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

49.0ms	132×	body	1280	valid
16.0ms	18×	body	2560	valid
15.0ms	66×	body	640	valid
4.0ms	25×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	8×	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: 36.8b

Counts

2 → 1

localize14.0ms

Local error

Found 2 expressions with local error:

0.3b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
2.3b	(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))
4.0ms	(cos.f64 (+.f64 x eps))

series15.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
6.0ms	(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

prune52.0ms

Filtered

23 candidates to 29 candidates (-26.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	21	8	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	8	30

Merged error: 0.3b

Counts

30 → 8

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)))
2.2b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite38.0ms

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))

series39.0ms

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))))
6.0ms	(+.f64 x (+.f64 x eps))
12.0ms	(*.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))

simplify59.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4907	890
1	4907	890

prune107.0ms

Filtered

53 candidates to 72 candidates (-35.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	65	7	72
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	67	13	80

Merged error: 0.2b

Counts

80 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
2.2b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.2b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.2b	(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))

series43.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(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))

simplify55.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5090	468

prune96.0ms

Filtered

38 candidates to 44 candidates (-15.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	44	13	57

Merged error: 0.2b

Counts

57 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

2.2b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.3b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
6.3b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
6.3b	(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))))

series100.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
30.0ms	(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))))
30.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))

simplify55.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5057	721

prune85.0ms

Filtered

42 candidates to 49 candidates (-16.7%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	49	13	62

Merged error: 0.2b

Counts

62 → 13

regimes252.0ms

Accuracy

90.8% (1.4b remaining)

Error of 1.8b against oracle of 0.4b and baseline of 15.6b

bsearch82.0ms

Steps

Iters	Range		Point
7	1.5238667119354926e+45	5.280225517840204e+46	1.55223562688049e+45
11	-0.013396683979028528	-6.339096501967977e-23	-3.0439497322623832e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	81	51
1	81	51

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.7s	4519×	body	1280	valid
584.0ms	626×	body	2560	valid
453.0ms	1835×	body	640	valid
106.0ms	651×	body	320	valid
33.0ms	287×	body	160	valid
5.0ms	82×	body	80	valid

Details

analyze2.0ms

sample93.0ms

simplify7.0ms

prune3.0ms

localize14.0ms

rewrite12.0ms

series15.0ms

simplify28.0ms

prune52.0ms

localize13.0ms

rewrite38.0ms

series39.0ms

simplify59.0ms

prune107.0ms

localize17.0ms

rewrite31.0ms

series43.0ms

simplify55.0ms

prune96.0ms

localize19.0ms

rewrite35.0ms

series100.0ms

simplify55.0ms

prune85.0ms

regimes252.0ms

bsearch82.0ms

simplify2.0ms

end0.0ms

sample3.1s

Profiling