Details

analyze1.6s (9.9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4881	464
1	4881	464
0	6	6
1	6	6

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	74.8%	25.2%	8
0%	74.8%	25.2%	9
0%	74.8%	25.2%	10
0%	74.8%	25.2%	11
0%	74.8%	25.2%	12
24.9%	49.9%	25.2%	13
24.9%	37.4%	37.7%	14

Symmetry

sort(z t)

Compiler

Compiled 20 to 20 computations (0% saved)

sample83.0ms (0.5%)

Algorithm

1×

intervals

Results

19.0ms	58×	body	1024	valid
11.0ms	142×	body	128	valid
8.0ms	17×	body	2048	valid
7.0ms	26×	body	512	valid
5.0ms	61×	body	128	nan
2.0ms	13×	body	256	valid
2.0ms	30×	body	128	invalid

Compiler

Compiled 39 to 45 computations (-15.4% saved)

simplify51.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	757	29
1	757	29

prune8.0ms (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

Error

20.1b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 z t) 3)
0.2b	(/.f64 a (*.f64 b 3))
0.2b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
22.6b	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))

rewrite177.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

18.6b

Rules

19×	`add-exp-log_binary64_20235` `add-cbrt-cube_binary64_20233`
11×	`add-cube-cbrt_binary64_20232` `add-sqr-sqrt_binary64_20219` `*-un-lft-identity_binary64_20197`
9×	`times-frac_binary64_20203` `pow1_binary64_20258`
8×	`cos-sum_binary64_20331`
7×	`cancel-sign-sub-inv_binary64_20163`
5×	`prod-exp_binary64_20246` `cbrt-unprod_binary64_20230`
4×	`add-log-exp_binary64_20236` `div-exp_binary64_20248` `cbrt-undiv_binary64_20231` `associate-/l_binary64_20142` `associate-/r_binary64_20141`
3×	`cos-diff_binary64_20334` `div-inv_binary64_20194` `pow-prod-down_binary64_20268` `associate-r_binary64_20137`
2×	`frac-2neg_binary64_20208` `clear-num_binary64_20196`
1×	`sub-neg_binary64_20190` `distribute-rgt-in_binary64_20147` `distribute-lft-in_binary64_20146` `associate-l_binary64_20138` `*-commutative_binary64_20128`

Counts

4 → 78

Calls

4 calls:

8.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
7.0ms	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))
4.0ms	(/.f64 (*.f64 z t) 3)
4.0ms	(/.f64 a (*.f64 b 3))

Compiler

Compiled 2173 to 1334 computations (38.6% saved)

series550.0ms (3.3%)

Error

16.1b

Counts

4 → 45

Calls

4 calls:

279.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
105.0ms	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))
61.0ms	(/.f64 a (*.f64 b 3))
51.0ms	(/.f64 (*.f64 z t) 3)

Compiler

Compiled 2890 to 2315 computations (19.9% saved)

simplify85.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4932	1991
1	4932	1991

prune214.0ms (1.3%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	99	24	123
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	24	124

Error

15.5b

Counts

124 → 24

Compiler

Compiled 3456 to 2240 computations (35.2% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 a (*.f64 b 3)))
0.2b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
0.2b	(/.f64 a (*.f64 b 3))

rewrite104.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

15.5b

Rules

13×	`add-exp-log_binary64_20235` `add-cbrt-cube_binary64_20233`
8×	`pow1_binary64_20258` `add-cube-cbrt_binary64_20232` `add-sqr-sqrt_binary64_20219` `*-un-lft-identity_binary64_20197`
7×	`cancel-sign-sub-inv_binary64_20163`
6×	`times-frac_binary64_20203`
5×	`add-log-exp_binary64_20236`
4×	`prod-exp_binary64_20246` `cbrt-unprod_binary64_20230`
3×	`associate-/l_binary64_20142` `pow-prod-down_binary64_20268` `associate-r*_binary64_20137`
2×	`div-exp_binary64_20248` `cbrt-undiv_binary64_20231` `div-inv_binary64_20194`
1×	`frac-2neg_binary64_20208` `clear-num_binary64_20196` `associate-/r_binary64_20141` `associate-l_binary64_20138` `-commutative_binary64_20128` `diff-log_binary64_20289` `flip3--_binary64_20201` `sub-neg_binary64_20190` `flip--_binary64_20172`

