Details

analyze2.0ms

Algorithm

Search

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

sample94.0ms

Algorithm

intervals

Results

55.0ms	148×	body	1280	valid
15.0ms	16×	body	2560	valid
13.0ms	58×	body	640	valid
4.0ms	23×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	2×	body	80	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

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: 38.4b

Counts

2 → 1

localize14.0ms

Local error

Found 2 expressions with local error:

1.4b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
2.9b	(cos.f64 (+.f64 x eps))

rewrite11.0ms

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))
4.0ms	(cos.f64 (+.f64 x eps))

series54.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
15.0ms	(cos.f64 (+.f64 x eps))

simplify46.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4945	429
1	4945	429

prune34.0ms

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: 0.5b

Counts

30 → 7

localize12.0ms

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))
0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
2.8b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite37.0ms

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))
10.0ms	(*.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))

series156.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
18.0ms	(+.f64 x (+.f64 x eps))
54.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
24.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify117.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4897	1369
1	4897	1369

prune85.0ms

Filtered

53 candidates to 72 candidates (-35.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	63	9	72
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	64	15	79

Merged error: 0.4b

Counts

79 → 15

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
2.8b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.8b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.8b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite29.0ms

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

series159.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
20.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
22.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
24.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify82.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5079	727

prune91.0ms

Filtered

38 candidates to 44 candidates (-15.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	0	13	13
Picked	1	0	1
Done	0	1	1
Total	44	15	59

Merged error: 0.4b

Counts

59 → 15

localize22.0ms

Local error

Found 4 expressions with local error:

2.8b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.8b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.8b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.8b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`

Counts

4 → 28

Calls

4 calls:

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

series88.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
21.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
25.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
22.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify92.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4990	596
1	4990	596

prune92.0ms

Filtered

36 candidates to 40 candidates (-11.1%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	40	15	55

Merged error: 0.4b

Counts

55 → 15

regimes123.0ms

Accuracy

97.3% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 15.0b

bsearch68.0ms

Steps

Iters	Range		Point
8	3.113136890514365e-11	4.985137664145584e-08	4.923419680012861e-08
8	-1.9460658352402853	-0.0007004325775336613	-0.0008870636453624816

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	71	60
1	71	60

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.7s	4481×	body	1280	valid
553.0ms	605×	body	2560	valid
446.0ms	1836×	body	640	valid
120.0ms	713×	body	320	valid
36.0ms	290×	body	160	valid
4.0ms	75×	body	80	valid

Details

analyze2.0ms

sample94.0ms

simplify14.0ms

prune1.0ms

localize14.0ms

rewrite11.0ms

series54.0ms

simplify46.0ms

prune34.0ms

localize12.0ms

rewrite37.0ms

series156.0ms

simplify117.0ms

prune85.0ms

localize17.0ms

rewrite29.0ms

series159.0ms

simplify82.0ms

prune91.0ms

localize22.0ms

rewrite32.0ms

series88.0ms

simplify92.0ms

prune92.0ms

regimes123.0ms

bsearch68.0ms

simplify4.0ms

end0.0ms

sample3.0s

Profiling