Details

analyze687.0ms (8.4%)

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

sample190.0ms (2.3%)

Algorithm

1×

intervals

Results

62.0ms	42×	body	5120	exit
48.0ms	95×	body	1280	valid
29.0ms	83×	body	640	valid
12.0ms	32×	body	1280	nan
10.0ms	44×	body	320	valid
8.0ms	32×	body	640	nan
3.0ms	19×	body	320	nan
2.0ms	17×	body	160	valid
1.0ms	17×	body	80	valid
1.0ms	10×	body	160	nan
0.0ms	6×	body	80	nan

simplify80.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (78.0ms)

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: 60.0b

Counts

2 → 1

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/ (fmod (exp x) (sqrt (cos x))) (exp x))
0.0b	(sqrt (cos x))
4.3b	(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))
2.0ms	(fmod (exp x) (sqrt (cos x)))

simplify54.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5687	564

prune74.0ms (0.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	2	57

Merged error: 60.0b

Counts

57 → 2

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x))))
0.1b	(cbrt (cos x))
0.1b	(cbrt (cos x))
4.3b	(fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

6.0ms	(* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x))))
1.0ms	(cbrt (cos x))
1.0ms	(cbrt (cos x))
1.0ms	(fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))

series57.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x))))
16.0ms	(cbrt (cos x))
16.0ms	(cbrt (cos x))
3.0ms	(fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))

simplify55.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5053	606

prune98.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	66	3	69

Merged error: 60.0b

Counts

69 → 3

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(exp (fmod (exp x) (sqrt (cos x))))
0.0b	(sqrt (cos x))
2.1b	(log (exp (fmod (exp x) (sqrt (cos x)))))
4.3b	(fmod (exp x) (sqrt (cos x)))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `exp-prod`
5×	`add-log-exp`
4×	`add-exp-log` `log-pow` `add-cbrt-cube`
3×	`log-prod` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `rem-exp-log`

Counts

4 → 46

Calls

4 calls:

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

series16.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

8.0ms	(exp (fmod (exp x) (sqrt (cos x))))
5.0ms	(sqrt (cos x))
1.0ms	(log (exp (fmod (exp x) (sqrt (cos x)))))
1.0ms	(fmod (exp x) (sqrt (cos x)))

simplify76.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4769	409
1	4769	409

prune76.0ms (0.9%)

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: 60.0b

Counts

61 → 3

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(cbrt (cos x))
4.3b	(fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))
4.3b	(fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))
4.3b	(fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 32

Calls

4 calls:

1.0ms	(cbrt (cos x))
1.0ms	(fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))
1.0ms	(fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))
1.0ms	(fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))

series24.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

16.0ms	(cbrt (cos x))
3.0ms	(fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))
2.0ms	(fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))
2.0ms	(fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))

simplify55.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4934	497
1	4934	497

prune72.0ms (0.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	44	3	47

Merged error: 60.0b

Counts

47 → 3

regimes32.0ms (0.4%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	10	15

end0.0ms (0%)

sample6.5s (78.9%)

Algorithm

1×

intervals

Results

2.4s	1609×	body	5120	exit
1.8s	3158×	body	1280	valid
810.0ms	2490×	body	640	valid
476.0ms	1229×	body	1280	nan
265.0ms	1226×	body	320	valid
252.0ms	968×	body	640	nan
93.0ms	486×	body	320	nan
89.0ms	616×	body	160	valid
40.0ms	510×	body	80	valid
34.0ms	265×	body	160	nan
17.0ms	234×	body	80	nan

Details

analyze687.0ms (8.4%)

sample190.0ms (2.3%)

simplify80.0ms (1%)

prune7.0ms (0.1%)

localize8.0ms (0.1%)

rewrite7.0ms (0.1%)

series11.0ms (0.1%)

simplify54.0ms (0.7%)

prune74.0ms (0.9%)

localize11.0ms (0.1%)

rewrite10.0ms (0.1%)

series57.0ms (0.7%)

simplify55.0ms (0.7%)

prune98.0ms (1.2%)

localize10.0ms (0.1%)

rewrite6.0ms (0.1%)

series16.0ms (0.2%)

simplify76.0ms (0.9%)

prune76.0ms (0.9%)

localize16.0ms (0.2%)

rewrite4.0ms (0%)

series24.0ms (0.3%)

simplify55.0ms (0.7%)

prune72.0ms (0.9%)

regimes32.0ms (0.4%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample6.5s (78.9%)

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