Details

analyze2.0ms

Algorithm

Search

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

sample93.0ms

Algorithm

intervals

Results

48.0ms	136×	body	1280	valid
17.0ms	19×	body	2560	valid
14.0ms	65×	body	640	valid
4.0ms	23×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	2×	body	80	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune3.0ms

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: 40.2b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.6b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
3.3b	(cos.f64 (+.f64 x eps))

rewrite18.0ms

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` `add-exp-log_binary64` `add-cbrt-cube_binary64` `cos-sum_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `associate--l-_binary64` `diff-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `diff-cos_binary64`

Counts

2 → 23

Calls

2 calls:

7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
10.0ms	(cos.f64 (+.f64 x eps))

series13.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify72.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5171	262

prune47.0ms

Filtered

23 candidates to 29 candidates (-26.1%)

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

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
0.0b	(+.f64 x (+.f64 x eps))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.3b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
11×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`associate-l_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64`
3×	`distribute-lft-out_binary64` `sum-log_binary64`
2×	`sin-mult_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-+r+_binary64`

Counts

4 → 60

Calls

4 calls:

12.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
6.0ms	(+.f64 x (+.f64 x eps))
11.0ms	(*.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))

series38.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
3.0ms	(+.f64 x (+.f64 x eps))
13.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
7.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify66.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4984	872
1	4984	872

prune100.0ms

Filtered

52 candidates to 72 candidates (-38.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	64	8	72
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	66	13	79

Merged error: 0.4b

Counts

79 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
3.3b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod_binary64`
7×	`*-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`
3×	`pow1/3_binary64`

Counts

4 → 40

Calls

4 calls:

2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series69.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
19.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
21.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
6.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify77.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5910	436

prune107.0ms

Filtered

45 candidates to 52 candidates (-15.6%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	51	14	65

Merged error: 0.4b

Counts

65 → 14

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.3b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.3b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.3b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite31.0ms

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`
3×	`cbrt-prod_binary64`
1×	`pow1/3_binary64`

Counts

4 → 32

Calls

4 calls:

6.0ms	(cbrt.f64 (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))
8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series45.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
6.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify30.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4953	450
1	4953	450

prune62.0ms

Filtered

38 candidates to 44 candidates (-15.8%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	0	11	11
Picked	1	0	1
Done	0	2	2
Total	44	14	58

Merged error: 0.4b

Counts

58 → 14

regimes186.0ms

Accuracy

97.3% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 14.9b

bsearch60.0ms

Steps

Iters	Range		Point
9	0.17949788472177558	45623308.59113779	0.18290653919849093
7	-9.494300489779706e-09	-4.726833690786262e-10	-9.370340767231984e-09

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	78	38
1	78	38

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.7s	4510×	body	1280	valid
572.0ms	631×	body	2560	valid
417.0ms	1814×	body	640	valid
108.0ms	660×	body	320	valid
37.0ms	299×	body	160	valid
5.0ms	86×	body	80	valid

Details

analyze2.0ms

sample93.0ms

simplify7.0ms

prune3.0ms

localize8.0ms

rewrite18.0ms

series13.0ms

simplify72.0ms

prune47.0ms

localize13.0ms

rewrite39.0ms

series38.0ms

simplify66.0ms

prune100.0ms

localize18.0ms

rewrite15.0ms

series69.0ms

simplify77.0ms

prune107.0ms

localize16.0ms

rewrite31.0ms

series45.0ms

simplify30.0ms

prune62.0ms

regimes186.0ms

bsearch60.0ms

simplify3.0ms

end0.0ms

sample3.0s

Profiling