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

53.0ms	143×	body	1280	valid
14.0ms	15×	body	2560	valid
13.0ms	61×	body	640	valid
3.0ms	21×	body	320	valid
2.0ms	13×	body	160	valid
0.0ms	3×	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

prune2.0ms

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: 37.4b

Counts

2 → 1

localize14.0ms

Local error

Found 2 expressions with local error:

1.4b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
2.8b	(cos.f64 (+.f64 x eps))

rewrite13.0ms

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

series15.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
5.0ms	(cos.f64 (+.f64 x eps))

simplify28.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4999	270
1	4999	270

prune36.0ms

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

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite41.0ms

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:

7.0ms	(+.f64 x (+.f64 x eps))
13.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
12.0ms	(*.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))

series39.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+.f64 x (+.f64 x eps))
15.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
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))

simplify61.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4907	890
1	4907	890

prune71.0ms

Filtered

53 candidates to 72 candidates (-35.8%)

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: 0.3b

Counts

79 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite34.0ms

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:

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

series42.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(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))

simplify53.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5090	468

prune78.0ms

Filtered

38 candidates to 44 candidates (-15.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	40	4	44
Fresh	1	10	11
Picked	1	0	1
Done	0	1	1
Total	42	15	57

Merged error: 0.3b

Counts

57 → 15

localize20.0ms

Local error

Found 4 expressions with local error:

3.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite33.0ms

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:

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

series26.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify64.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4888	388
1	4888	388

prune59.0ms

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: 0.3b

Counts

55 → 15

regimes169.0ms

Accuracy

97.9% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.4b

bsearch62.0ms

Steps

Iters	Range		Point
5	0.00022528005411696429	0.000752773965564729	0.00023498571328606823
11	-6428.5598610616225	-1.7374184253756152e-16	-0.00029507773736298554

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	81	51
1	81	51

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.7s	4510×	body	1280	valid
569.0ms	629×	body	2560	valid
416.0ms	1804×	body	640	valid
114.0ms	676×	body	320	valid
35.0ms	284×	body	160	valid
6.0ms	97×	body	80	valid

Details

analyze2.0ms

sample93.0ms

simplify7.0ms

prune2.0ms

localize14.0ms

rewrite13.0ms

series15.0ms

simplify28.0ms

prune36.0ms

localize12.0ms

rewrite41.0ms

series39.0ms

simplify61.0ms

prune71.0ms

localize16.0ms

rewrite34.0ms

series42.0ms

simplify53.0ms

prune78.0ms

localize20.0ms

rewrite33.0ms

series26.0ms

simplify64.0ms

prune59.0ms

regimes169.0ms

bsearch62.0ms

simplify2.0ms

end0.0ms

sample3.0s

Profiling