Counts

3 → 57

Calls

3 calls:

9.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 a (*.f64 b 3)))
9.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
4.0ms	(/.f64 a (*.f64 b 3))

Compiler

Compiled 1174 to 678 computations (42.2% saved)

series474.0ms (2.9%)

Error

15.2b

Counts

3 → 32

Calls

3 calls:

309.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 a (*.f64 b 3)))
73.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
64.0ms	(/.f64 a (*.f64 b 3))

Compiler

Compiled 1123 to 1034 computations (7.9% saved)

simplify96.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4915	1209
1	4915	1209

prune131.0ms (0.8%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	79	10	89
Fresh	5	18	23
Picked	1	0	1
Done	0	0	0
Total	85	28	113

Error

15.2b

Counts

113 → 28

Compiler

Compiled 2042 to 1310 computations (35.8% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 (/.f64 a b) 3))
0.2b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
0.2b	(/.f64 (/.f64 a b) 3)

rewrite210.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

15.2b

Rules

141×	`times-frac_binary64_20203`
81×	`add-cube-cbrt_binary64_20232` `add-sqr-sqrt_binary64_20219` `*-un-lft-identity_binary64_20197`
43×	`cancel-sign-sub-inv_binary64_20163`
13×	`add-exp-log_binary64_20235` `add-cbrt-cube_binary64_20233` `associate-/l*_binary64_20142`
9×	`div-inv_binary64_20194`
8×	`pow1_binary64_20258`
5×	`add-log-exp_binary64_20236`
3×	`div-exp_binary64_20248` `cbrt-undiv_binary64_20231` `associate-/r_binary64_20141` `pow-prod-down_binary64_20268` `prod-exp_binary64_20246` `cbrt-unprod_binary64_20230` `associate-r*_binary64_20137`
1×	`frac-2neg_binary64_20208` `clear-num_binary64_20196` `associate-/l/_binary64_20144` `associate-l_binary64_20138` `*-commutative_binary64_20128` `diff-log_binary64_20289` `flip3--_binary64_20201` `sub-neg_binary64_20190` `flip--_binary64_20172`

Counts

3 → 142

Calls

3 calls:

20.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 (/.f64 a b) 3))
6.0ms	(/.f64 (/.f64 a b) 3)
6.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))

Compiler

Compiled 3320 to 1701 computations (48.8% saved)

series488.0ms (3%)

Error

15.2b

Counts

3 → 32

Calls

3 calls:

322.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 (/.f64 a b) 3))
74.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
70.0ms	(/.f64 (/.f64 a b) 3)

Compiler

Compiled 1123 to 1027 computations (8.5% saved)

simplify79.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5215	2940

prune203.0ms (1.2%)

Pruning

28 alts after pruning (27 fresh and 1 done)

	Pruned	Kept	Total
New	173	1	174
Fresh	1	26	27
Picked	0	1	1
Done	0	0	0
Total	174	28	202

