Details

analyze1.1s (15.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
26.5%	72.9%	0.5%	9
38.2%	60.7%	1.1%	10
41.7%	54.9%	3.4%	11
47.6%	47.4%	5%	12
53.4%	39.4%	7.2%	13
54.9%	34.5%	10.6%	14

sample67.0ms (1%)

Algorithm

1×

intervals

Results

18.0ms	205×	body	80	valid
9.0ms	18×	body	1280	valid
7.0ms	19×	body	640	valid
6.0ms	61×	body	80	invalid
4.0ms	14×	body	640	invalid
4.0ms	7×	body	1280	invalid
3.0ms	12×	body	320	valid
2.0ms	10×	body	320	invalid
0.0ms	3×	body	160	invalid
0.0ms	2×	body	160	valid

simplify79.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4845	16
1	4845	16

prune12.0ms (0.2%)

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: 28.4b

Counts

2 → 1

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
5.1b	(* (* x (pow s 2.0)) x)
6.6b	(* x (pow s 2.0))
18.1b	(* (pow c 2.0) (* (* x (pow s 2.0)) x))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`add-exp-log`
82×	`prod-exp`
34×	`add-cbrt-cube`
18×	`pow-to-exp` `pow-exp`
17×	`add-sqr-sqrt`
16×	`div-exp` `cbrt-unprod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`associate-r` `associate-l`
7×	`unpow-prod-down`
6×	`pow1`
4×	`cbrt-undiv` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l` `unswap-sqr` `sqr-pow`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 115

Calls

4 calls:

10.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
9.0ms	(* (pow c 2.0) (* (* x (pow s 2.0)) x))
5.0ms	(* (* x (pow s 2.0)) x)
5.0ms	(* x (pow s 2.0))

series215.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (pow c 2.0) (* (* x (pow s 2.0)) x))
75.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
30.0ms	(* (* x (pow s 2.0)) x)
29.0ms	(* x (pow s 2.0))

simplify68.0ms (1%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4965	1594
1	4965	1594

prune343.0ms (4.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	117	10	127
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	10	128

Merged error: 15.9b

Counts

128 → 10

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
0.7b	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
5.1b	(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
18.1b	(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

rewrite55.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

416×	`add-exp-log`
343×	`prod-exp`
84×	`pow-to-exp` `pow-exp`
52×	`add-cbrt-cube`
43×	`div-exp`
29×	`cbrt-unprod`
11×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
9×	`associate-l`
6×	`pow1` `unpow-prod-down`
5×	`cbrt-undiv`
4×	`add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`sqr-pow`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 186

Calls

4 calls:

13.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
12.0ms	(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))
9.0ms	(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
7.0ms	(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))

series213.0ms (3%)

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))
73.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
33.0ms	(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
31.0ms	(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))

simplify44.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5220	2915

prune529.0ms (7.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	192	6	198
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	197	11	208

Merged error: 3.2b

Counts

208 → 11

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(* (fabs (* (* x (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))) (fabs (* (* x (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))))
0.7b	(/ (cos (* 2.0 x)) (* (fabs (* (* x (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))) (fabs (* (* x (pow s (/ 2.0 2))) (pow c (/ 2.0 2))))))
4.9b	(* (* x (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))
4.9b	(* (* x (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`add-exp-log`
44×	`prod-exp`
21×	`add-cbrt-cube`
17×	`associate-r`
16×	`add-sqr-sqrt`
14×	`pow-to-exp` `add-cube-cbrt` `*-un-lft-identity` `pow-exp`
11×	`pow1`
8×	`cbrt-unprod`
6×	`unpow-prod-down`
5×	`associate-l`
4×	`add-log-exp`
3×	`times-frac` `swap-sqr` `-commutative` `associate-/l`
2×	`cbrt-undiv` `div-exp` `sqr-pow`
1×	`pow2` `frac-2neg` `pow-plus` `pow-prod-down` `clear-num` `associate-/r*` `pow-sqr` `pow-prod-up` `div-inv` `unswap-sqr`

