Details

analyze1.4s (9.3%)

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)

sample92.0ms (0.6%)

Algorithm

1×

intervals

Results

18.0ms	54×	body	1024	valid
11.0ms	145×	body	128	valid
10.0ms	23×	body	2048	valid
7.0ms	28×	body	512	valid
6.0ms	76×	body	128	nan
3.0ms	47×	body	128	invalid
1.0ms	6×	body	256	valid

Compiler

Compiled 39 to 45 computations (-15.4% saved)

simplify51.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	757	29
1	757	29

prune4.0ms (0%)

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

21.5b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 z t) 3)
0.2b	(/.f64 a (*.f64 b 3))
0.3b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
25.6b	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))

rewrite183.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

19.9b

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:

12.0ms	(.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 a (*.f64 b 3))
4.0ms	(/.f64 (*.f64 z t) 3)

Compiler

Compiled 2173 to 1334 computations (38.6% saved)

series545.0ms (3.5%)

Error

16.7b

Counts

4 → 49

Calls

4 calls:

252.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
107.0ms	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))
63.0ms	(/.f64 a (*.f64 b 3))
57.0ms	(/.f64 (*.f64 z t) 3)

Compiler

Compiled 3100 to 2429 computations (21.6% saved)

simplify82.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4977	2213
1	4977	2213

prune210.0ms (1.4%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	102	25	127
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	25	128

Error

16.1b

Counts

128 → 25

Compiler

Compiled 3678 to 2353 computations (36% saved)

localize10.0ms (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))

rewrite97.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

16.1b

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:

8.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 a (*.f64 b 3)))
6.0ms	(.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)

series499.0ms (3.2%)

Error

15.8b

Counts

3 → 36

Calls

3 calls:

327.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 a (*.f64 b 3)))
82.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
57.0ms	(/.f64 a (*.f64 b 3))

Compiler

Compiled 1315 to 1166 computations (11.3% saved)

simplify70.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4917	1339
1	4917	1339

prune137.0ms (0.9%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	81	12	93
Fresh	7	17	24
Picked	1	0	1
Done	0	0	0
Total	89	29	118

Error

15.8b

Counts

118 → 29

Compiler

Compiled 2147 to 1380 computations (35.7% 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 1 b) (/.f64 a 3)))
0.2b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
0.3b	(*.f64 (/.f64 1 b) (/.f64 a 3))

rewrite132.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

15.8b

Rules

35×	`add-sqr-sqrt_binary64_20219`
30×	`add-exp-log_binary64_20235`
25×	`times-frac_binary64_20203`
20×	`add-cbrt-cube_binary64_20233` `*-un-lft-identity_binary64_20197`
18×	`add-cube-cbrt_binary64_20232`
16×	`associate-r_binary64_20137`
14×	`associate-l_binary64_20138`
11×	`prod-exp_binary64_20246`
10×	`pow1_binary64_20258`
8×	`div-exp_binary64_20248`
7×	`cbrt-unprod_binary64_20230`
6×	`unswap-sqr_binary64_20165`
5×	`add-log-exp_binary64_20236`
4×	`pow-prod-down_binary64_20268` `cbrt-undiv_binary64_20231`
2×	`1-exp_binary64_20241` `rec-exp_binary64_20247` `div-inv_binary64_20194` `*-commutative_binary64_20128`
1×	`frac-times_binary64_20207` `associate-l/_binary64_20140` `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

3 → 86

Calls

3 calls:

13.0ms	(*.f64 (/.f64 1 b) (/.f64 a 3))
6.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (*.f64 (/.f64 1 b) (/.f64 a 3)))
6.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))

Compiler

Compiled 2020 to 1285 computations (36.4% saved)

series490.0ms (3.2%)

Error

15.8b

Counts

3 → 36

Calls

3 calls:

314.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (*.f64 (/.f64 1 b) (/.f64 a 3)))
85.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
65.0ms	(*.f64 (/.f64 1 b) (/.f64 a 3))

Compiler

Compiled 1361 to 1212 computations (10.9% saved)

simplify102.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4942	1737
1	4942	1737

prune153.0ms (1%)

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	1	27	28
Picked	0	1	1
Done	0	0	0
Total	122	29	151

