ms	(* x 1/6)
3.0ms	(log (pow (exp x) (+ (* x 1/6) 1/2)))

series43.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(* x (log (pow (exp x) (+ (* x 1/6) 1/2))))
15.0ms	(log (pow (exp x) (+ (* x 1/6) 1/2)))
5.0ms	(pow (exp x) (+ (* x 1/6) 1/2))
2.0ms	(* x 1/6)

simplify67.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4973	1060
1	4973	1060

prune169.0ms (7.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	104	4	108

Merged error: 0.1b

Counts

108 → 4

localize14.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.3b	(* x 1/6)
0.3b	(* x 1/6)
5.5b	(log (cbrt (pow (exp x) (+ (* x 1/6) 1/2))))
5.5b	(log (cbrt (pow (exp x) (+ (* x 1/6) 1/2))))

rewrite16.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`log-prod`
18×	`add-sqr-sqrt`
16×	`cbrt-prod`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1` `add-exp-log`
8×	`add-cbrt-cube`
6×	`unpow-prod-down` `associate-r` `associate-l`
4×	`log-pow` `add-log-exp`
2×	`unpow-prod-up` `pow1/3` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `sqr-pow`

Counts

4 → 78

Calls

4 calls:

4.0ms	(log (cbrt (pow (exp x) (+ (* x 1/6) 1/2))))
4.0ms	(log (cbrt (pow (exp x) (+ (* x 1/6) 1/2))))
4.0ms	(* x 1/6)
3.0ms	(* x 1/6)

series71.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

35.0ms	(log (cbrt (pow (exp x) (+ (* x 1/6) 1/2))))
32.0ms	(log (cbrt (pow (exp x) (+ (* x 1/6) 1/2))))
2.0ms	(* x 1/6)
2.0ms	(* x 1/6)

simplify61.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4759	862
1	4759	862

prune272.0ms (11.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	89	5	94

Merged error: 0.1b

Counts

94 → 5

regimes117.0ms (5.1%)

Accuracy

Total 0.4b remaining (89.9%)

Threshold costs 0.4b (89.9%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	11
1	13	11

end0.0ms (0%)

sample1.1s (47.3%)

Algorithm

1×

intervals

Results

533.0ms	3385×	body	1280	valid
249.0ms	2581×	body	640	valid
83.0ms	8001×	pre	80	true
75.0ms	1241×	body	320	valid
24.0ms	609×	body	160	valid
4.0ms	184×	body	80	valid
0.0ms	1×	body	80	invalid

Details

analyze3.0ms (0.1%)

sample39.0ms (1.7%)

simplify4.0ms (0.2%)

prune5.0ms (0.2%)

localize3.0ms (0.1%)

rewrite4.0ms (0.2%)

series2.0ms (0.1%)

simplify65.0ms (2.8%)

prune35.0ms (1.5%)

localize6.0ms (0.3%)

rewrite17.0ms (0.7%)

series14.0ms (0.6%)

simplify47.0ms (2.1%)

prune98.0ms (4.3%)

localize10.0ms (0.4%)

rewrite20.0ms (0.9%)

series43.0ms (1.9%)

simplify67.0ms (2.9%)

prune169.0ms (7.4%)

localize14.0ms (0.6%)

rewrite16.0ms (0.7%)

series71.0ms (3.1%)

simplify61.0ms (2.7%)

prune272.0ms (11.9%)

regimes117.0ms (5.1%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample1.1s (47.3%)

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