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)

sample93.0ms (1.6%)

Algorithm

1×

intervals

Results

41.0ms	67×	body	2048	valid
35.0ms	123×	body	1024	valid
8.0ms	45×	body	512	valid
2.0ms	16×	body	256	valid
0.0ms	5×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify174.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

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: 41.0b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.1b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
4.3b	(cos.f64 (+.f64 x eps))

rewrite13.0ms (0.2%)

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:

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

series107.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

79.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
28.0ms	(cos.f64 (+.f64 x eps))

simplify98.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4863	429
1	4863	429

prune34.0ms (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: 0.4b

Counts

30 → 7

Compiler

Compiled 485 to 178 computations (63.3% saved)

localize13.0ms (0.2%)

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)))
4.4b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite33.0ms (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:

14.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
9.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(+.f64 x (+.f64 x eps))

series152.0ms (2.6%)

Counts

3 → 9

Calls

3 calls:

83.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
39.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
30.0ms	(+.f64 x (+.f64 x eps))

simplify69.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5074	836

prune74.0ms (1.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	42	8	50
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	46	11	57

Merged error: 0.3b

Counts

57 → 11

Compiler

Compiled 1244 to 820 computations (34.1% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
4.4b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
4.4b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
4.4b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite37.0ms (0.6%)

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:

9.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
9.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
7.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))

series269.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

162.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
37.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
36.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
33.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify64.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4814	675
1	4814	675

prune91.0ms (1.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	44	11	55

Merged error: 0.3b

Counts

55 → 11

Compiler

Compiled 1975 to 1204 computations (39% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

4.4b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
5.9b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
5.9b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
5.9b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))

rewrite46.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `add-log-exp_binary64_113` `pow1_binary64_135` `add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77` `add-sqr-sqrt_binary64_98`
3×	`sin-mult_binary64_229` `cbrt-div_binary64_106` `cbrt-prod_binary64_105` `pow1/3_binary64_156`

Counts

4 → 37

Calls

4 calls:

13.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
10.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
10.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
9.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series838.0ms (14.3%)

Counts

4 → 12

Calls

4 calls:

269.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
264.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
263.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
42.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify71.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4855	1133
1	4855	1133

prune113.0ms (1.9%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	49	11	60

Merged error: 0.3b

Counts

60 → 11

Compiler

Compiled 2536 to 1598 computations (37% saved)

regimes105.0ms (1.8%)

Compiler: Compiled 518 to 402 computations (22.4% saved)

bsearch64.0ms (1.1%)

Steps

Iters	Range		Point
4	35473230918.31673	61608729631.80446	36289965253.11321
12	-1.8712321116120458e+18	-8.865849221424071e-26	-0.0002078600849444932

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	80	60
1	80	60

end0.0ms (0%)

sample3.3s (55.7%)

Algorithm

1×

intervals

Results

1.3s	2067×	body	2048	valid
1.2s	3883×	body	1024	valid
240.0ms	1317×	body	512	valid
58.0ms	502×	body	256	valid
15.0ms	230×	body	128	valid
2.0ms	1×	body	4096	valid

Compiler

Compiled 303 to 234 computations (22.8% saved)

Details

analyze2.0ms (0%)

sample93.0ms (1.6%)

simplify174.0ms (3%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite13.0ms (0.2%)

series107.0ms (1.8%)

simplify98.0ms (1.7%)

prune34.0ms (0.6%)

localize13.0ms (0.2%)

rewrite33.0ms (0.6%)

series152.0ms (2.6%)

simplify69.0ms (1.2%)

prune74.0ms (1.3%)

localize17.0ms (0.3%)

rewrite37.0ms (0.6%)

series269.0ms (4.6%)

simplify64.0ms (1.1%)

prune91.0ms (1.5%)

localize17.0ms (0.3%)

rewrite46.0ms (0.8%)

series838.0ms (14.3%)

simplify71.0ms (1.2%)

prune113.0ms (1.9%)

regimes105.0ms (1.8%)

bsearch64.0ms (1.1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.3s (55.7%)

Profiling