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

sample235.0ms

Algorithm

intervals

Results

70.0ms	115×	body	1280	valid
40.0ms	34×	body	1280	nan
26.0ms	57×	body	640	valid
21.0ms	27×	body	640	nan
19.0ms	97×	body	80	overflowed
8.0ms	21×	body	320	valid
7.0ms	13×	body	320	nan
6.0ms	4×	body	1280	invalid
6.0ms	8×	body	640	invalid
5.0ms	51×	body	80	valid
4.0ms	19×	body	80	nan
3.0ms	9×	body	160	nan
2.0ms	12×	body	160	valid
2.0ms	3×	body	320	invalid
1.0ms	4×	body	160	invalid
0.0ms	4×	body	80	invalid

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4977	13
1	4977	13

prune3.0ms

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: 34.4b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow.f64 x (/.f64 1.0 n))
2.4b	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
13×	`pow-unpow_binary64` `unpow-prod-down_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×	`add-cbrt-cube_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `pow-pow_binary64` `div-inv_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

2 → 50

Calls

2 calls:

4.0ms	(pow.f64 x (/.f64 1.0 n))
10.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))

series62.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(pow.f64 x (/.f64 1.0 n))
49.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))

simplify54.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4977	893
1	4977	893

prune234.0ms

Filtered

46 candidates to 56 candidates (-21.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	51	5	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	5	57

Merged error: 22.7b

Counts

57 → 5

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow.f64 x (/.f64 1.0 n))
2.4b	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))))
2.4b	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
23×	`unpow-prod-down_binary64`
18×	`difference-of-squares_binary64`
16×	`log-pow_binary64`
15×	`exp-prod_binary64`
13×	`pow-unpow_binary64` `add-cube-cbrt_binary64` `sqr-pow_binary64`
9×	`times-frac_binary64`
6×	`distribute-lft-out--_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
4×	`log-prod_binary64` `add-exp-log_binary64`
3×	`add-cbrt-cube_binary64`
2×	`sub-neg_binary64` `distribute-lft-out_binary64`
1×	`pow-to-exp_binary64` `flip3--_binary64` `diff-log_binary64` `rem-log-exp_binary64` `pow-pow_binary64` `exp-diff_binary64` `exp-sum_binary64` `div-inv_binary64` `log-div_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

3 → 79

Calls

3 calls:

4.0ms	(pow.f64 x (/.f64 1.0 n))
12.0ms	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))))
11.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))

series105.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(pow.f64 x (/.f64 1.0 n))
45.0ms	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))))
47.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))

simplify46.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5048	1409

prune146.0ms

Filtered

71 candidates to 88 candidates (-23.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	87	6	93

Merged error: 22.6b

Counts

93 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (pow.f64 (sqrt.f64 x) (/.f64 1.0 n)) (pow.f64 (sqrt.f64 x) (/.f64 1.0 n)))
0.0b	(pow.f64 (sqrt.f64 x) (/.f64 1.0 n))
0.0b	(pow.f64 (sqrt.f64 x) (/.f64 1.0 n))
3.9b	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (*.f64 (pow.f64 (sqrt.f64 x) (/.f64 1.0 n)) (pow.f64 (sqrt.f64 x) (/.f64 1.0 n))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt_binary64`
57×	`unpow-prod-down_binary64`
34×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
28×	`sqrt-prod_binary64`
26×	`pow-unpow_binary64`
18×	`add-exp-log_binary64` `times-frac_binary64`
16×	`unswap-sqr_binary64`
15×	`sqr-pow_binary64`
12×	`swap-sqr_binary64`
10×	`associate-r_binary64` `associate-l_binary64`
9×	`prod-exp_binary64`
8×	`pow-to-exp_binary64` `pow1_binary64` `pow-exp_binary64`
6×	`add-log-exp_binary64` `pow-pow_binary64` `add-cbrt-cube_binary64`
3×	`difference-of-squares_binary64`
2×	`pow1/2_binary64` `sqrt-pow2_binary64` `sqrt-pow1_binary64` `div-inv_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `pow-sqr_binary64` `flip--_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 150

