Details

analyze1.1s

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

sample216.0ms

Algorithm

intervals

Results

51.0ms	53×	body	1024	nan
43.0ms	85×	body	1024	valid
38.0ms	52×	body	2048	valid
16.0ms	87×	body	128	overflowed
16.0ms	48×	body	512	valid
13.0ms	25×	body	512	nan
6.0ms	5×	body	1024	invalid
5.0ms	54×	body	128	valid
4.0ms	17×	body	256	valid
3.0ms	13×	body	256	nan
2.0ms	4×	body	512	invalid
2.0ms	22×	body	128	nan
1.0ms	11×	body	128	invalid
1.0ms	4×	body	256	invalid

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5193	19

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: 34.8b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
2.0b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
14×	`unpow-prod-down_binary64`
13×	`pow-unpow_binary64`
10×	`add-cube-cbrt_binary64`
9×	`difference-of-squares_binary64` `times-frac_binary64`
7×	`sqr-pow_binary64`
4×	`add-log-exp_binary64`
3×	`pow1_binary64` `add-exp-log_binary64` `distribute-lft-out--_binary64`
2×	`distribute-lft-out_binary64` `add-cbrt-cube_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `pow-pow_binary64` `div-inv_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

2 → 51

Calls

2 calls:

9.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
11.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

series359.0ms

Counts

2 → 6

Calls

2 calls:

102.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
256.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

simplify75.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4927	1244
1	4927	1244

prune68.0ms

Filtered

44 candidates to 57 candidates (-29.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	53	4	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	4	58

Merged error: 25.1b

Counts

58 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(/.f64 (log.f64 (+.f64 x 1)) n)
2.0b	(-.f64 (exp.f64 (/.f64 (log.f64 (+.f64 x 1)) n)) (pow.f64 x (/.f64 1 n)))
2.6b	(log.f64 (+.f64 x 1))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`pow1_binary64`
6×	`add-exp-log_binary64`
5×	`add-log-exp_binary64` `log-pow_binary64` `add-cbrt-cube_binary64`
4×	`log-prod_binary64` `associate-/l*_binary64` `log-div_binary64`
3×	`associate-/r*_binary64` `difference-of-squares_binary64`
2×	`flip3-+_binary64` `div-sub_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `sqr-pow_binary64` `clear-num_binary64` `unpow-prod-down_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64`

Counts

3 → 63

Calls

3 calls:

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

series380.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(/.f64 (log.f64 (+.f64 x 1)) n)
284.0ms	(-.f64 (exp.f64 (/.f64 (log.f64 (+.f64 x 1)) n)) (pow.f64 x (/.f64 1 n)))
22.0ms	(log.f64 (+.f64 x 1))

simplify63.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5323	1389

prune66.0ms

Filtered

53 candidates to 72 candidates (-35.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	72	4	76

Merged error: 24.4b

Counts

76 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
0.7b	(/.f64 1/2 (.f64 x (.f64 x n)))
2.8b	(-.f64 (/.f64 1 (.f64 x n)) (/.f64 1/2 (.f64 x (*.f64 x n))))
8.7b	(.f64 x (.f64 n n))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`
9×	`cbrt-unprod_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64` `times-frac_binary64`
7×	`associate-/l*_binary64`
6×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow-prod-down_binary64` `associate-l_binary64` `distribute-lft-out--_binary64` `div-inv_binary64`
2×	`associate-/r*_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-r_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `flip--_binary64` `frac-sub_binary64` `*-commutative_binary64`

Counts

4 → 83

Calls

4 calls:

10.0ms	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
6.0ms	(/.f64 1/2 (.f64 x (.f64 x n)))
11.0ms	(-.f64 (/.f64 1 (.f64 x n)) (/.f64 1/2 (.f64 x (*.f64 x n))))
6.0ms	(.f64 x (.f64 n n))

series202.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
26.0ms	(/.f64 1/2 (.f64 x (.f64 x n)))
46.0ms	(-.f64 (/.f64 1 (.f64 x n)) (/.f64 1/2 (.f64 x (*.f64 x n))))
44.0ms	(.f64 x (.f64 n n))

simplify57.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5294	1403

prune78.0ms

Filtered

58 candidates to 95 candidates (-63.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	89	6	95
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	90	9	99

