Details

analyze2.0ms (0%)

Algorithm

1×

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)

sample85.0ms (1.6%)

Algorithm

1×

intervals

Results

35.0ms	69×	body	2048	valid
25.0ms	103×	body	1024	valid
16.0ms	61×	body	512	valid
2.0ms	15×	body	256	valid
0.0ms	8×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify100.0ms (1.9%)

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

37.4b

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))
3.9b	(cos.f64 (+.f64 x eps))

rewrite14.0ms (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:

7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
5.0ms	(cos.f64 (+.f64 x eps))

series57.0ms (1.1%)

Counts

2 → 6

Calls

2 calls:

42.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
15.0ms	(cos.f64 (+.f64 x eps))

simplify87.0ms (1.7%)

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

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	24	8	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	8	33

Error

0.5b

Counts

33 → 8

Compiler

Compiled 497 to 179 computations (64% 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)))
4.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite46.0ms (0.9%)

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:

14.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
13.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(+.f64 x (+.f64 x eps))

series152.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

65.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
48.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
24.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
15.0ms	(+.f64 x (+.f64 x eps))

simplify81.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4916	1369
1	4916	1369

prune90.0ms (1.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	71	9	80

Error

0.4b

Counts

80 → 9

Compiler

Compiled 1580 to 1043 computations (34% saved)

localize18.0ms (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)))
4.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite18.0ms (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:

8.0ms	(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)))

series247.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

77.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
76.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
72.0ms	(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 (79.0ms)

Iter	Nodes	Cost
0	5651	701

prune99.0ms (1.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	49	3	52
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	51	10	61

Error

0.4b

Counts

61 → 10

Compiler

Compiled 1920 to 1433 computations (25.4% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
4.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
4.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
4.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`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×	`cbrt-prod_binary64_109`
1×	`pow1/3_binary64_160`

Counts

4 → 32

Calls

4 calls:

8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))

series144.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

81.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
25.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
20.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
19.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify89.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5651	631

prune101.0ms (1.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	42	2	44
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	43	11	54

Error

0.4b

Counts

54 → 11

Compiler

Compiled 2353 to 1535 computations (34.8% saved)

regimes281.0ms (5.3%)

Accuracy

Total 0.4b remaining (50%)

Threshold costs 0.4b (50%)

Compiler

Compiled 2282 to 1732 computations (24.1% saved)

bsearch46.0ms (0.9%)

Steps

Iters	Range		Point
9	1.1941300066793848e-12	0.0007794748927502307	0.00016323189196578065
4	-0.00017806805562616074	-0.00010248124561627069	-0.0001394028556381279

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	83	78
1	83	78

end0.0ms (0%)

sample3.3s (62.8%)

Algorithm

1×

intervals

Results

1.1s	2120×	body	2048	valid
965.0ms	3828×	body	1024	valid
226.0ms	1315×	body	512	valid
56.0ms	494×	body	256	valid
15.0ms	242×	body	128	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 793 to 596 computations (24.8% saved)

Details

analyze2.0ms (0%)

sample85.0ms (1.6%)

simplify100.0ms (1.9%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite14.0ms (0.3%)

series57.0ms (1.1%)

simplify87.0ms (1.7%)

prune34.0ms (0.6%)

localize11.0ms (0.2%)

rewrite46.0ms (0.9%)

series152.0ms (2.9%)

simplify81.0ms (1.5%)

prune90.0ms (1.7%)

localize18.0ms (0.3%)

rewrite18.0ms (0.3%)

series247.0ms (4.7%)

simplify91.0ms (1.7%)

prune99.0ms (1.9%)

localize21.0ms (0.4%)

rewrite31.0ms (0.6%)

series144.0ms (2.7%)

simplify89.0ms (1.7%)

prune101.0ms (1.9%)

regimes281.0ms (5.3%)

bsearch46.0ms (0.9%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample3.3s (62.8%)

Profiling