Counts

4 → 106

Calls

4 calls:

7.0ms	(* (* x (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))
7.0ms	(* (* x (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))
5.0ms	(/ (cos (* 2.0 x)) (* (fabs (* (* x (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))) (fabs (* (* x (pow s (/ 2.0 2))) (pow c (/ 2.0 2))))))
3.0ms	(* (fabs (* (* x (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))) (fabs (* (* x (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))))

series162.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (* x (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))
50.0ms	(* (* x (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))
44.0ms	(/ (cos (* 2.0 x)) (* (fabs (* (* x (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))) (fabs (* (* x (pow s (/ 2.0 2))) (pow c (/ 2.0 2))))))
15.0ms	(* (fabs (* (* x (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))) (fabs (* (* x (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))))

simplify39.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5030	1942

prune494.0ms (7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	105	13	118
Fresh	7	2	9
Picked	1	0	1
Done	1	0	1
Total	114	15	129

Merged error: 0.0b

Counts

129 → 15

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (cos (* x 2.0)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2)))))) (fabs (* (* x (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))))
0.9b	(/ (cos (* x 2.0)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
4.9b	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
4.9b	(* (* x (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac`
63×	`add-exp-log`
58×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
42×	`prod-exp`
21×	`add-cbrt-cube`
16×	`associate-/l*`
14×	`pow-to-exp` `pow-exp`
8×	`associate-r` `associate-l`
6×	`unpow-prod-down` `associate-/r*` `cbrt-unprod` `div-inv`
4×	`pow1` `cbrt-undiv` `div-exp` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative` `sqr-pow`
1×	`associate-/l/`

Counts

4 → 157

Calls

4 calls:

7.0ms	(* (* x (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))
7.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
5.0ms	(/ (/ (cos (* x 2.0)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2)))))) (fabs (* (* x (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))))
3.0ms	(/ (cos (* x 2.0)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))

series187.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
52.0ms	(* (* x (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))
42.0ms	(/ (/ (cos (* x 2.0)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2)))))) (fabs (* (* x (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))))
28.0ms	(/ (cos (* x 2.0)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))

simplify71.0ms (1%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4928	4767
1	4928	4767

prune795.0ms (11.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	163	6	169
Fresh	10	4	14
Picked	0	1	1
Done	0	0	0
Total	173	11	184

Merged error: 0.0b

Counts

184 → 11

regimes425.0ms (6.1%)

Accuracy

Total 2.2b remaining (93.5%)

Threshold costs 0b (0%)

bsearch2.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	59
1	33	59

end0.0ms (0%)

sample2.0s (28.2%)

Algorithm

1×

intervals

Results

541.0ms	6000×	body	80	valid
360.0ms	685×	body	1280	valid
275.0ms	755×	body	640	valid
166.0ms	1836×	body	80	invalid
98.0ms	382×	body	320	valid
84.0ms	260×	body	640	invalid
57.0ms	123×	body	1280	invalid
49.0ms	204×	body	320	invalid
36.0ms	178×	body	160	valid
22.0ms	130×	body	160	invalid

Details

analyze1.1s (15.3%)

sample67.0ms (1%)

simplify79.0ms (1.1%)

prune12.0ms (0.2%)

localize15.0ms (0.2%)

rewrite33.0ms (0.5%)

series215.0ms (3.1%)

simplify68.0ms (1%)

prune343.0ms (4.9%)

localize16.0ms (0.2%)

rewrite55.0ms (0.8%)

series213.0ms (3%)

simplify44.0ms (0.6%)

prune529.0ms (7.5%)

localize16.0ms (0.2%)

rewrite25.0ms (0.4%)

series162.0ms (2.3%)

simplify39.0ms (0.6%)

prune494.0ms (7%)

localize18.0ms (0.3%)

rewrite28.0ms (0.4%)

series187.0ms (2.7%)

simplify71.0ms (1%)

prune795.0ms (11.4%)

regimes425.0ms (6.1%)

bsearch2.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.0s (28.2%)

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