Details

analyze4.0ms (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)

sample175.0ms (1.7%)

Algorithm

1×

intervals

Results

72.0ms	62×	body	2048	valid
71.0ms	128×	body	1024	valid
15.0ms	43×	body	512	valid
4.0ms	16×	body	256	valid
1.0ms	7×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify313.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune4.0ms (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: 41.1b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize16.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.7b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
3.7b	(cos.f64 (+.f64 x eps))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-log-exp_binary64_113` `*-un-lft-identity_binary64_77` `add-sqr-sqrt_binary64_98`
2×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `pow1_binary64_135` `cos-sum_binary64_208` `add-cube-cbrt_binary64_109`
1×	`associate--l-_binary64_17` `distribute-lft-out--_binary64_31` `sub-neg_binary64_70` `flip--_binary64_52` `difference-of-squares_binary64_46` `flip3--_binary64_81` `diff-log_binary64_166` `diff-cos_binary64_225`

Counts

2 → 23

Calls

2 calls:

13.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
9.0ms	(cos.f64 (+.f64 x eps))

series179.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

134.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
45.0ms	(cos.f64 (+.f64 x eps))

simplify170.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (152.0ms)

Iter	Nodes	Cost
0	4863	429
1	4863	429

prune65.0ms (0.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	22	7	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	7	30

Merged error: 0.3b

Counts

30 → 7

Compiler

Compiled 491 to 177 computations (64% saved)

localize25.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.5b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite57.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_77`
8×	`add-log-exp_binary64_113`
7×	`add-sqr-sqrt_binary64_98`
5×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `pow1_binary64_135` `add-cube-cbrt_binary64_109`
3×	`associate-l_binary64_20` `distribute-lft-out_binary64_30` `sum-log_binary64_165` `associate-r_binary64_19`
1×	`pow-prod-down_binary64_145` `sin-mult_binary64_229` `flip-+_binary64_51` `cbrt-unprod_binary64_107` `flip3-+_binary64_80` `+-commutative_binary64_9` `unswap-sqr_binary64_45` `prod-exp_binary64_123` `*-commutative_binary64_10` `associate-+r+_binary64_11`

Counts

3 → 41

Calls

3 calls:

21.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
18.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
11.0ms	(+.f64 x (+.f64 x eps))

series294.0ms (2.9%)

Counts

3 → 9

Calls

3 calls:

162.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
70.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
62.0ms	(+.f64 x (+.f64 x eps))

simplify131.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	5074	836

prune139.0ms (1.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	42	8	50
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	43	14	57

Merged error: 0.3b

Counts

57 → 14

Compiler

Compiled 1315 to 857 computations (34.8% saved)

localize34.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.5b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.5b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.5b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite68.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77` `add-sqr-sqrt_binary64_98`
4×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `add-log-exp_binary64_113` `pow1_binary64_135`
3×	`cbrt-prod_binary64_105`
1×	`pow1/3_binary64_156`

Counts

4 → 32

Calls

4 calls:

16.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
16.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
16.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
14.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))

series511.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

323.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
66.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
62.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
61.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify113.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4814	675
1	4814	675

prune180.0ms (1.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	42	2	44
Fresh	1	11	12
Picked	1	0	1
Done	0	1	1
Total	44	14	58

Merged error: 0.3b

Counts

58 → 14

Compiler

Compiled 2117 to 1285 computations (39.3% saved)

localize37.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.5b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.5b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.5b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite68.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77` `add-sqr-sqrt_binary64_98`
4×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `add-log-exp_binary64_113` `pow1_binary64_135`
3×	`cbrt-prod_binary64_105`
1×	`pow1/3_binary64_156`

Counts

4 → 32

Calls

4 calls:

16.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
16.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
16.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
13.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))

series504.0ms (5%)

Counts

4 → 12

Calls

4 calls:

296.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
79.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
65.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
63.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify115.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4814	675
1	4814	675

prune143.0ms (1.4%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	44	14	58

Merged error: 0.3b

Counts

58 → 14

Compiler

Compiled 1769 to 1044 computations (41% saved)

regimes387.0ms (3.8%)

Compiler: Compiled 1157 to 812 computations (29.8% saved)

bsearch115.0ms (1.1%)

Steps

Iters	Range		Point
6	10595184.02732332	64634447.55721988	10769720.307495052
9	-0.010239150145348796	-1.3763013233941708e-09	-6.49332843509305e-05

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	71	60
1	71	60

end0.0ms (0%)

sample6.2s (61.6%)

Algorithm

1×

intervals

Results

2.4s	2031×	body	2048	valid
2.2s	3833×	body	1024	valid
470.0ms	1358×	body	512	valid
123.0ms	536×	body	256	valid
28.0ms	238×	body	128	valid
12.0ms	4×	body	4096	valid

Compiler

Compiled 409 to 291 computations (28.9% saved)

Details

analyze4.0ms (0%)

sample175.0ms (1.7%)

simplify313.0ms (3.1%)

prune4.0ms (0%)

localize16.0ms (0.2%)

rewrite25.0ms (0.3%)

series179.0ms (1.8%)

simplify170.0ms (1.7%)

prune65.0ms (0.6%)

localize25.0ms (0.3%)

rewrite57.0ms (0.6%)

series294.0ms (2.9%)

simplify131.0ms (1.3%)

prune139.0ms (1.4%)

localize34.0ms (0.3%)

rewrite68.0ms (0.7%)

series511.0ms (5.1%)

simplify113.0ms (1.1%)

prune180.0ms (1.8%)

localize37.0ms (0.4%)

rewrite68.0ms (0.7%)

series504.0ms (5%)

simplify115.0ms (1.1%)

prune143.0ms (1.4%)

regimes387.0ms (3.8%)

bsearch115.0ms (1.1%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample6.2s (61.6%)

Profiling