Details

analyze2.0ms

Algorithm

Search

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

sample92.0ms

Algorithm

intervals

Results

36.0ms	129×	body	1024	valid
35.0ms	57×	body	2048	valid
12.0ms	48×	body	512	valid
1.0ms	13×	body	256	valid
1.0ms	9×	body	128	valid

simplify10.0ms

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: 40.2b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.7b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
2.6b	(cos.f64 (+.f64 x eps))

rewrite15.0ms

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:

8.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
5.0ms	(cos.f64 (+.f64 x eps))

series106.0ms

Counts

2 → 6

Calls

2 calls:

80.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
26.0ms	(cos.f64 (+.f64 x eps))

simplify36.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4955	429
1	4955	429

prune29.0ms

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: 0.3b

Counts

30 → 7

localize13.0ms

Local error

Found 3 expressions with local error:

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)))

2.6b

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64`
3×	`add-log-exp_binary64`
2×	`sin-mult_binary64` `*-commutative_binary64`
1×	`associate-*r/_binary64` `unswap-sqr_binary64`

Counts

3 → 45

Calls

3 calls:

15.0ms

(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))

16.0ms

(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))

9.0ms

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

series242.0ms

Counts

3 → 9

Calls

3 calls:

118.0ms

(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))

86.0ms

(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))

39.0ms

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

simplify78.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4909	1192
1	4909	1192

prune67.0ms

Filtered

42 candidates to 54 candidates (-28.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	46	8	54
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	48	13	61

Merged error: 0.3b

Counts

61 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
2.6b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.6b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.6b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite41.0ms

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:

8.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
9.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
11.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
9.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series279.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
34.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
38.0ms	(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

prune89.0ms

Filtered

38 candidates to 44 candidates (-15.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	0	11	11
Picked	1	0	1
Done	0	1	1
Total	44	13	57

Merged error: 0.3b

Counts

57 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

2.6b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
4.5b	(cbrt.f64 (.f64 (.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))) -2))
4.5b	(cbrt.f64 (.f64 (.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))) -2))
4.5b	(cbrt.f64 (.f64 (.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))) -2))

rewrite54.0ms

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` `associate-*l/_binary64`

Counts

4 → 37

Calls

4 calls:

9.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
13.0ms	(cbrt.f64 (.f64 (.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))) -2))
13.0ms	(cbrt.f64 (.f64 (.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))) -2))
13.0ms	(cbrt.f64 (.f64 (.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))) -2))

series1.0s

Counts

4 → 12

Calls

4 calls:

36.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
318.0ms	(cbrt.f64 (.f64 (.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))) -2))
332.0ms	(cbrt.f64 (.f64 (.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))) -2))
325.0ms	(cbrt.f64 (.f64 (.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))) -2))

simplify48.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4936	1328
1	4936	1328

prune111.0ms

Filtered

42 candidates to 49 candidates (-16.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	49	13	62

Merged error: 0.3b

Counts

62 → 13

regimes148.0ms

Accuracy

97.2% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 15.1b

bsearch62.0ms

Steps

Iters	Range		Point
10	8.84181087252949e-05	13836035.971103767	0.00026894651815447717
6	-5.513963221533067	-1.268645633089922	-1.2851287984984638

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	83	81
1	83	81

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.3s	2049×	body	2048	valid
1.1s	3841×	body	1024	valid
222.0ms	1321×	body	512	valid
58.0ms	509×	body	256	valid
16.0ms	277×	body	128	valid
5.0ms	3×	body	4096	valid

Details

analyze2.0ms

sample92.0ms

simplify10.0ms

prune1.0ms

localize8.0ms

rewrite15.0ms

series106.0ms

simplify36.0ms

prune29.0ms

localize13.0ms

rewrite43.0ms

series242.0ms

simplify78.0ms

prune67.0ms

localize16.0ms

rewrite41.0ms

series279.0ms

simplify65.0ms

prune89.0ms

localize19.0ms

rewrite54.0ms

series1.0s

simplify48.0ms

prune111.0ms

regimes148.0ms

bsearch62.0ms

simplify3.0ms

end0.0ms

sample2.9s

Profiling