Details

analyze237.0ms (6.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

sample61.0ms (1.6%)

Algorithm

1×

intervals

Results

26.0ms	49×	body	2560	valid
12.0ms	45×	body	1280	valid
9.0ms	52×	body	640	valid
4.0ms	31×	body	320	valid
2.0ms	68×	body	80	valid
1.0ms	11×	body	160	valid

simplify20.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	500	8
1	500	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: 31.2b

Counts

2 → 1

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

1.2b	(- 1.0 (cos x))
16.3b	(/ (- 1.0 (cos x)) (* x x))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 41

Calls

2 calls:

7.0ms	(/ (- 1.0 (cos x)) (* x x))
4.0ms	(- 1.0 (cos x))

series9.0ms (0.2%)

Counts

2 → 6

Calls

2 calls:

6.0ms	(/ (- 1.0 (cos x)) (* x x))
3.0ms	(- 1.0 (cos x))

simplify52.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4894	437
1	4894	437

prune117.0ms (3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	36	11	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	11	48

Merged error: 0.2b

Counts

48 → 11

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b	(/ (- 1.0 (cos x)) x)
1.2b	(- 1.0 (cos x))

rewrite26.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
46×	`times-frac`
29×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-r`
17×	`add-cbrt-cube`
13×	`associate-l`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod`
3×	`associate-/r*` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 113

Calls

3 calls:

13.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
5.0ms	(/ (- 1.0 (cos x)) x)
4.0ms	(- 1.0 (cos x))

series14.0ms (0.4%)

Counts

3 → 9

Calls

3 calls:

6.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
5.0ms	(/ (- 1.0 (cos x)) x)
3.0ms	(- 1.0 (cos x))

simplify49.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5658	1207

prune205.0ms (5.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	115	7	122
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	119	14	133

Merged error: 0.2b

Counts

133 → 14

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (+ 1.0 (cos x)))
0.3b	(pow (cos x) 3)
0.4b	(+ 1.0 (cos x))
1.0b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite25.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt` `sqr-pow`
8×	`add-log-exp`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out--`
4×	`associate-r`
3×	`pow-unpow` `associate-l`
2×	`flip3-+` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`difference-cubes` `+-commutative` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `distribute-lft-in` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

11.0ms	(- (pow 1.0 3) (pow (cos x) 3))
6.0ms	(* (cos x) (+ 1.0 (cos x)))
4.0ms	(+ 1.0 (cos x))
2.0ms	(pow (cos x) 3)

series21.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (pow 1.0 3) (pow (cos x) 3))
5.0ms	(pow (cos x) 3)
4.0ms	(* (cos x) (+ 1.0 (cos x)))
2.0ms	(+ 1.0 (cos x))

simplify53.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5011	963

prune285.0ms (7.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	98	5	103
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	102	15	117

Merged error: 0.1b

Counts

117 → 15

localize20.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(pow (pow (cos x) 3) 3)
0.3b	(cbrt (pow (pow (cos x) 3) 3))
0.4b	(+ 1.0 (cos x))
1.0b	(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

rewrite41.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

83×	`add-sqr-sqrt`
71×	`unpow-prod-down` `cube-prod`
70×	`cbrt-prod`
44×	`difference-of-squares`
29×	`sqr-pow`
22×	`*-un-lft-identity`
18×	`add-cube-cbrt`
8×	`add-log-exp`
6×	`add-exp-log` `cube-mult` `unpow3`
5×	`add-cbrt-cube`
4×	`pow1` `pow-exp`
3×	`pow-unpow`
2×	`pow-to-exp`
1×	`+-commutative` `sub-neg` `flip3--` `pow-pow` `flip3-+` `pow1/3` `diff-log` `sum-log` `flip--` `rem-cbrt-cube` `flip-+` `distribute-lft-out` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 150

Calls

4 calls:

22.0ms	(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))
5.0ms	(cbrt (pow (pow (cos x) 3) 3))
5.0ms	(pow (pow (cos x) 3) 3)
4.0ms	(+ 1.0 (cos x))

series27.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))
9.0ms	(pow (pow (cos x) 3) 3)
5.0ms	(cbrt (pow (pow (cos x) 3) 3))
2.0ms	(+ 1.0 (cos x))

simplify59.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4972	1780
1	4972	1780

prune470.0ms (12.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	160	2	162
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	163	14	177

Merged error: 0.1b

Counts

177 → 14

regimes171.0ms (4.4%)

Accuracy

Total 0.3b remaining (77.4%)

Threshold costs 0.3b (77.4%)

bsearch37.0ms (1%)

Steps

Iters	Range		Point
10	2.98076717192152e-15	30.40509460772629	0.03609453174808888
9	-0.051510977943339656	-4.761091517906183e-09	-0.03368084982938704

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	77	93
1	77	93

end0.0ms (0%)

sample1.8s (47.1%)

Algorithm

1×

intervals

Results

801.0ms	1565×	body	2560	valid
374.0ms	1324×	body	1280	valid
259.0ms	1493×	body	640	valid
114.0ms	908×	body	320	valid
93.0ms	2278×	body	80	valid
37.0ms	432×	body	160	valid

Details

analyze237.0ms (6.1%)

sample61.0ms (1.6%)

simplify20.0ms (0.5%)

prune5.0ms (0.1%)

localize6.0ms (0.2%)

rewrite11.0ms (0.3%)

series9.0ms (0.2%)

simplify52.0ms (1.3%)

prune117.0ms (3%)

localize8.0ms (0.2%)

rewrite26.0ms (0.7%)

series14.0ms (0.4%)

simplify49.0ms (1.3%)

prune205.0ms (5.3%)

localize16.0ms (0.4%)

rewrite25.0ms (0.6%)

series21.0ms (0.5%)

simplify53.0ms (1.4%)

prune285.0ms (7.4%)

localize20.0ms (0.5%)

rewrite41.0ms (1.1%)

series27.0ms (0.7%)

simplify59.0ms (1.5%)

prune470.0ms (12.2%)

regimes171.0ms (4.4%)

bsearch37.0ms (1%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.8s (47.1%)

Profiling