Details

analyze102.0ms (1.9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	117	22
1	117	22
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample76.0ms (1.4%)

Algorithm

1×

intervals

Results

31.0ms	66×	body	2048	valid
29.0ms	126×	body	1024	valid
6.0ms	35×	body	512	valid
2.0ms	20×	body	256	valid
1.0ms	9×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune2.0ms (0%)

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: 39.0b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.5b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
3.7b	(cos.f64 (+.f64 x eps))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
4×	`add-log-exp_binary64_117`
3×	`add-cube-cbrt_binary64_113` `cancel-sign-sub-inv_binary64_44`
2×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `cos-sum_binary64_212` `pow1_binary64_139`
1×	`distribute-lft-out--_binary64_30` `flip3--_binary64_82` `diff-log_binary64_170` `diff-cos_binary64_229` `flip--_binary64_53` `difference-of-squares_binary64_47` `associate--l-_binary64_16` `sub-neg_binary64_71`

Counts

2 → 26

Calls

2 calls:

11.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
4.0ms	(cos.f64 (+.f64 x eps))

series54.0ms (1%)

Counts

2 → 6

Calls

2 calls:

40.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
15.0ms	(cos.f64 (+.f64 x eps))

simplify88.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4855	444
1	4855	444

prune34.0ms (0.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	26	6	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	6	33

Merged error: 0.5b

Counts

33 → 6

Compiler

Compiled 492 to 164 computations (66.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
0.0b	(+.f64 x (+.f64 x eps))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.8b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64_78`
11×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `pow1_binary64_139`
9×	`add-sqr-sqrt_binary64_100` `add-log-exp_binary64_117`
7×	`add-cube-cbrt_binary64_113`
6×	`associate-l_binary64_19`
4×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `associate-r_binary64_18` `pow-prod-down_binary64_149`
3×	`distribute-lft-out_binary64_29` `sum-log_binary64_169`
2×	`*-commutative_binary64_9` `sin-mult_binary64_233`
1×	`+-commutative_binary64_8` `flip-+_binary64_52` `associate-+r+_binary64_10` `unswap-sqr_binary64_46` `associate-*r/_binary64_20` `flip3-+_binary64_81`

Counts

4 → 60

Calls

4 calls:

11.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
11.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
7.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(+.f64 x (+.f64 x eps))

series153.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
49.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
22.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
18.0ms	(+.f64 x (+.f64 x eps))

simplify83.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4916	1369
1	4916	1369

prune102.0ms (1.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	63	9	72
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	65	13	78

Merged error: 0.4b

Counts

78 → 13

Compiler

Compiled 1706 to 1133 computations (33.6% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
3.8b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64_109`
7×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `add-exp-log_binary64_116` `pow1_binary64_139`
3×	`pow1/3_binary64_160`

Counts

4 → 40

Calls

4 calls:

7.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))

series250.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

79.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
79.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
71.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
21.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify91.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5651	701

prune100.0ms (1.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	52	13	65

Merged error: 0.4b

Counts

65 → 13

Compiler

Compiled 1958 to 1455 computations (25.7% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.8b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
5.5b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
5.5b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
5.5b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))

rewrite37.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-cbrt-cube_binary64_114` `add-sqr-sqrt_binary64_100` `add-log-exp_binary64_117` `add-cube-cbrt_binary64_113` `add-exp-log_binary64_116` `*-un-lft-identity_binary64_78` `pow1_binary64_139`
3×	`cbrt-div_binary64_110` `pow1/3_binary64_160` `cbrt-prod_binary64_109` `sin-mult_binary64_233`

Counts

4 → 37

Calls

4 calls:

8.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
8.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
8.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
7.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series450.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

149.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
141.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
139.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
20.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify53.0ms (1%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5082	1133

prune113.0ms (2.1%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	48	1	49
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	48	14	62

Merged error: 0.4b

Counts

62 → 14

Compiler

Compiled 2536 to 1598 computations (37% saved)

regimes295.0ms (5.5%)

Compiler: Compiled 2009 to 1489 computations (25.9% saved)

bsearch73.0ms (1.4%)

Steps

Iters	Range		Point
8	1.2754341939463802e-11	4.409235077006948e-08	4.3409775702025784e-08
9	-0.02329983982683788	-1.342197564908979e-07	-1.184923447826453e-05

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	71	57
1	71	57

end0.0ms (0%)

sample3.1s (57.4%)

Algorithm

1×

intervals

Results

990.0ms	2035×	body	2048	valid
960.0ms	3891×	body	1024	valid
215.0ms	1322×	body	512	valid
53.0ms	487×	body	256	valid
15.0ms	264×	body	128	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 689 to 514 computations (25.4% saved)

Details

analyze102.0ms (1.9%)

sample76.0ms (1.4%)

simplify10.0ms (0.2%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite16.0ms (0.3%)

series54.0ms (1%)

simplify88.0ms (1.6%)

prune34.0ms (0.6%)

localize11.0ms (0.2%)

rewrite39.0ms (0.7%)

series153.0ms (2.8%)

simplify83.0ms (1.5%)

prune102.0ms (1.9%)

localize16.0ms (0.3%)

rewrite17.0ms (0.3%)

series250.0ms (4.6%)

simplify91.0ms (1.7%)

prune100.0ms (1.9%)

localize18.0ms (0.3%)

rewrite37.0ms (0.7%)

series450.0ms (8.4%)

simplify53.0ms (1%)

prune113.0ms (2.1%)

regimes295.0ms (5.5%)

bsearch73.0ms (1.4%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample3.1s (57.4%)

Profiling