Details

analyze327.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	68.7%	12.6%	6
28.1%	59.3%	12.6%	7
32.8%	48.4%	18.8%	8
38.2%	42.9%	18.8%	9
41%	37.1%	22%	10
43.9%	34.1%	22%	11
45.5%	31%	23.5%	12
46.9%	29.6%	23.5%	13
47.7%	28%	24.3%	14

sample45.0ms

Algorithm

intervals

Results

22.0ms	101×	body	5120	exit
7.0ms	197×	body	80	valid
3.0ms	27×	body	320	valid
2.0ms	10×	body	640	valid
2.0ms	22×	body	160	valid
0.0ms	2×	body	80	overflowed

simplify75.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	6196	12

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 13.1b

Counts

2 → 2

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (exp.f64 wj))
0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
6.1b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity_binary64`
48×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
9×	`associate-/l*_binary64`
8×	`distribute-lft-out_binary64`
7×	`associate-/r*_binary64` `add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
5×	`add-log-exp_binary64` `distribute-lft-out--_binary64`
3×	`pow1_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`
1×	`associate-+r-_binary64` `flip3--_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

3 → 91

Calls

3 calls:

5.0ms	(/.f64 x (exp.f64 wj))
12.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
22.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

series28.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(/.f64 x (exp.f64 wj))
10.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
10.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

simplify57.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5860	1345

prune68.0ms

Filtered

73 candidates to 100 candidates (-37.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	97	3	100
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	99	3	102

Merged error: 0.4b

Counts

102 → 3

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(.f64 wj (+.f64 wj (.f64 x -2)))
0.0b	(+.f64 x (.f64 wj (+.f64 wj (.f64 x -2))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `associate-*r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip-+_binary64` `associate-+r+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

2 → 35

Calls

2 calls:

6.0ms	(.f64 wj (+.f64 wj (.f64 x -2)))
4.0ms	(+.f64 x (.f64 wj (+.f64 wj (.f64 x -2))))

series14.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(.f64 wj (+.f64 wj (.f64 x -2)))
7.0ms	(+.f64 x (.f64 wj (+.f64 wj (.f64 x -2))))

simplify56.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4935	405
1	4935	405

prune29.0ms

Filtered

28 candidates to 41 candidates (-46.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	38	3	41
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	38	6	44

Merged error: 0.4b

Counts

44 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(.f64 (cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2)))) (cbrt.f64 (.f64 wj (+.f64 wj (*.f64 x -2)))))
11.4b	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
11.4b	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
11.4b	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-*r/_binary64`
18×	`cbrt-div_binary64`
11×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`flip3-+_binary64` `pow1/3_binary64` `flip-+_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`cbrt-prod_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `add-cbrt-cube_binary64` `associate-l_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64` `associate-*l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 72

Calls

4 calls:

7.0ms	(.f64 (cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2)))) (cbrt.f64 (.f64 wj (+.f64 wj (*.f64 x -2)))))
4.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
5.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
4.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))

series200.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(.f64 (cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2)))) (cbrt.f64 (.f64 wj (+.f64 wj (*.f64 x -2)))))
47.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
45.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
48.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))

simplify40.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5296	991

prune82.0ms

Filtered

67 candidates to 84 candidates (-25.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	81	3	84
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	83	7	90

Merged error: 0.4b

Counts

90 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(pow.f64 (cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2)))) 6)
11.4b	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
11.4b	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
28.6b	(pow.f64 (pow.f64 (cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2)))) 6) 1/3)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

16×	`unpow-prod-down_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
7×	`add-exp-log_binary64`
6×	`pow-unpow_binary64`
5×	`pow1_binary64` `pow-exp_binary64`
4×	`cbrt-div_binary64` `add-log-exp_binary64` `associate-*r/_binary64` `add-cbrt-cube_binary64` `cbrt-prod_binary64`
3×	`pow-to-exp_binary64` `pow1/3_binary64` `pow-pow_binary64` `sqr-pow_binary64`
2×	`flip3-+_binary64` `flip-+_binary64`
1×	`unpow1/3_binary64`

Counts

4 → 66

Calls

4 calls:

4.0ms	(pow.f64 (cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2)))) 6)
4.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
4.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
5.0ms	(pow.f64 (pow.f64 (cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2)))) 6) 1/3)

series291.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(pow.f64 (cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2)))) 6)
46.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
48.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
115.0ms	(pow.f64 (pow.f64 (cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2)))) 6) 1/3)

simplify46.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4957	849
1	4957	849

prune64.0ms

Filtered

61 candidates to 78 candidates (-27.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	79	6	85

Merged error: 0.4b

Counts

85 → 6

regimes66.0ms

Accuracy

68.2% (0.6b remaining)

Error of 0.9b against oracle of 0.3b and baseline of 2.1b

bsearch15.0ms

Steps

Iters	Range		Point
8	1.9788722064013258e-11	1.844272894626153e-08	7.616267884561549e-09

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	26
1	34	26

end0.0ms

sample1.5s

Algorithm

intervals

Results

877.0ms	3819×	body	5120	exit
222.0ms	6127×	body	80	valid
95.0ms	822×	body	320	valid
88.0ms	486×	body	640	valid
42.0ms	565×	body	160	valid
3.0ms	72×	body	80	invalid
0.0ms	13×	body	80	overflowed

Details

analyze327.0ms

sample45.0ms

simplify75.0ms

prune6.0ms

localize8.0ms

rewrite42.0ms

series28.0ms

simplify57.0ms

prune68.0ms

localize5.0ms

rewrite10.0ms

series14.0ms

simplify56.0ms

prune29.0ms

localize10.0ms

rewrite22.0ms

series200.0ms

simplify40.0ms

prune82.0ms

localize15.0ms

rewrite19.0ms

series291.0ms

simplify46.0ms

prune64.0ms

regimes66.0ms

bsearch15.0ms

simplify2.0ms

end0.0ms

sample1.5s

Profiling