Details

analyze100.0ms (1.1%)

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample87.0ms (1%)

Algorithm

1×

intervals

Results

34.0ms	121×	body	1024	valid
33.0ms	68×	body	2048	valid
7.0ms	40×	body	512	valid
2.0ms	21×	body	256	valid
0.0ms	6×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify10.0ms (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

38.7b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.2b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
2.1b	(cos.f64 (+.f64 x eps))

rewrite43.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

18.4b

Rules

5×	`add-sqr-sqrt_binary64_441` `*-un-lft-identity_binary64_419`
4×	`add-log-exp_binary64_458`
3×	`add-cube-cbrt_binary64_454` `cancel-sign-sub-inv_binary64_385`
2×	`cos-sum_binary64_553` `pow1_binary64_480` `add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
1×	`diff-cos_binary64_570` `diff-log_binary64_511` `flip3--_binary64_423` `sub-neg_binary64_412` `flip--_binary64_394` `difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371` `associate--l-_binary64_357`

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)

series146.0ms (1.6%)

Error

13.1b

Counts

2 → 23

Calls

2 calls:

78.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
41.0ms	(cos.f64 (+.f64 x eps))

Compiler

Compiled 674 to 426 computations (36.8% saved)

simplify62.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4917	732
1	4917	732

prune57.0ms (0.6%)

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 712 to 272 computations (61.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
0.0b	(+.f64 x (+.f64 eps x))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
2.1b	(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

rewrite122.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

12×	`*-un-lft-identity_binary64_419`
11×	`pow1_binary64_480` `add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
9×	`add-log-exp_binary64_458` `add-sqr-sqrt_binary64_441`
7×	`add-cube-cbrt_binary64_454`
6×	`associate-l_binary64_360`
4×	`pow-prod-down_binary64_490` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-r_binary64_359`
3×	`sum-log_binary64_510` `distribute-lft-out_binary64_370`
2×	`sin-mult_binary64_574` `*-commutative_binary64_350`
1×	`unswap-sqr_binary64_387` `flip3-+_binary64_422` `flip-+_binary64_393` `associate-+r+_binary64_351` `+-commutative_binary64_349` `associate-*r/_binary64_361`

Counts

4 → 60

Calls

4 calls:

12.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
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 1452 to 895 computations (38.4% saved)

series434.0ms (4.8%)

Error

0.2b

Counts

4 → 48

Calls

4 calls:

147.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
121.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
59.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))
56.0ms	(+.f64 x (+.f64 eps x))

Compiler

Compiled 2082 to 1744 computations (16.2% saved)

simplify79.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4912	2057
1	4912	2057

prune133.0ms (1.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	97	11	108
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	102	14	116

Error

0.2b

Counts

116 → 14

Compiler

Compiled 2410 to 1627 computations (32.5% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
2.1b	(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))
2.1b	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
2.1b	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))

rewrite91.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

5×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `*-un-lft-identity_binary64_419`
4×	`pow1_binary64_480` `add-log-exp_binary64_458` `add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
3×	`cbrt-prod_binary64_450`
1×	`pow1/3_binary64_501`

Counts

4 → 32

Calls

4 calls:

9.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
9.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
7.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))
6.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))

Compiler

Compiled 1431 to 810 computations (43.4% saved)

series620.0ms (6.9%)

Error

0.2b

Counts

4 → 46

Calls

4 calls:

321.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
70.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))
70.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
70.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))

Compiler

Compiled 4756 to 3426 computations (28% saved)

simplify50.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5177	1478

prune163.0ms (1.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	78	14	92

Error

0.2b

Counts

92 → 14

Compiler

Compiled 3549 to 2180 computations (38.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.1b	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
6.1b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
6.1b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
6.1b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))

rewrite136.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

4×	`pow1_binary64_480` `add-log-exp_binary64_458` `add-exp-log_binary64_457` `add-cbrt-cube_binary64_455` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `*-un-lft-identity_binary64_419`
3×	`pow1/3_binary64_501` `sin-mult_binary64_574` `cbrt-div_binary64_451` `cbrt-prod_binary64_450`

Counts

4 → 37

Calls

4 calls:

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

Compiler

Compiled 2079 to 1284 computations (38.2% saved)

series1.5s (16.2%)

Error

0.2b

Counts

4 → 42

Calls

4 calls:

436.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
428.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
425.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
71.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))

Compiler

Compiled 6500 to 4751 computations (26.9% saved)

simplify59.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5468	2188

prune200.0ms (2.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	76	3	79
Fresh	2	10	12
Picked	1	0	1
Done	0	1	1
Total	79	14	93

Error

0.2b

Counts

93 → 14

Compiler

Compiled 4216 to 2688 computations (36.2% saved)

regimes683.0ms (7.6%)

Accuracy

Total 0.3b remaining (58.9%)

Threshold costs 0.3b (58.9%)

Compiler

Compiled 4983 to 3700 computations (25.7% saved)

bsearch86.0ms (0.9%)

Steps

Iters	Range		Point
10	4.882282480559376e-22	0.0029060785001664598	0.0026088415052572663
10	-27.42946591198322	-1.8830078121915895e-09	-0.002800293132587222

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	145	85
1	145	85

end0.0ms (0%)

sample4.2s (45.9%)

Algorithm

1×

intervals

Results

1.0s	2025×	body	2048	valid
973.0ms	3953×	body	1024	valid
225.0ms	1282×	body	512	valid
56.0ms	504×	body	256	valid
14.0ms	234×	body	128	valid
2.0ms	2×	body	4096	valid

Compiler

Compiled 1707 to 1263 computations (26% saved)

Details

analyze100.0ms (1.1%)

sample87.0ms (1%)

simplify10.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite43.0ms (0.5%)

series146.0ms (1.6%)

simplify62.0ms (0.7%)

prune57.0ms (0.6%)

localize12.0ms (0.1%)

rewrite122.0ms (1.4%)

series434.0ms (4.8%)

simplify79.0ms (0.9%)

prune133.0ms (1.5%)

localize22.0ms (0.2%)

rewrite91.0ms (1%)

series620.0ms (6.9%)

simplify50.0ms (0.6%)

prune163.0ms (1.8%)

localize16.0ms (0.2%)

rewrite136.0ms (1.5%)

series1.5s (16.2%)

simplify59.0ms (0.7%)

prune200.0ms (2.2%)

regimes683.0ms (7.6%)

bsearch86.0ms (0.9%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample4.2s (45.9%)

Profiling