Details

analyze1.1s (10.7%)

Algorithm

1×

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

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample213.0ms (2.2%)

Algorithm

1×

intervals

Results

50.0ms	89×	body	1024	valid
44.0ms	55×	body	1024	nan
33.0ms	57×	body	2048	valid
18.0ms	98×	body	128	overflowed
14.0ms	31×	body	512	nan
12.0ms	34×	body	512	valid
8.0ms	16×	body	512	invalid
5.0ms	57×	body	128	valid
5.0ms	19×	body	256	valid
4.0ms	4×	body	1024	invalid
2.0ms	9×	body	256	nan
2.0ms	31×	body	128	nan
2.0ms	6×	body	256	invalid
1.0ms	5×	body	128	invalid

Compiler

Compiled 27 to 25 computations (7.4% saved)

simplify146.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4831	19
1	4831	19

prune2.0ms (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: 32.6b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

1.9b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_100`
13×	`unpow-prod-down_binary64_157`
10×	`*-un-lft-identity_binary64_78`
9×	`difference-of-squares_binary64_47`
7×	`sqr-pow_binary64_50` `cancel-sign-sub-inv_binary64_44`
3×	`add-log-exp_binary64_117` `add-cube-cbrt_binary64_113` `distribute-lft-out--_binary64_30`
1×	`add-cbrt-cube_binary64_114` `flip3--_binary64_82` `diff-log_binary64_170` `flip--_binary64_53` `add-exp-log_binary64_116` `distribute-lft-out_binary64_29` `sub-neg_binary64_71` `pow1_binary64_139`

Counts

1 → 30

Calls

1 calls:

11.0ms

(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

series139.0ms (1.4%)

Counts

1 → 3

Calls

1 calls:

139.0ms

(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

simplify40.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4917	911
1	4917	911

prune47.0ms (0.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	29	4	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	4	34

Merged error: 21.6b

Counts

34 → 4

Compiler

Compiled 840 to 594 computations (29.3% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b	(exp.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
1.9b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_100`
23×	`unpow-prod-down_binary64_157`
20×	`*-un-lft-identity_binary64_78`
18×	`difference-of-squares_binary64_47`
15×	`exp-sum_binary64_124` `log-prod_binary64_164`
13×	`sqr-pow_binary64_50`
7×	`cancel-sign-sub-inv_binary64_44`
6×	`add-cube-cbrt_binary64_113` `distribute-lft-out--_binary64_30`
4×	`add-log-exp_binary64_117` `exp-prod_binary64_130`
3×	`pow1_binary64_139`
2×	`add-cbrt-cube_binary64_114` `flip3--_binary64_82` `flip--_binary64_53` `exp-diff_binary64_126` `add-exp-log_binary64_116` `log-div_binary64_165` `distribute-lft-out_binary64_29`
1×	`diff-log_binary64_170` `rem-exp-log_binary64_118` `log-pow_binary64_167` `sub-neg_binary64_71`

Counts

2 → 59

Calls

2 calls:

13.0ms	(exp.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
12.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

series489.0ms (5%)

Counts

2 → 6

Calls

2 calls:

360.0ms	(exp.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
129.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

simplify60.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4964	1888
1	4964	1888

prune84.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	65	4	69

Merged error: 21.6b

Counts

69 → 4

Compiler

Compiled 1673 to 1201 computations (28.2% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(/.f64 1/2 (.f64 x (.f64 x n)))
1.2b	(/.f64 1 (*.f64 x n))
2.8b	(-.f64 (/.f64 1 (.f64 x n)) (/.f64 1/2 (.f64 x (*.f64 x n))))
7.0b	(.f64 x (.f64 n n))

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-exp-log_binary64_116`
23×	`add-cbrt-cube_binary64_114`
16×	`*-un-lft-identity_binary64_78`
14×	`add-sqr-sqrt_binary64_100`
12×	`pow1_binary64_139`
11×	`add-cube-cbrt_binary64_113` `times-frac_binary64_84`
9×	`prod-exp_binary64_127`
7×	`cbrt-unprod_binary64_111` `div-exp_binary64_129` `cancel-sign-sub-inv_binary64_44`
6×	`add-log-exp_binary64_117` `associate-/l*_binary64_23`
5×	`cbrt-undiv_binary64_112`
4×	`div-inv_binary64_75` `pow-prod-down_binary64_149`
3×	`associate-l_binary64_19` `distribute-lft-out--_binary64_30`
2×	`frac-2neg_binary64_89` `1-exp_binary64_122` `pow-flip_binary64_152` `rec-exp_binary64_128` `associate-/r*_binary64_22` `clear-num_binary64_77`
1×	`-commutative_binary64_9` `inv-pow_binary64_163` `frac-sub_binary64_87` `flip3--_binary64_82` `diff-log_binary64_170` `associate-r*_binary64_18` `flip--_binary64_53` `unswap-sqr_binary64_46` `difference-of-squares_binary64_47` `sub-neg_binary64_71`