Calls

4 calls:

10.0ms	(*.f64 (pow.f64 (sqrt.f64 x) (/.f64 1.0 n)) (pow.f64 (sqrt.f64 x) (/.f64 1.0 n)))
5.0ms	(pow.f64 (sqrt.f64 x) (/.f64 1.0 n))
5.0ms	(pow.f64 (sqrt.f64 x) (/.f64 1.0 n))
8.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (*.f64 (pow.f64 (sqrt.f64 x) (/.f64 1.0 n)) (pow.f64 (sqrt.f64 x) (/.f64 1.0 n))))

series226.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(*.f64 (pow.f64 (sqrt.f64 x) (/.f64 1.0 n)) (pow.f64 (sqrt.f64 x) (/.f64 1.0 n)))
31.0ms	(pow.f64 (sqrt.f64 x) (/.f64 1.0 n))
31.0ms	(pow.f64 (sqrt.f64 x) (/.f64 1.0 n))
108.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (*.f64 (pow.f64 (sqrt.f64 x) (/.f64 1.0 n)) (pow.f64 (sqrt.f64 x) (/.f64 1.0 n))))

simplify63.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4954	2118
1	4954	2118

prune156.0ms

Filtered

103 candidates to 162 candidates (-57.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	162	6	168

Merged error: 22.6b

Counts

168 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

2.4b	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))
2.4b	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))
2.5b	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n))))))
2.5b	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n))))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
20×	`unpow-prod-down_binary64`
18×	`difference-of-squares_binary64`
14×	`log-prod_binary64`
12×	`sqr-pow_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `cbrt-prod_binary64`
6×	`pow1_binary64` `add-exp-log_binary64` `distribute-lft-out--_binary64`
4×	`sub-neg_binary64` `log-pow_binary64` `add-cbrt-cube_binary64`
2×	`cbrt-div_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `rem-log-exp_binary64` `pow1/3_binary64` `exp-diff_binary64` `exp-sum_binary64` `log-div_binary64` `flip--_binary64`

Counts

4 → 82

Calls

4 calls:

11.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))
11.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))
13.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n))))))
11.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n))))))

series372.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))
46.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))
129.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n))))))
153.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n))))))

simplify100.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4934	1996
1	4934	1996

prune187.0ms

Filtered

82 candidates to 94 candidates (-14.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	89	5	94
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	90	10	100

Merged error: 22.2b

Counts

100 → 10

regimes380.0ms

Accuracy

77.5% (2.5b remaining)

Error of 24.2b against oracle of 21.6b and baseline of 32.9b

bsearch1.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	208	89
1	208	89

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.2s	3816×	body	1280	valid
1.3s	1191×	body	1280	nan
738.0ms	1618×	body	640	valid
678.0ms	962×	body	640	nan
503.0ms	2793×	body	80	overflowed
205.0ms	654×	body	320	valid
188.0ms	436×	body	320	nan
175.0ms	253×	body	640	invalid
144.0ms	113×	body	1280	invalid
141.0ms	1589×	body	80	valid
73.0ms	178×	body	320	invalid
63.0ms	323×	body	160	valid
56.0ms	233×	body	160	nan
35.0ms	252×	body	80	invalid
31.0ms	504×	body	80	nan
20.0ms	82×	body	160	invalid

Details

analyze1.1s

sample235.0ms

simplify57.0ms

prune3.0ms

localize8.0ms

rewrite16.0ms

series62.0ms

simplify54.0ms

prune234.0ms

localize10.0ms

rewrite30.0ms

series105.0ms

simplify46.0ms

prune146.0ms

localize10.0ms

rewrite35.0ms

series226.0ms

simplify63.0ms

prune156.0ms

localize14.0ms

rewrite48.0ms

series372.0ms

simplify100.0ms

prune187.0ms

regimes380.0ms

bsearch1.0ms

simplify4.0ms

end0.0ms

sample6.9s

Profiling