Details

analyze705.0ms (8.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
50%	50%	0%	6
50%	50%	0%	7
50%	50%	0%	8
50%	50%	0%	9
50%	50%	0%	10
50%	50%	0%	11
50%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0.1%	14

sample211.0ms (2.6%)

Algorithm

1×

intervals

Results

78.0ms	51×	body	5120	exit
47.0ms	94×	body	1280	valid
30.0ms	88×	body	640	valid
19.0ms	49×	body	1280	nan
9.0ms	41×	body	320	valid
8.0ms	29×	body	640	nan
3.0ms	19×	body	160	valid
3.0ms	14×	body	320	nan
1.0ms	14×	body	80	valid
1.0ms	6×	body	160	nan
0.0ms	4×	body	80	nan

simplify95.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4797	9
1	4797	9

prune7.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 59.7b

Counts

2 → 1

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt (cos x))
0.3b	(/ (fmod (exp x) (sqrt (cos x))) (exp x))
5.2b	(fmod (exp x) (sqrt (cos x)))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-cbrt-cube`
4×	`pow1` `add-exp-log`
3×	`associate-/r` `sqrt-prod` `associate-/l` `add-log-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

3 → 47

Calls

3 calls:

4.0ms	(/ (fmod (exp x) (sqrt (cos x))) (exp x))
1.0ms	(sqrt (cos x))
1.0ms	(fmod (exp x) (sqrt (cos x)))

series11.0ms (0.1%)

Counts

3 → 9

Calls

3 calls:

6.0ms	(/ (fmod (exp x) (sqrt (cos x))) (exp x))
3.0ms	(sqrt (cos x))
3.0ms	(fmod (exp x) (sqrt (cos x)))

simplify56.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5687	564

prune73.0ms (0.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	52	4	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	4	57

Merged error: 59.7b

Counts

57 → 4

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(exp (- (log (fmod (exp x) (sqrt (cos x)))) x))
2.0b	(- (log (fmod (exp x) (sqrt (cos x)))) x)
3.3b	(log (fmod (exp x) (sqrt (cos x))))
5.2b	(fmod (exp x) (sqrt (cos x)))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
9×	`log-prod`
8×	`add-cube-cbrt`
7×	`pow1` `add-log-exp`
6×	`exp-prod` `associate--l+`
5×	`add-exp-log`
4×	`exp-sum` `add-cbrt-cube` `distribute-lft-out--`
3×	`log-pow`
2×	`sub-neg` `diff-log` `rem-exp-log` `difference-of-squares`
1×	`flip3--` `exp-diff` `rem-log-exp` `flip--`

Counts

4 → 56

Calls

4 calls:

5.0ms	(exp (- (log (fmod (exp x) (sqrt (cos x)))) x))
4.0ms	(- (log (fmod (exp x) (sqrt (cos x)))) x)
1.0ms	(log (fmod (exp x) (sqrt (cos x))))
1.0ms	(fmod (exp x) (sqrt (cos x)))

series42.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(- (log (fmod (exp x) (sqrt (cos x)))) x)
17.0ms	(log (fmod (exp x) (sqrt (cos x))))
4.0ms	(exp (- (log (fmod (exp x) (sqrt (cos x)))) x))
1.0ms	(fmod (exp x) (sqrt (cos x)))

simplify58.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4902	681
1	4902	681

prune86.0ms (1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	68	4	72

Merged error: 59.7b

Counts

72 → 4

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.0b	(- (log (log (exp (fmod (exp x) (sqrt (cos x)))))) x)
2.1b	(log (exp (fmod (exp x) (sqrt (cos x)))))
3.0b	(log (log (exp (fmod (exp x) (sqrt (cos x))))))
5.2b	(fmod (exp x) (sqrt (cos x)))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`log-prod`
14×	`log-pow`
13×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
9×	`pow1` `exp-prod`
7×	`associate--l+`
5×	`add-exp-log` `add-log-exp`
4×	`add-cbrt-cube`
2×	`rem-log-exp` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`

