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

sample93.0ms (1.8%)

Algorithm

1×

intervals

Results

56.0ms	115×	body	1280	valid
21.0ms	72×	body	640	valid
8.0ms	47×	body	320	valid
2.0ms	16×	body	160	valid
0.0ms	6×	body	80	valid

simplify195.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (193.0ms)

Iter	Nodes	Cost
0	4889	12
1	4889	12

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 58.8b

Counts

2 → 1

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite17.0ms (0.3%)

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-/r*`
4×	`associate-/r/` `add-cbrt-cube` `associate-/l*`
3×	`pow1`
2×	`flip3--` `div-exp` `rem-log-exp` `flip--` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 82

Calls

2 calls:

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

series8.0ms (0.2%)

Counts

2 → 6

Calls

2 calls:

6.0ms	(log (/ (+ 1.0 x) (- 1.0 x)))
2.0ms	(/ (+ 1.0 x) (- 1.0 x))

simplify47.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5006	1111

prune185.0ms (3.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	85	3	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	3	89

Merged error: 0.1b

Counts

89 → 3

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+ (* x (* x 2.0)) (+ (log 1.0) (* 2.0 (- x (* (/ x 1.0) (/ x 1.0))))))
0.0b	(- x (* (/ x 1.0) (/ x 1.0)))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp`
3×	`add-sqr-sqrt` `sum-log`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
1×	`+-commutative` `sub-neg` `associate-+r+` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+` `difference-of-squares`

Counts

2 → 25

Calls

2 calls:

8.0ms	(+ (* x (* x 2.0)) (+ (log 1.0) (* 2.0 (- x (* (/ x 1.0) (/ x 1.0))))))
3.0ms	(- x (* (/ x 1.0) (/ x 1.0)))

series22.0ms (0.4%)

Counts

2 → 6

Calls

2 calls:

17.0ms	(+ (* x (* x 2.0)) (+ (log 1.0) (* 2.0 (- x (* (/ x 1.0) (/ x 1.0))))))
5.0ms	(- x (* (/ x 1.0) (/ x 1.0)))

simplify53.0ms (1%)

Algorithm

1×	egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4934	456
1	4934	456

prune83.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	29	2	31
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	29	5	34

Merged error: 0.1b

Counts

34 → 5

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (- x (pow (/ x 1.0) 2))) (cbrt (- x (pow (/ x 1.0) 2))))
0.7b	(cbrt (- x (pow (/ x 1.0) 2)))
0.7b	(cbrt (- x (pow (/ x 1.0) 2)))
0.7b	(cbrt (- x (pow (/ x 1.0) 2)))

rewrite56.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`add-sqr-sqrt`
71×	`cbrt-prod`
35×	`*-un-lft-identity` `difference-of-squares`
18×	`cbrt-div`
15×	`add-cube-cbrt`
14×	`unpow-prod-down` `swap-sqr`
12×	`associate-r` `associate-l`
11×	`pow1`
9×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--`
7×	`times-frac` `unpow2` `sqr-pow`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 125

Calls

4 calls:

25.0ms	(* (cbrt (- x (pow (/ x 1.0) 2))) (cbrt (- x (pow (/ x 1.0) 2))))
9.0ms	(cbrt (- x (pow (/ x 1.0) 2)))
8.0ms	(cbrt (- x (pow (/ x 1.0) 2)))
8.0ms	(cbrt (- x (pow (/ x 1.0) 2)))

series42.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (cbrt (- x (pow (/ x 1.0) 2))) (cbrt (- x (pow (/ x 1.0) 2))))
11.0ms	(cbrt (- x (pow (/ x 1.0) 2)))
10.0ms	(cbrt (- x (pow (/ x 1.0) 2)))
10.0ms	(cbrt (- x (pow (/ x 1.0) 2)))

simplify77.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4940	2347
1	4940	2347

prune657.0ms (12.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	136	6	142

Merged error: 0.1b

Counts

142 → 6

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.7b	(pow (cbrt (- x (pow (/ x 1.0) 2))) 6)
0.7b	(cbrt (- x (pow (/ x 1.0) 2)))
0.7b	(cbrt (- x (pow (/ x 1.0) 2)))
32.1b	(pow (pow (cbrt (- x (pow (/ x 1.0) 2))) 6) 1/3)

rewrite46.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
48×	`unpow-prod-down`
36×	`cbrt-prod`
21×	`*-un-lft-identity`
20×	`difference-of-squares`
13×	`add-cube-cbrt`
7×	`add-exp-log` `sqr-pow`
6×	`pow-unpow`
5×	`pow1` `pow-exp`
4×	`cbrt-div` `times-frac` `add-cbrt-cube` `distribute-lft-out--` `unpow2` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `pow1/3`
2×	`flip3--` `flip--`
1×	`unpow1/3`

Counts

4 → 98

Calls

4 calls:

15.0ms	(pow (pow (cbrt (- x (pow (/ x 1.0) 2))) 6) 1/3)
11.0ms	(pow (cbrt (- x (pow (/ x 1.0) 2))) 6)
9.0ms	(cbrt (- x (pow (/ x 1.0) 2)))
8.0ms	(cbrt (- x (pow (/ x 1.0) 2)))

series85.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

36.0ms	(pow (pow (cbrt (- x (pow (/ x 1.0) 2))) 6) 1/3)
27.0ms	(pow (cbrt (- x (pow (/ x 1.0) 2))) 6)
13.0ms	(cbrt (- x (pow (/ x 1.0) 2)))
10.0ms	(cbrt (- x (pow (/ x 1.0) 2)))

simplify36.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5293	1793

prune439.0ms (8.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	110	6	116

Merged error: 0.1b

Counts

116 → 6

regimes123.0ms (2.4%)

Accuracy

Total 0.5b remaining (74.2%)

Threshold costs 0.5b (74.2%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	24
1	45	24

end0.0ms (0%)

sample2.8s (54.6%)

Algorithm

1×

intervals

Results

1.7s	3381×	body	1280	valid
717.0ms	2506×	body	640	valid
227.0ms	1283×	body	320	valid
68.0ms	629×	body	160	valid
10.0ms	201×	body	80	valid

Details

analyze4.0ms (0.1%)

sample93.0ms (1.8%)

simplify195.0ms (3.8%)

prune5.0ms (0.1%)

localize11.0ms (0.2%)

rewrite17.0ms (0.3%)

series8.0ms (0.2%)

simplify47.0ms (0.9%)

prune185.0ms (3.6%)

localize12.0ms (0.2%)

rewrite11.0ms (0.2%)

series22.0ms (0.4%)

simplify53.0ms (1%)

prune83.0ms (1.6%)

localize17.0ms (0.3%)

rewrite56.0ms (1.1%)

series42.0ms (0.8%)

simplify77.0ms (1.5%)

prune657.0ms (12.7%)

localize23.0ms (0.4%)

rewrite46.0ms (0.9%)

series85.0ms (1.6%)

simplify36.0ms (0.7%)

prune439.0ms (8.5%)

regimes123.0ms (2.4%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample2.8s (54.6%)

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