Error

15.8b

Counts

151 → 29

Compiler

Compiled 2825 to 1811 computations (35.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 (*.f64 1/3 a) b))
0.2b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
0.2b	(/.f64 (*.f64 1/3 a) b)
0.3b	(*.f64 1/3 a)

rewrite103.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

15.8b

Rules

16×	`add-exp-log_binary64_20235` `add-cbrt-cube_binary64_20233`
13×	`add-sqr-sqrt_binary64_20219`
11×	`pow1_binary64_20258` `add-cube-cbrt_binary64_20232` `*-un-lft-identity_binary64_20197`
7×	`cancel-sign-sub-inv_binary64_20163`
6×	`add-log-exp_binary64_20236` `associate-r_binary64_20137` `times-frac_binary64_20203`
5×	`prod-exp_binary64_20246` `cbrt-unprod_binary64_20230`
4×	`pow-prod-down_binary64_20268` `associate-l_binary64_20138`
3×	`associate-/r*_binary64_20141`
2×	`*-commutative_binary64_20128` `div-exp_binary64_20248` `cbrt-undiv_binary64_20231` `div-inv_binary64_20194`
1×	`unswap-sqr_binary64_20165` `frac-2neg_binary64_20208` `clear-num_binary64_20196` `associate-/l*_binary64_20142` `diff-log_binary64_20289` `flip3--_binary64_20201` `sub-neg_binary64_20190` `flip--_binary64_20172`

Counts

4 → 75

Calls

4 calls:

9.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 (*.f64 1/3 a) b))
6.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
4.0ms	(/.f64 (*.f64 1/3 a) b)
4.0ms	(*.f64 1/3 a)

Compiler

Compiled 1490 to 867 computations (41.8% saved)

series511.0ms (3.3%)

Error

15.8b

Counts

4 → 39

Calls

4 calls:

319.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 (*.f64 1/3 a) b))
85.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
58.0ms	(/.f64 (*.f64 1/3 a) b)
19.0ms	(*.f64 1/3 a)

Compiler

Compiled 1432 to 1277 computations (10.8% saved)

simplify63.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4948	1470
1	4948	1470

prune96.0ms (0.6%)

Pruning

29 alts after pruning (27 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	27	27
Picked	0	1	1
Done	0	1	1
Total	114	29	143

Error

15.8b

Counts

143 → 29

Compiler

Compiled 1788 to 935 computations (47.7% saved)

regimes5.2s (33.7%)

Accuracy

Total 1.8b remaining (11.4%)

Threshold costs 0b (0%)

Compiler

Compiled 57504 to 52560 computations (8.6% saved)

bsearch6.0ms (0%)

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

simplify17.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	116	98
1	116	98

Remove

(sort z t)

Compiler

Compiled 128 to 92 computations (28.1% saved)

end0.0ms (0%)

sample5.1s (33.3%)

Algorithm

1×

intervals

Results

550.0ms	1640×	body	1024	valid
357.0ms	4556×	body	128	valid
324.0ms	690×	body	2048	valid
194.0ms	813×	body	512	valid
174.0ms	2237×	body	128	nan
89.0ms	1174×	body	128	invalid
49.0ms	300×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 3262 to 2962 computations (9.2% saved)

Details

analyze1.4s (9.3%)

sample92.0ms (0.6%)

simplify51.0ms (0.3%)

prune4.0ms (0%)

localize15.0ms (0.1%)

rewrite183.0ms (1.2%)

series545.0ms (3.5%)

simplify82.0ms (0.5%)

prune210.0ms (1.4%)

localize10.0ms (0.1%)

rewrite97.0ms (0.6%)

series499.0ms (3.2%)

simplify70.0ms (0.5%)

prune137.0ms (0.9%)

localize11.0ms (0.1%)

rewrite132.0ms (0.9%)

series490.0ms (3.2%)

simplify102.0ms (0.7%)

prune153.0ms (1%)

localize10.0ms (0.1%)

rewrite103.0ms (0.7%)

series511.0ms (3.3%)

simplify63.0ms (0.4%)

prune96.0ms (0.6%)

regimes5.2s (33.7%)

bsearch6.0ms (0%)

simplify17.0ms (0.1%)

end0.0ms (0%)

sample5.1s (33.3%)

Profiling