Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

sample137.0ms (3.4%)

Algorithm

1×

intervals

Results

54.0ms	115×	body	1280	valid
18.0ms	72×	body	640	valid
7.0ms	47×	body	320	valid
1.0ms	16×	body	160	valid
0.0ms	6×	body	80	valid

simplify184.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (182.0ms)

Iter	Nodes	Cost
0	5041	8

prune5.0ms (0.1%)

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: 58.9b

Counts

2 → 1

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/ (- 1.0 eps) (+ 1.0 eps))
5.1b	(log (/ (- 1.0 eps) (+ 1.0 eps)))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`*-un-lft-identity`
41×	`add-sqr-sqrt`
40×	`times-frac`
26×	`log-prod`
23×	`add-cube-cbrt`
11×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
7×	`add-exp-log`
5×	`associate-/l*`
4×	`associate-/r*` `associate-/r/` `add-cbrt-cube`
3×	`pow1`
2×	`flip3-+` `div-exp` `rem-log-exp` `flip-+` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `div-sub` `clear-num` `log-pow` `flip--`

Counts

2 → 83

Calls

2 calls:

7.0ms	(/ (- 1.0 eps) (+ 1.0 eps))
7.0ms	(log (/ (- 1.0 eps) (+ 1.0 eps)))

series7.0ms (0.2%)

Counts

2 → 6

Calls

2 calls:

5.0ms	(log (/ (- 1.0 eps) (+ 1.0 eps)))
2.0ms	(/ (- 1.0 eps) (+ 1.0 eps))

simplify59.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4955	1113
1	4955	1113

prune174.0ms (4.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	3	90

Merged error: 0.1b

Counts

90 → 3

localize11.0ms (0.3%)

Local error

Found 1 expressions with local error:

0.0b	(+ eps (* (/ eps 1.0) (/ eps 1.0)))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `sum-log` `add-cbrt-cube` `flip-+`

Counts

1 → 11

Calls

1 calls:

3.0ms

(+ eps (* (/ eps 1.0) (/ eps 1.0)))

series5.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

5.0ms

(+ eps (* (/ eps 1.0) (/ eps 1.0)))

simplify29.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

14 → 14

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4972	135
1	4972	135

prune39.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	12	2	14
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	12	5	17

Merged error: 0.1b

Counts

17 → 5

localize15.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(log (+ eps (pow (/ eps 1.0) 2)))
0.0b	(+ eps (pow (/ eps 1.0) 2))
2.8b	(exp (log (+ eps (pow (/ eps 1.0) 2))))

rewrite26.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity`
8×	`log-prod`
6×	`add-sqr-sqrt` `add-cube-cbrt`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `log-div` `exp-prod` `exp-sum`
3×	`flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out`
2×	`exp-diff` `log-pow`
1×	`+-commutative` `rem-log-exp` `sum-log` `rem-exp-log`

Counts

3 → 45

Calls

3 calls:

9.0ms	(exp (log (+ eps (pow (/ eps 1.0) 2))))
8.0ms	(log (+ eps (pow (/ eps 1.0) 2)))
8.0ms	(+ eps (pow (/ eps 1.0) 2))

series14.0ms (0.4%)

Counts

3 → 9

Calls

3 calls:

5.0ms	(exp (log (+ eps (pow (/ eps 1.0) 2))))
5.0ms	(+ eps (pow (/ eps 1.0) 2))
4.0ms	(log (+ eps (pow (/ eps 1.0) 2)))

simplify42.0ms (1%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5134	573

prune138.0ms (3.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	54	5	59

Merged error: 0.1b

Counts

59 → 5

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(+ (* 2 (log (cbrt (+ eps (pow (/ eps 1.0) 2))))) (log (cbrt (+ eps (pow (/ eps 1.0) 2)))))
0.7b	(cbrt (+ eps (pow (/ eps 1.0) 2)))
0.7b	(cbrt (+ eps (pow (/ eps 1.0) 2)))
2.8b	(exp (+ (* 2 (log (cbrt (+ eps (pow (/ eps 1.0) 2))))) (log (cbrt (+ eps (pow (/ eps 1.0) 2))))))

rewrite48.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity`
21×	`log-prod`
20×	`cbrt-prod`
14×	`associate-+l+`
13×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`cbrt-div`
7×	`pow1` `distribute-rgt-in` `associate-+r+` `distribute-lft-in` `add-log-exp`
6×	`exp-prod` `distribute-rgt-out`
5×	`flip3-+` `flip-+` `distribute-lft-out`
4×	`add-exp-log` `associate-+r-` `log-div` `add-cbrt-cube`
3×	`log-pow`
2×	`exp-to-pow` `distribute-lft1-in` `exp-diff` `pow1/3` `sum-log` `rem-exp-log`
1×	`+-commutative` `exp-sum`

Counts

4 → 85

Calls

4 calls:

22.0ms	(+ (* 2 (log (cbrt (+ eps (pow (/ eps 1.0) 2))))) (log (cbrt (+ eps (pow (/ eps 1.0) 2)))))
8.0ms	(cbrt (+ eps (pow (/ eps 1.0) 2)))
8.0ms	(cbrt (+ eps (pow (/ eps 1.0) 2)))
7.0ms	(exp (+ (* 2 (log (cbrt (+ eps (pow (/ eps 1.0) 2))))) (log (cbrt (+ eps (pow (/ eps 1.0) 2))))))

series49.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(exp (+ (* 2 (log (cbrt (+ eps (pow (/ eps 1.0) 2))))) (log (cbrt (+ eps (pow (/ eps 1.0) 2))))))
11.0ms	(+ (* 2 (log (cbrt (+ eps (pow (/ eps 1.0) 2))))) (log (cbrt (+ eps (pow (/ eps 1.0) 2)))))
8.0ms	(cbrt (+ eps (pow (/ eps 1.0) 2)))
8.0ms	(cbrt (+ eps (pow (/ eps 1.0) 2)))

simplify44.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4977	1460
1	4977	1460

prune351.0ms (8.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	96	6	102

Merged error: 0.1b

Counts

102 → 6

regimes131.0ms (3.2%)

Accuracy

Total 0.4b remaining (73%)

Threshold costs 0.4b (73%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	18
1	49	18

end0.0ms (0%)

sample2.5s (61.7%)

Algorithm

1×

intervals

Results

1.5s	3379×	body	1280	valid
626.0ms	2509×	body	640	valid
190.0ms	1279×	body	320	valid
58.0ms	635×	body	160	valid
8.0ms	198×	body	80	valid

Details

analyze4.0ms (0.1%)

sample137.0ms (3.4%)

simplify184.0ms (4.5%)

prune5.0ms (0.1%)

localize5.0ms (0.1%)

rewrite17.0ms (0.4%)

series7.0ms (0.2%)

simplify59.0ms (1.4%)

prune174.0ms (4.3%)

localize11.0ms (0.3%)

rewrite4.0ms (0.1%)

series5.0ms (0.1%)

simplify29.0ms (0.7%)

prune39.0ms (1%)

localize15.0ms (0.4%)

rewrite26.0ms (0.7%)

series14.0ms (0.4%)

simplify42.0ms (1%)

prune138.0ms (3.4%)

localize17.0ms (0.4%)

rewrite48.0ms (1.2%)

series49.0ms (1.2%)

simplify44.0ms (1.1%)

prune351.0ms (8.6%)

regimes131.0ms (3.2%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample2.5s (61.7%)

Profiling