Error

15.2b

Counts

202 → 28

Compiler

Compiled 3914 to 2204 computations (43.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (*.f64 a (/.f64 1/3 b)))
0.2b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
0.2b	(*.f64 a (/.f64 1/3 b))
0.4b	(/.f64 1/3 b)

rewrite126.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

15.2b

Rules

26×	`add-sqr-sqrt_binary64_20219`
21×	`add-cube-cbrt_binary64_20232` `*-un-lft-identity_binary64_20197`
19×	`times-frac_binary64_20203`
16×	`add-exp-log_binary64_20235` `add-cbrt-cube_binary64_20233` `associate-r_binary64_20137`
11×	`pow1_binary64_20258`
6×	`add-log-exp_binary64_20236`
5×	`prod-exp_binary64_20246` `cbrt-unprod_binary64_20230`
4×	`pow-prod-down_binary64_20268` `associate-l_binary64_20138`
3×	`associate-/l_binary64_20142` `associate-/r_binary64_20141`
2×	`div-exp_binary64_20248` `cbrt-undiv_binary64_20231` `div-inv_binary64_20194` `unswap-sqr_binary64_20165` `*-commutative_binary64_20128`
1×	`frac-2neg_binary64_20208` `clear-num_binary64_20196` `associate-*r/_binary64_20139` `diff-log_binary64_20289` `flip3--_binary64_20201` `sub-neg_binary64_20190` `flip--_binary64_20172` `cancel-sign-sub-inv_binary64_20163`

Counts

4 → 89

Calls

4 calls:

9.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
7.0ms	(*.f64 a (/.f64 1/3 b))
6.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (*.f64 a (/.f64 1/3 b)))
3.0ms	(/.f64 1/3 b)

Compiler

Compiled 1804 to 1060 computations (41.2% saved)

series475.0ms (2.9%)

Error

15.2b

Counts

4 → 35

Calls

4 calls:

306.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (*.f64 a (/.f64 1/3 b)))
70.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
57.0ms	(*.f64 a (/.f64 1/3 b))
17.0ms	(/.f64 1/3 b)

Compiler

Compiled 1240 to 1145 computations (7.7% saved)

simplify78.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4996	1564
1	4996	1564

prune108.0ms (0.7%)

Pruning

28 alts after pruning (26 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	26	26
Picked	0	1	1
Done	0	1	1
Total	124	28	152

Error

15.2b

Counts

152 → 28

Compiler

Compiled 2036 to 1087 computations (46.6% saved)

regimes5.6s (34.1%)

Accuracy

Total 1.8b remaining (11.1%)

Threshold costs 0b (0%)

Compiler

Compiled 60424 to 56229 computations (6.9% saved)

bsearch6.0ms (0%)

Compiler: Compiled 3 to 7 computations (-133.3% saved)

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	126	111
1	126	111

Removed

((sort z t))

Compiler

Compiled 144 to 100 computations (30.6% saved)

end0.0ms (0%)

sample5.4s (32.8%)

Algorithm

1×

intervals

Results

549.0ms	1612×	body	1024	valid
376.0ms	4569×	body	128	valid
354.0ms	746×	body	2048	valid
192.0ms	751×	body	512	valid
172.0ms	2207×	body	128	nan
95.0ms	1138×	body	128	invalid
55.0ms	321×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 3385 to 3119 computations (7.9% saved)

Details

analyze1.6s (9.9%)

sample83.0ms (0.5%)

simplify51.0ms (0.3%)

prune8.0ms (0.1%)

localize16.0ms (0.1%)

rewrite177.0ms (1.1%)

series550.0ms (3.3%)

simplify85.0ms (0.5%)

prune214.0ms (1.3%)

localize11.0ms (0.1%)

rewrite104.0ms (0.6%)

series474.0ms (2.9%)

simplify96.0ms (0.6%)

prune131.0ms (0.8%)

localize11.0ms (0.1%)

rewrite210.0ms (1.3%)

series488.0ms (3%)

simplify79.0ms (0.5%)

prune203.0ms (1.2%)

localize11.0ms (0.1%)

rewrite126.0ms (0.8%)

series475.0ms (2.9%)

simplify78.0ms (0.5%)

prune108.0ms (0.7%)

regimes5.6s (34.1%)

bsearch6.0ms (0%)

simplify16.0ms (0.1%)

end0.0ms (0%)

sample5.4s (32.8%)

Profiling