Details

analyze1.3s

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
25%	62.4%	12.6%	5
25%	56.2%	18.8%	6
28.1%	50%	22%	7
28.1%	46.8%	25.1%	8
29.7%	41.4%	29%	9
29.7%	39.4%	30.9%	10
31.1%	35.8%	33.1%	11
31.1%	34.4%	34.5%	12
31.5%	32.9%	35.6%	13
31.5%	32.1%	36.4%	14

sample231.0ms

Algorithm

intervals

Results

69.0ms	110×	body	1280	valid
46.0ms	32×	body	1280	nan
25.0ms	52×	body	640	valid
17.0ms	21×	body	640	nan
17.0ms	83×	body	80	overflowed
9.0ms	25×	body	320	valid
8.0ms	17×	body	320	nan
6.0ms	56×	body	80	valid
5.0ms	10×	body	320	invalid
4.0ms	4×	body	640	invalid
3.0ms	2×	body	1280	invalid
3.0ms	13×	body	160	valid
2.0ms	7×	body	160	nan
2.0ms	20×	body	80	nan
0.0ms	2×	body	160	invalid
0.0ms	2×	body	80	invalid

simplify83.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5194	19

prune4.0ms

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: 31.0b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow.f64 x (/.f64 1 n))
0.1b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
2.4b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
26×	`pow-unpow_binary64`
19×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
17×	`unpow-prod-down_binary64`
9×	`difference-of-squares_binary64`
8×	`sqr-pow_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64`
3×	`add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
2×	`pow-to-exp_binary64` `distribute-lft-out_binary64` `pow-pow_binary64` `div-inv_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64`

Counts

3 → 78

Calls

3 calls:

3.0ms	(pow.f64 x (/.f64 1 n))
6.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
10.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

series229.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(pow.f64 x (/.f64 1 n))
57.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
130.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

simplify86.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4928	1611
1	4928	1611

prune94.0ms

Filtered

65 candidates to 87 candidates (-33.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	81	6	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	6	88

Merged error: 21.4b

Counts

88 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 x (/.f64 1/2 n)) (pow.f64 (+.f64 x 1) (/.f64 1/2 n)))
0.0b	(pow.f64 (+.f64 x 1) (/.f64 1/2 n))
0.0b	(pow.f64 (+.f64 x 1) (/.f64 1/2 n))
2.4b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
32×	`add-sqr-sqrt_binary64`
26×	`pow-unpow_binary64`
22×	`unpow-prod-down_binary64`
20×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
9×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64` `sqr-pow_binary64`
7×	`distribute-lft-out_binary64`
6×	`pow1_binary64` `add-exp-log_binary64`
4×	`add-cbrt-cube_binary64`
3×	`distribute-lft-out--_binary64`
2×	`pow-to-exp_binary64` `pow-pow_binary64` `div-inv_binary64` `pow-exp_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 93

Calls

4 calls:

9.0ms	(+.f64 (pow.f64 x (/.f64 1/2 n)) (pow.f64 (+.f64 x 1) (/.f64 1/2 n)))
6.0ms	(pow.f64 (+.f64 x 1) (/.f64 1/2 n))
6.0ms	(pow.f64 (+.f64 x 1) (/.f64 1/2 n))
12.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n)))

series391.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(+.f64 (pow.f64 x (/.f64 1/2 n)) (pow.f64 (+.f64 x 1) (/.f64 1/2 n)))
62.0ms	(pow.f64 (+.f64 x 1) (/.f64 1/2 n))
61.0ms	(pow.f64 (+.f64 x 1) (/.f64 1/2 n))
162.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n)))

simplify73.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5012	2157

prune187.0ms

Filtered

86 candidates to 105 candidates (-22.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	105	6	111

Merged error: 21.4b

Counts

111 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n))))
0.7b	(cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n))))
0.7b	(cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n))))
2.4b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
22×	`unpow-prod-down_binary64`
19×	`add-sqr-sqrt_binary64`
18×	`cbrt-prod_binary64`
13×	`distribute-lft-out_binary64`
9×	`difference-of-squares_binary64`
7×	`add-cube-cbrt_binary64`
6×	`cbrt-div_binary64` `add-log-exp_binary64` `sqr-pow_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `pow1/3_binary64` `distribute-lft-out--_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64`

Counts

4 → 71

Calls

4 calls:

11.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n))))
11.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n))))
10.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n))))
12.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n)))

series1.4s

Counts

4 → 12

Calls

4 calls:

377.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n))))
465.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n))))
369.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n))))
150.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n)))

simplify117.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5037	2608

prune311.0ms

Filtered

68 candidates to 83 candidates (-22.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	81	8	89

Merged error: 21.4b

Counts

89 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n))))
0.7b	(cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n))))
0.7b	(cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n))))
2.4b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
22×	`unpow-prod-down_binary64`
19×	`add-sqr-sqrt_binary64`
18×	`cbrt-prod_binary64`
13×	`distribute-lft-out_binary64`
9×	`difference-of-squares_binary64`
7×	`add-cube-cbrt_binary64`
6×	`cbrt-div_binary64` `add-log-exp_binary64` `sqr-pow_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `pow1/3_binary64` `distribute-lft-out--_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64`

Counts

4 → 71

Calls

4 calls:

19.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n))))
18.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n))))
10.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n))))
11.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n)))

series1.4s

Counts

4 → 12

Calls

4 calls:

412.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n))))
424.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n))))
409.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n))))
154.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n)))

simplify110.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5037	2608

prune381.0ms

Filtered

68 candidates to 83 candidates (-22.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	83	8	91

Merged error: 21.4b

Counts

91 → 8

regimes184.0ms

Accuracy

83.2% (1.7b remaining)

Error of 24.1b against oracle of 22.4b and baseline of 32.6b

bsearch1.0ms

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	118	121
1	118	121

end0.0ms

sample7.3s

Algorithm

intervals

Results

2.3s	3711×	body	1280	valid
1.3s	1029×	body	1280	nan
794.0ms	1601×	body	640	valid
710.0ms	892×	body	640	nan
539.0ms	2666×	body	80	overflowed
256.0ms	713×	body	320	valid
243.0ms	489×	body	320	nan
202.0ms	263×	body	640	invalid
163.0ms	1620×	body	80	valid
145.0ms	96×	body	1280	invalid
93.0ms	193×	body	320	invalid
76.0ms	355×	body	160	valid
65.0ms	242×	body	160	nan
39.0ms	527×	body	80	nan
33.0ms	235×	body	80	invalid
24.0ms	88×	body	160	invalid

Details

analyze1.3s

sample231.0ms

simplify83.0ms

prune4.0ms

localize9.0ms

rewrite22.0ms

series229.0ms

simplify86.0ms

prune94.0ms

localize11.0ms

rewrite36.0ms

series391.0ms

simplify73.0ms

prune187.0ms

localize18.0ms

rewrite49.0ms

series1.4s

simplify117.0ms

prune311.0ms

localize19.0ms

rewrite62.0ms

series1.4s

simplify110.0ms

prune381.0ms

regimes184.0ms

bsearch1.0ms

simplify5.0ms

end0.0ms

sample7.3s

Profiling