Counts

4 → 93

Calls

4 calls:

12.0ms	(-.f64 (/.f64 1 (.f64 x n)) (/.f64 1/2 (.f64 x (*.f64 x n))))
6.0ms	(.f64 x (.f64 n n))
6.0ms	(/.f64 1/2 (.f64 x (.f64 x n)))
5.0ms	(/.f64 1 (*.f64 x n))

series77.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

26.0ms	(.f64 x (.f64 n n))
25.0ms	(-.f64 (/.f64 1 (.f64 x n)) (/.f64 1/2 (.f64 x (*.f64 x n))))
15.0ms	(/.f64 1/2 (.f64 x (.f64 x n)))
10.0ms	(/.f64 1 (*.f64 x n))

simplify73.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4962	1297
1	4962	1297

prune110.0ms (1.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	100	5	105
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	101	8	109

Merged error: 20.6b

Counts

109 → 8

Compiler

Compiled 2869 to 1055 computations (63.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
0.6b	(/.f64 1/2 (.f64 x (.f64 x n)))
2.8b	(-.f64 (/.f64 (/.f64 1 x) n) (/.f64 1/2 (.f64 x (.f64 x n))))
7.0b	(.f64 x (.f64 n n))

rewrite60.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
24×	`add-sqr-sqrt_binary64_100`
16×	`times-frac_binary64_84`
15×	`*-un-lft-identity_binary64_78`
11×	`add-cube-cbrt_binary64_113` `pow1_binary64_139`
9×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
7×	`associate-/l*_binary64_23` `cancel-sign-sub-inv_binary64_44`
6×	`add-log-exp_binary64_117` `cbrt-undiv_binary64_112` `div-exp_binary64_129`
4×	`div-inv_binary64_75` `difference-of-squares_binary64_47`
3×	`associate-l_binary64_19` `pow-prod-down_binary64_149`
2×	`distribute-lft-out--_binary64_30` `frac-2neg_binary64_89` `associate-/r*_binary64_22` `clear-num_binary64_77` `log-pow_binary64_167`
1×	`-commutative_binary64_9` `frac-sub_binary64_87` `flip3--_binary64_82` `diff-log_binary64_170` `associate-r*_binary64_18` `flip--_binary64_53` `unswap-sqr_binary64_46` `sub-neg_binary64_71`

Counts

4 → 92

Calls

4 calls:

32.0ms	(-.f64 (/.f64 (/.f64 1 x) n) (/.f64 1/2 (.f64 x (.f64 x n))))
7.0ms	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
6.0ms	(/.f64 1/2 (.f64 x (.f64 x n)))
6.0ms	(.f64 x (.f64 n n))

series114.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

48.0ms	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
26.0ms	(.f64 x (.f64 n n))
25.0ms	(-.f64 (/.f64 (/.f64 1 x) n) (/.f64 1/2 (.f64 x (.f64 x n))))
15.0ms	(/.f64 1/2 (.f64 x (.f64 x n)))

simplify71.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5028	1626

prune97.0ms (1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	103	9	112

Merged error: 20.6b

Counts

112 → 9

Compiler

Compiled 2748 to 1047 computations (61.9% saved)

regimes236.0ms (2.4%)

Compiler: Compiled 1774 to 1234 computations (30.4% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 4 computations (-33.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	83	141
1	83	141

end0.0ms (0%)

sample6.6s (67.1%)

Algorithm

1×

intervals

Results

1.5s	2623×	body	1024	valid
1.1s	1452×	body	1024	nan
1.1s	1886×	body	2048	valid
513.0ms	2711×	body	128	overflowed
442.0ms	1196×	body	512	valid
344.0ms	757×	body	512	nan
168.0ms	186×	body	1024	invalid
164.0ms	1705×	body	128	valid
134.0ms	590×	body	256	valid
115.0ms	232×	body	512	invalid
80.0ms	341×	body	256	nan
49.0ms	165×	body	256	invalid
49.0ms	756×	body	128	nan
35.0ms	265×	body	128	invalid
7.0ms	5×	body	2048	nan

Compiler

Compiled 534 to 374 computations (30% saved)

Details

analyze1.1s (10.7%)

sample213.0ms (2.2%)

simplify146.0ms (1.5%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite14.0ms (0.1%)

series139.0ms (1.4%)

simplify40.0ms (0.4%)

prune47.0ms (0.5%)

localize9.0ms (0.1%)

rewrite31.0ms (0.3%)

series489.0ms (5%)

simplify60.0ms (0.6%)

prune84.0ms (0.9%)

localize16.0ms (0.2%)

rewrite36.0ms (0.4%)

series77.0ms (0.8%)

simplify73.0ms (0.7%)

prune110.0ms (1.1%)

localize14.0ms (0.1%)

rewrite60.0ms (0.6%)

series114.0ms (1.2%)

simplify71.0ms (0.7%)

prune97.0ms (1%)

regimes236.0ms (2.4%)

bsearch1.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample6.6s (67.1%)

Profiling