Details

analyze2.0ms

Algorithm

Search

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

sample97.0ms

Algorithm

intervals

Results

53.0ms	142×	body	1280	valid
17.0ms	18×	body	2560	valid
14.0ms	57×	body	640	valid
5.0ms	31×	body	320	valid
1.0ms	6×	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

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: 40.0b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.9b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
2.6b	(cos.f64 (+.f64 x eps))

rewrite12.0ms

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))

series20.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
11.0ms	(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

prune38.0ms

Filtered

23 candidates to 29 candidates (-26.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	20	9	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	21	9	30

Merged error: 0.5b

Counts

30 → 9

localize16.0ms

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)))
2.4b	(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:

13.0ms	(.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:

14.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
4.0ms	(+.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))

simplify58.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4907	890
1	4907	890

prune78.0ms

Filtered

53 candidates to 72 candidates (-35.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	63	9	72
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	67	14	81

Merged error: 0.4b

Counts

81 → 14

localize16.0ms

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)))
2.4b	(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))

series58.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
18.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
17.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
6.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify33.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5501	442

prune82.0ms

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	1	11	12
Picked	0	1	1
Done	0	1	1
Total	52	14	66

Merged error: 0.4b

Counts

66 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

2.4b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
7.4b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
7.4b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
7.4b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))

rewrite35.0ms

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`
3×	`cbrt-div_binary64` `pow1/3_binary64` `sin-mult_binary64` `cbrt-prod_binary64`

Counts

4 → 37

Calls

4 calls:

8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
9.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
9.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
9.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))

series102.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
31.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
33.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
31.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))

simplify56.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5057	721

prune66.0ms

Filtered

42 candidates to 49 candidates (-16.7%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	48	1	49
Fresh	1	10	11
Picked	0	1	1
Done	0	2	2
Total	49	14	63

Merged error: 0.4b

Counts

63 → 14

regimes221.0ms

Accuracy

97.8% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.2b

bsearch75.0ms

Steps

Iters	Range		Point
9	9.548151851389376e-12	4.798688009906535e-06	4.586953767858916e-06
8	-0.0045913724923496105	-1.0278274854661441e-05	-8.75008903732586e-05

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	78	38
1	78	38

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.8s	4447×	body	1280	valid
539.0ms	572×	body	2560	valid
460.0ms	1880×	body	640	valid
130.0ms	722×	body	320	valid
37.0ms	304×	body	160	valid
5.0ms	75×	body	80	valid

Details

analyze2.0ms

sample97.0ms

simplify7.0ms

prune2.0ms

localize8.0ms

rewrite12.0ms

series20.0ms

simplify28.0ms

prune38.0ms

localize16.0ms

rewrite39.0ms

series38.0ms

simplify58.0ms

prune78.0ms

localize16.0ms

rewrite15.0ms

series58.0ms

simplify33.0ms

prune82.0ms

localize19.0ms

rewrite35.0ms

series102.0ms

simplify56.0ms

prune66.0ms

regimes221.0ms

bsearch75.0ms

simplify3.0ms

end0.0ms

sample3.1s

Profiling