Counts

4 → 59

Calls

4 calls:

7.0ms	(- (log (log (exp (fmod (exp x) (sqrt (cos x)))))) x)
2.0ms	(log (exp (fmod (exp x) (sqrt (cos x)))))
2.0ms	(log (log (exp (fmod (exp x) (sqrt (cos x))))))
1.0ms	(fmod (exp x) (sqrt (cos x)))

series38.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(- (log (log (exp (fmod (exp x) (sqrt (cos x)))))) x)
15.0ms	(log (log (exp (fmod (exp x) (sqrt (cos x))))))
1.0ms	(log (exp (fmod (exp x) (sqrt (cos x)))))
1.0ms	(fmod (exp x) (sqrt (cos x)))

simplify95.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4885	697
1	4885	697

prune94.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	71	4	75

Merged error: 59.7b

Counts

75 → 4

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt (cos x))
0.3b	(/ (fmod (exp x) (sqrt (cos x))) (exp x))
2.3b	(log (exp (/ (fmod (exp x) (sqrt (cos x))) (exp x))))
5.2b	(fmod (exp x) (sqrt (cos x)))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
14×	`log-pow`
13×	`exp-prod`
6×	`pow1` `add-cbrt-cube`
5×	`add-exp-log`
4×	`add-log-exp`
3×	`log-prod` `associate-/r` `sqrt-prod` `associate-/l`
2×	`div-inv`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `clear-num`

Counts

4 → 72

Calls

4 calls:

4.0ms	(log (exp (/ (fmod (exp x) (sqrt (cos x))) (exp x))))
4.0ms	(/ (fmod (exp x) (sqrt (cos x))) (exp x))
1.0ms	(sqrt (cos x))
1.0ms	(fmod (exp x) (sqrt (cos x)))

series17.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

6.0ms	(log (exp (/ (fmod (exp x) (sqrt (cos x))) (exp x))))
6.0ms	(/ (fmod (exp x) (sqrt (cos x))) (exp x))
3.0ms	(sqrt (cos x))
1.0ms	(fmod (exp x) (sqrt (cos x)))

simplify73.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4843	892
1	4843	892

prune100.0ms (1.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	84	4	88

Merged error: 59.7b

Counts

88 → 4

regimes34.0ms (0.4%)

Accuracy

Total 0.1b remaining (0.1%)

Threshold costs 0.1b (0.1%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms (0%)

sample6.4s (77.2%)

Algorithm

1×

intervals

Results

2.4s	1574×	body	5120	exit
1.6s	3169×	body	1280	valid
854.0ms	2518×	body	640	valid
478.0ms	1215×	body	1280	nan
299.0ms	1253×	body	320	valid
269.0ms	984×	body	640	nan
98.0ms	491×	body	320	nan
91.0ms	615×	body	160	valid
37.0ms	445×	body	80	valid
31.0ms	239×	body	160	nan
19.0ms	247×	body	80	nan

Details

analyze705.0ms (8.5%)

sample211.0ms (2.6%)

simplify95.0ms (1.1%)

prune7.0ms (0.1%)

localize11.0ms (0.1%)

rewrite7.0ms (0.1%)

series11.0ms (0.1%)

simplify56.0ms (0.7%)

prune73.0ms (0.9%)

localize10.0ms (0.1%)

rewrite12.0ms (0.1%)

series42.0ms (0.5%)

simplify58.0ms (0.7%)

prune86.0ms (1%)

localize12.0ms (0.1%)

rewrite14.0ms (0.2%)

series38.0ms (0.5%)

simplify95.0ms (1.2%)

prune94.0ms (1.1%)

localize10.0ms (0.1%)

rewrite13.0ms (0.2%)

series17.0ms (0.2%)

simplify73.0ms (0.9%)

prune100.0ms (1.2%)

regimes34.0ms (0.4%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample6.4s (77.2%)

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