Details

analyze99.0ms (1.3%)

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

Symmetry

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample83.0ms (1.1%)

Algorithm

1×

intervals

Results

36.0ms	135×	body	1024	valid
29.0ms	61×	body	2048	valid
5.0ms	30×	body	512	valid
2.0ms	20×	body	256	valid
1.0ms	10×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify9.0ms (0.1%)

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

Error

41.7b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.0b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
2.7b	(cos.f64 (+.f64 x eps))

rewrite42.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

17.3b

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×	`cos-sum_binary64_212` `pow1_binary64_139` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
1×	`diff-cos_binary64_229` `diff-log_binary64_170` `flip3--_binary64_82` `sub-neg_binary64_71` `flip--_binary64_53` `difference-of-squares_binary64_47` `distribute-lft-out--_binary64_30` `associate--l-_binary64_16`

Counts

2 → 26

Calls

2 calls:

7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
4.0ms	(cos.f64 (+.f64 x eps))

Compiler

Compiled 382 to 101 computations (73.6% saved)

series142.0ms (1.9%)

Error

15.7b

Counts

2 → 23

Calls

2 calls:

74.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
43.0ms	(cos.f64 (+.f64 x eps))

Compiler

Compiled 669 to 420 computations (37.2% saved)

simplify93.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4900	724
1	4900	724

prune56.0ms (0.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	41	8	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	8	50

Error

0.3b

Counts

50 → 8

Compiler

Compiled 719 to 277 computations (61.5% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (+.f64 eps x))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
2.7b	(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

rewrite85.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

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

Counts

3 → 41

Calls

3 calls:

11.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
10.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))
6.0ms	(+.f64 x (+.f64 eps x))

Compiler

Compiled 969 to 586 computations (39.5% saved)

series296.0ms (4%)

Error

0.3b

Counts

3 → 36

Calls

3 calls:

133.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
68.0ms	(+.f64 x (+.f64 eps x))
58.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

Compiler

Compiled 1530 to 1293 computations (15.5% saved)

simplify74.0ms (1%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5057	1282

prune101.0ms (1.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	68	9	77
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	72	13	85

Error

0.2b

Counts

85 → 13

Compiler

Compiled 1746 to 1187 computations (32% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)))
2.7b	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
2.7b	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
2.7b	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))

rewrite102.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

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

Counts

4 → 32

Calls

4 calls:

11.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
9.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
9.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
8.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)))

Compiler

Compiled 1431 to 808 computations (43.5% saved)

series611.0ms (8.2%)

Error

0.2b

Counts

4 → 46

Calls

4 calls:

321.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)))
71.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
69.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
66.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))

Compiler

Compiled 4756 to 3360 computations (29.4% saved)

simplify48.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5177	1478

prune158.0ms (2.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	12	12
Picked	1	0	1
Done	0	0	0
Total	78	13	91

Error

0.2b

Counts

91 → 13

Compiler

Compiled 3510 to 2153 computations (38.7% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.7b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.7b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
2.7b	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))

rewrite91.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

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

Counts

4 → 40

Calls

4 calls:

9.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 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)))

Compiler

Compiled 1389 to 1024 computations (26.3% saved)

series350.0ms (4.7%)

Error

0.2b

Counts

4 → 24

Calls

4 calls:

83.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
79.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
77.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
69.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))

Compiler

Compiled 2075 to 1705 computations (17.8% saved)

simplify51.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5173	854

prune106.0ms (1.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	64	13	77

Error

0.2b

Counts

77 → 13

Compiler

Compiled 2060 to 1523 computations (26.1% saved)

regimes636.0ms (8.6%)

Accuracy

Total 0.3b remaining (58.6%)

Threshold costs 0.3b (58.6%)

Compiler

Compiled 4533 to 3385 computations (25.3% saved)

bsearch68.0ms (0.9%)

Steps

Iters	Range		Point
8	0.001695551822692593	69.34871191274691	0.003604158899811683
8	-4.791140900740207	-0.00015946487477725538	-0.0038847635134518256

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify25.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	616	85
1	616	85

Removed

()

end0.0ms (0%)

sample4.0s (54.4%)

Algorithm

1×

intervals

Results

1.0s	2021×	body	2048	valid
969.0ms	3826×	body	1024	valid
236.0ms	1417×	body	512	valid
56.0ms	494×	body	256	valid
14.0ms	240×	body	128	valid
2.0ms	2×	body	4096	valid

Compiler

Compiled 1549 to 1156 computations (25.4% saved)

Details

analyze99.0ms (1.3%)

sample83.0ms (1.1%)

simplify9.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite42.0ms (0.6%)

series142.0ms (1.9%)

simplify93.0ms (1.3%)

prune56.0ms (0.8%)

localize11.0ms (0.2%)

rewrite85.0ms (1.1%)

series296.0ms (4%)

simplify74.0ms (1%)

prune101.0ms (1.4%)

localize15.0ms (0.2%)

rewrite102.0ms (1.4%)

series611.0ms (8.2%)

simplify48.0ms (0.6%)

prune158.0ms (2.1%)

localize17.0ms (0.2%)

rewrite91.0ms (1.2%)

series350.0ms (4.7%)

simplify51.0ms (0.7%)

prune106.0ms (1.4%)

regimes636.0ms (8.6%)

bsearch68.0ms (0.9%)

simplify25.0ms (0.3%)

end0.0ms (0%)

sample4.0s (54.4%)

Profiling