Merged error: 24.1b

Counts

99 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (/.f64 1 x) (-.f64 (/.f64 1 n) (/.f64 1/2 (.f64 x n))))
0.3b	(/.f64 1/2 (*.f64 x n))
0.6b	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
8.7b	(.f64 x (.f64 n n))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
30×	`add-exp-log_binary64`
28×	`add-cbrt-cube_binary64`
22×	`*-un-lft-identity_binary64`
20×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
16×	`associate-l_binary64`
13×	`pow1_binary64`
10×	`prod-exp_binary64`
9×	`cbrt-unprod_binary64` `associate-r_binary64`
7×	`associate-/l*_binary64`
6×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `unswap-sqr_binary64` `div-inv_binary64`
3×	`associate-*r/_binary64` `difference-of-squares_binary64` `frac-times_binary64`
2×	`associate-/r_binary64` `sub-neg_binary64` `flip3--_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `frac-sub_binary64` `-commutative_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `rec-exp_binary64` `associate-*l/_binary64`

Counts

4 → 112

Calls

4 calls:

19.0ms	(.f64 (/.f64 1 x) (-.f64 (/.f64 1 n) (/.f64 1/2 (.f64 x n))))
5.0ms	(/.f64 1/2 (*.f64 x n))
8.0ms	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
6.0ms	(.f64 x (.f64 n n))

series217.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(.f64 (/.f64 1 x) (-.f64 (/.f64 1 n) (/.f64 1/2 (.f64 x n))))
24.0ms	(/.f64 1/2 (*.f64 x n))
86.0ms	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
46.0ms	(.f64 x (.f64 n n))

simplify62.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4969	1831
1	4969	1831

prune236.0ms

Filtered

81 candidates to 124 candidates (-53.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	119	5	124
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	123	10	133

Merged error: 24.1b

Counts

133 → 10

regimes74.0ms

Accuracy

91.8% (1.6b remaining)

Error of 23.1b against oracle of 21.5b and baseline of 40.6b

bsearch124.0ms

Steps

Iters	Range		Point
8	567954678.7997086	205180895787.0147	1919560313.2622035
9	-89960637460313.14	-184541.30259417772	-61669447.7829862

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	66	81
1	66	81

end0.0ms

sample6.5s

Algorithm

intervals

Results

1.5s	2740×	body	1024	valid
1.3s	1530×	body	1024	nan
1.2s	1759×	body	2048	valid
498.0ms	2633×	body	128	overflowed
425.0ms	1190×	body	512	valid
381.0ms	733×	body	512	nan
197.0ms	201×	body	1024	invalid
171.0ms	1759×	body	128	valid
118.0ms	231×	body	512	invalid
117.0ms	552×	body	256	valid
97.0ms	392×	body	256	nan
64.0ms	812×	body	128	nan
42.0ms	150×	body	256	invalid
36.0ms	258×	body	128	invalid
4.0ms	4×	body	2048	nan

Details

analyze1.1s

sample216.0ms

simplify68.0ms

prune1.0ms

localize8.0ms

rewrite24.0ms

series359.0ms

simplify75.0ms

prune68.0ms

localize10.0ms

rewrite25.0ms

series380.0ms

simplify63.0ms

prune66.0ms

localize13.0ms

rewrite40.0ms

series202.0ms

simplify57.0ms

prune78.0ms

localize15.0ms

rewrite51.0ms

series217.0ms

simplify62.0ms

prune236.0ms

regimes74.0ms

bsearch124.0ms

simplify3.0ms

end0.0ms

sample6.5s

Profiling