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)

sample98.0ms (1.7%)

Algorithm

1×

intervals

Results

42.0ms	66×	body	2048	valid
38.0ms	124×	body	1024	valid
8.0ms	45×	body	512	valid
2.0ms	12×	body	256	valid
1.0ms	9×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify176.0ms (3.1%)

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: 39.9b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.0b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
3.5b	(cos.f64 (+.f64 x eps))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64_414` `add-log-exp_binary64_450` `add-sqr-sqrt_binary64_435`
2×	`pow1_binary64_472` `add-cube-cbrt_binary64_446` `cos-sum_binary64_545` `add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
1×	`flip3--_binary64_418` `distribute-lft-out--_binary64_368` `difference-of-squares_binary64_383` `diff-log_binary64_503` `associate--l-_binary64_354` `sub-neg_binary64_407` `diff-cos_binary64_562` `flip--_binary64_389`

Counts

2 → 23

Calls

2 calls:

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

series99.0ms (1.7%)

Counts

2 → 6

Calls

2 calls:

73.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
26.0ms	(cos.f64 (+.f64 x eps))

simplify102.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (90.0ms)

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: 0.2b

Counts

30 → 7

Compiler

Compiled 482 to 179 computations (62.9% 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)))
3.4b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_414`
8×	`add-log-exp_binary64_450`
7×	`add-sqr-sqrt_binary64_435`
5×	`pow1_binary64_472` `add-cube-cbrt_binary64_446` `add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
3×	`associate-l_binary64_357` `associate-r_binary64_356` `distribute-lft-out_binary64_367` `sum-log_binary64_502`
1×	`flip3-+_binary64_417` `*-commutative_binary64_347` `+-commutative_binary64_346` `prod-exp_binary64_460` `pow-prod-down_binary64_482` `associate-+r+_binary64_348` `flip-+_binary64_388` `unswap-sqr_binary64_382` `cbrt-unprod_binary64_444` `sin-mult_binary64_566`

Counts

3 → 41

Calls

3 calls:

14.0ms	(*.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))

series167.0ms (2.9%)

Counts

3 → 9

Calls

3 calls:

94.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
41.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
32.0ms	(+.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

prune77.0ms (1.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	43	7	50
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	47	10	57

Merged error: 0.2b

Counts

57 → 10

Compiler

Compiled 1228 to 806 computations (34.4% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.4b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.4b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.4b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414` `add-sqr-sqrt_binary64_435`
4×	`pow1_binary64_472` `add-exp-log_binary64_449` `add-cbrt-cube_binary64_447` `add-log-exp_binary64_450`
3×	`cbrt-prod_binary64_442`
1×	`pow1/3_binary64_493`

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

series413.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

174.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
166.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
38.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
35.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify64.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4814	675
1	4814	675

prune90.0ms (1.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	44	10	54

Merged error: 0.2b

Counts

54 → 10

Compiler

Compiled 1959 to 1190 computations (39.3% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.4b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.4b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.4b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite38.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414` `add-sqr-sqrt_binary64_435`
4×	`pow1_binary64_472` `add-exp-log_binary64_449` `add-cbrt-cube_binary64_447` `add-log-exp_binary64_450`
3×	`cbrt-prod_binary64_442`
1×	`pow1/3_binary64_493`

Counts

4 → 32

Calls

4 calls:

11.0ms	(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))
7.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))

series275.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
38.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
34.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
34.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify61.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4814	675
1	4814	675

prune79.0ms (1.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

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

Merged error: 0.2b

Counts

54 → 11

Compiler

Compiled 1769 to 1044 computations (41% saved)

regimes110.0ms (1.9%)

Compiler: Compiled 632 to 466 computations (26.3% saved)

bsearch84.0ms (1.5%)

Steps

Iters	Range		Point
6	2.38273682151872e-06	2.3912337599128073e-05	7.180247165522076e-06
11	-697988.6142033994	-1.144111223116443e-20	-9.564482726259974e-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	83	81
1	83	81

end0.0ms (0%)

sample3.5s (61.5%)

Algorithm

1×

intervals

Results

1.4s	2013×	body	2048	valid
1.2s	3865×	body	1024	valid
273.0ms	1367×	body	512	valid
78.0ms	530×	body	256	valid
15.0ms	225×	body	128	valid

Compiler

Compiled 373 to 267 computations (28.4% saved)

Details

analyze2.0ms (0%)

sample98.0ms (1.7%)

simplify176.0ms (3.1%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite14.0ms (0.2%)

series99.0ms (1.7%)

simplify102.0ms (1.8%)

prune34.0ms (0.6%)

localize13.0ms (0.2%)

rewrite32.0ms (0.6%)

series167.0ms (2.9%)

simplify69.0ms (1.2%)

prune77.0ms (1.4%)

localize18.0ms (0.3%)

rewrite36.0ms (0.6%)

series413.0ms (7.3%)

simplify64.0ms (1.1%)

prune90.0ms (1.6%)

localize18.0ms (0.3%)

rewrite38.0ms (0.7%)

series275.0ms (4.8%)

simplify61.0ms (1.1%)

prune79.0ms (1.4%)

regimes110.0ms (1.9%)

bsearch84.0ms (1.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample3.5s (61.5%)

Profiling