Details

analyze2.0ms

Algorithm

Search

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

sample102.0ms

Algorithm

intervals

Results

43.0ms	123×	body	1024	valid
41.0ms	64×	body	2048	valid
8.0ms	44×	body	512	valid
2.0ms	17×	body	256	valid
1.0ms	8×	body	128	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	72	11
1	72	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: 39.6b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.6b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
3.9b	(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))

series97.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
26.0ms	(cos.f64 (+.f64 x eps))

simplify37.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4955	429
1	4955	429

prune37.0ms

Filtered

23 candidates to 29 candidates (-26.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	19	10	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	20	10	30

Merged error: 0.3b

Counts

30 → 10

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.6b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 41

Calls

3 calls:

8.0ms	(+.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))

series152.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+.f64 x (+.f64 x eps))
84.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
38.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify69.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4892	835
1	4892	835

prune65.0ms

Filtered

38 candidates to 50 candidates (-31.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	42	8	50
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	46	14	60

Merged error: 0.2b

Counts

60 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.6b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.6b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.6b	(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:

7.0ms	(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))

series275.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
38.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
33.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
36.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify65.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5122	727

prune91.0ms

Filtered

38 candidates to 44 candidates (-15.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	42	2	44
Fresh	1	11	12
Picked	1	0	1
Done	0	1	1
Total	44	14	58

Merged error: 0.2b

Counts

58 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.7b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.7b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
3.6b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite18.0ms

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))

series416.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
134.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
129.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
36.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify88.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5874	701

prune78.0ms

Filtered

45 candidates to 52 candidates (-15.6%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	51	15	66

Merged error: 0.2b

Counts

66 → 15

regimes139.0ms

Accuracy

97.7% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.1b

bsearch78.0ms

Steps

Iters	Range		Point
10	2.518735553339976e-17	7.089942304529777	1.3174945297258676e-05
9	-32843.83719080005	-0.05167114385671851	-0.052261623524808724

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	83	81
1	83	81

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.3s	2084×	body	2048	valid
1.2s	3866×	body	1024	valid
255.0ms	1332×	body	512	valid
60.0ms	473×	body	256	valid
15.0ms	244×	body	128	valid
2.0ms	1×	body	4096	valid

Details

analyze2.0ms

sample102.0ms

simplify11.0ms

prune1.0ms

localize8.0ms

rewrite12.0ms

series97.0ms

simplify37.0ms

prune37.0ms

localize13.0ms

rewrite30.0ms

series152.0ms

simplify69.0ms

prune65.0ms

localize18.0ms

rewrite34.0ms

series275.0ms

simplify65.0ms

prune91.0ms

localize18.0ms

rewrite18.0ms

series416.0ms

simplify88.0ms

prune78.0ms

regimes139.0ms

bsearch78.0ms

simplify3.0ms

end0.0ms

sample3.0s

Profiling