Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

sample107.0ms

Algorithm

intervals

Results

56.0ms	114×	body	1280	valid
21.0ms	23×	body	2560	valid
16.0ms	59×	body	640	valid
4.0ms	20×	body	320	valid
2.0ms	29×	body	80	valid
1.0ms	11×	body	160	valid

simplify25.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	73	11
1	73	11

prune1.0ms

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: 39.1b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.5b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.9b	(sin.f64 (+.f64 x eps))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
2×	`pow1_binary64` `add-cube-cbrt_binary64` `sin-sum_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `diff-sin_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `associate--l+_binary64`

Counts

2 → 25

Calls

2 calls:

8.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	(sin.f64 (+.f64 x eps))

series408.0ms

Counts

2 → 6

Calls

2 calls:

216.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
192.0ms	(sin.f64 (+.f64 x eps))

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	680	103
1	680	103
0	680	103
1	680	103
0	34	12
1	34	12
0	741	215
1	741	215
0	741	215
1	741	215
0	20	9
1	20	9

simplify171.0ms

Counts

31 → 31

Iterations

Useful iterations: 0 (150.0ms)

Iter	Nodes	Cost
0	4934	405
1	4934	405

prune30.0ms

Filtered

27 candidates to 31 candidates (-14.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	28	3	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	3	32

Merged error: 0.4b

Counts

32 → 3

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
2.9b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
7×	`add-sqr-sqrt_binary64`
5×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`distribute-lft-out_binary64` `associate-r_binary64` `associate-l_binary64` `insert-posit16` `sum-log_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sin-cos-mult_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-+r+_binary64` `*-commutative_binary64`

Counts

3 → 44

Calls

3 calls:

7.0ms	(+.f64 x (+.f64 x eps))
7.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
9.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series1.3s

Counts

3 → 9

Calls

3 calls:

371.0ms	(+.f64 x (+.f64 x eps))
377.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
518.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	34	162
1	34	162
0	34	162
1	34	162
0	1	3
1	1	3
0	52	519
1	52	519
0	52	519
1	52	519
0	1	3
1	1	3
0	2242	51
1	2242	51
0	2242	51
1	2242	51
0	20	9
1	20	9

simplify147.0ms

Counts

53 → 53

Iterations

Useful iterations: 0 (124.0ms)

Iter	Nodes	Cost
0	4892	784
1	4892	784

prune65.0ms

Filtered

41 candidates to 53 candidates (-29.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	45	8	53
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	45	11	56

Merged error: 0.3b

Counts

56 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
0.5b	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
2.9b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`log-prod_binary64` `exp-prod_binary64`
8×	`pow1_binary64` `log-pow_binary64`
7×	`associate-r_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`add-log-exp_binary64`
4×	`insert-posit16`
3×	`distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 65

Calls

4 calls:

10.0ms	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
17.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
11.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
10.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series1.5s

Counts

4 → 12

Calls

4 calls:

276.0ms	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
427.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
319.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
514.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	34	162
1	34	162
0	34	162
1	34	162
0	1	3
1	1	3
0	47	510
1	47	510
0	47	510
1	47	510
0	1	3
1	1	3
0	70	945
1	70	945
0	70	945
1	70	945
0	1	3
1	1	3
0	37	252
1	37	252
0	37	252
1	37	252
0	1	3
1	1	3

simplify139.0ms

Counts

77 → 77

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	5695	1382

prune82.0ms

Filtered

52 candidates to 77 candidates (-48.1%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	75	13	88

Merged error: 0.3b

Counts

88 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
2.9b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.9b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.9b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16`
3×	`cbrt-prod_binary64`
1×	`pow1/3_binary64`

Counts

4 → 36

Calls

4 calls:

1.0ms	(cbrt.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
9.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
9.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
9.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series1.7s

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
521.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
518.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
516.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	34	162
1	34	162
0	34	162
1	34	162
0	1	3
1	1	3
0	34	162
1	34	162
0	34	162
1	34	162
0	1	3
1	1	3
0	34	162
1	34	162
0	34	162
1	34	162
0	1	3
1	1	3
0	476	1718
1	476	1718
0	476	1718
1	476	1718
0	1	3
1	1	3

simplify88.0ms

Counts

48 → 48

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4938	586
1	4938	586

prune71.0ms

Filtered

39 candidates to 48 candidates (-23.1%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	48	0	48
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	48	13	61

Merged error: 0.3b

Counts

61 → 13

regimes118.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 14.9b

bsearch75.0ms

Steps

Iters	Range		Point
8	1.8398143021311394e-11	9.412924937912301e-08	1.4226074865406582e-08
8	-0.005641666064101144	-2.355165639800751e-07	-2.3935202059354087e-07

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	47	60
1	47	60

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.6s	3310×	body	1280	valid
623.0ms	647×	body	2560	valid
505.0ms	1815×	body	640	valid
141.0ms	766×	body	320	valid
67.0ms	1136×	body	80	valid
41.0ms	326×	body	160	valid

Iter	Nodes	Cost
0	680	103
1	680	103
0	680	103
1	680	103
0	34	12
1	34	12
0	741	215
1	741	215
0	741	215
1	741	215
0	20	9
1	20	9

Iter	Nodes	Cost
0	34	162
1	34	162
0	34	162
1	34	162
0	1	3
1	1	3
0	47	510
1	47	510
0	47	510
1	47	510
0	1	3
1	1	3
0	70	945
1	70	945
0	70	945
1	70	945
0	1	3
1	1	3
0	37	252
1	37	252
0	37	252
1	37	252
0	1	3
1	1	3

Iter	Nodes	Cost
0	680	103
1	680	103
0	680	103
1	680	103
0	34	12
1	34	12
0	741	215
1	741	215
0	741	215
1	741	215
0	20	9
1	20	9

Iter	Nodes	Cost
0	34	162
1	34	162
0	34	162
1	34	162
0	1	3
1	1	3
0	47	510
1	47	510
0	47	510
1	47	510
0	1	3
1	1	3
0	70	945
1	70	945
0	70	945
1	70	945
0	1	3
1	1	3
0	37	252
1	37	252
0	37	252
1	37	252
0	1	3
1	1	3

Details

analyze2.0ms

sample107.0ms

simplify25.0ms

prune1.0ms

localize8.0ms

rewrite14.0ms

series408.0ms

simplify171.0ms

prune30.0ms

localize12.0ms

rewrite25.0ms

series1.3s

simplify147.0ms

prune65.0ms

localize16.0ms

rewrite50.0ms

series1.5s

simplify139.0ms

prune82.0ms

localize16.0ms

rewrite30.0ms

series1.7s

simplify88.0ms

prune71.0ms

regimes118.0ms

bsearch75.0ms

simplify7.0ms

end0.0ms

sample3.1s

Profiling

Iter	Nodes	Cost
0	680	103
1	680	103
0	680	103
1	680	103
0	34	12
1	34	12
0	741	215
1	741	215
0	741	215
1	741	215
0	20	9
1	20	9

Iter	Nodes	Cost
0	34	162
1	34	162
0	34	162
1	34	162
0	1	3
1	1	3
0	47	510
1	47	510
0	47	510
1	47	510
0	1	3
1	1	3
0	70	945
1	70	945
0	70	945
1	70	945
0	1	3
1	1	3
0	37	252
1	37	252
0	37	252
1	37	252
0	1	3
1	1	3