Details

analyze1.0s (10.2%)

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)

sample196.0ms (1.9%)

Algorithm

1×

intervals

Results

49.0ms	88×	body	1024	valid
34.0ms	62×	body	2048	valid
31.0ms	43×	body	1024	nan
16.0ms	45×	body	512	valid
15.0ms	87×	body	128	overflowed
11.0ms	25×	body	512	nan
6.0ms	7×	body	1024	invalid
6.0ms	11×	body	512	invalid
5.0ms	51×	body	128	valid
2.0ms	10×	body	256	nan
2.0ms	10×	body	256	valid
2.0ms	29×	body	128	nan
2.0ms	6×	body	256	invalid
1.0ms	11×	body	128	invalid

Compiler

Compiled 27 to 25 computations (7.4% saved)

simplify141.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

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

Error

31.9b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

1.6b	(-.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)))

series135.0ms (1.3%)

Counts

1 → 3

Calls

1 calls:

135.0ms

(-.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 (28.0ms)

Iter	Nodes	Cost
0	4917	911
1	4917	911

prune50.0ms (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

Error

20.0b

Counts

34 → 4

Compiler

Compiled 840 to 594 computations (29.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b

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

1.6b

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

1.6b

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

rewrite49.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64_100`
39×	`unpow-prod-down_binary64_157`
33×	`*-un-lft-identity_binary64_78`
30×	`exp-prod_binary64_130`
27×	`difference-of-squares_binary64_47`
21×	`sqr-pow_binary64_50` `cancel-sign-sub-inv_binary64_44`
16×	`exp-sum_binary64_124` `log-pow_binary64_167`
12×	`add-cube-cbrt_binary64_113`
11×	`log-prod_binary64_164`
9×	`distribute-lft-out--_binary64_30`
8×	`add-log-exp_binary64_117`
4×	`pow1_binary64_139`
3×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `distribute-lft-out_binary64_29` `sub-neg_binary64_71`
2×	`diff-log_binary64_170` `rem-exp-log_binary64_118` `exp-diff_binary64_126`
1×	`flip3--_binary64_82` `flip--_binary64_53` `rem-log-exp_binary64_119` `log-div_binary64_165`

Counts

3 → 99

Calls

3 calls:

15.0ms

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

13.0ms

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

11.0ms

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

series574.0ms (5.6%)

Counts

3 → 9

Calls

3 calls:

251.0ms

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

193.0ms

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

130.0ms

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

simplify83.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5009	2511

prune134.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	108	4	112

Error

20.0b

Counts

112 → 4

Compiler

Compiled 2596 to 1859 computations (28.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(/.f64 1 (*.f64 x n))
1.0b	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
3.5b	(-.f64 (/.f64 1 (.f64 x n)) (/.f64 1/2 (.f64 x (*.f64 x n))))
7.4b	(.f64 x (.f64 n n))

rewrite39.0ms (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` `pow1_binary64_139`
12×	`times-frac_binary64_84`
11×	`add-cube-cbrt_binary64_113`
9×	`prod-exp_binary64_127`
7×	`cbrt-unprod_binary64_111` `div-exp_binary64_129` `associate-/l*_binary64_23` `cancel-sign-sub-inv_binary64_44`
6×	`add-log-exp_binary64_117`
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` `log-pow_binary64_167`
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 → 95

Calls

4 calls:

13.0ms	(-.f64 (/.f64 1 (.f64 x n)) (/.f64 1/2 (.f64 x (*.f64 x n))))
7.0ms	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
6.0ms	(.f64 x (.f64 n n))
4.0ms	(/.f64 1 (*.f64 x n))

series111.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

52.0ms	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
25.0ms	(-.f64 (/.f64 1 (.f64 x n)) (/.f64 1/2 (.f64 x (*.f64 x n))))
24.0ms	(.f64 x (.f64 n n))
10.0ms	(/.f64 1 (*.f64 x n))

simplify58.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5071	1392

prune110.0ms (1.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	103	4	107
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	103	8	111

Error

19.2b

Counts

111 → 8

Compiler

Compiled 2905 to 1038 computations (64.3% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1/2 (.f64 x (.f64 x n)))
1.0b	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
3.5b	(-.f64 (/.f64 (/.f64 1 x) n) (/.f64 1/2 (.f64 x (.f64 x n))))
7.4b	(.f64 x (.f64 n n))

rewrite54.0ms (0.5%)

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:

27.0ms	(-.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))

series111.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
24.0ms	(-.f64 (/.f64 (/.f64 1 x) n) (/.f64 1/2 (.f64 x (.f64 x n))))
24.0ms	(.f64 x (.f64 n n))
15.0ms	(/.f64 1/2 (.f64 x (.f64 x n)))

simplify74.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5028	1626

prune103.0ms (1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	101	3	104
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	102	10	112

Error

19.1b

Counts

112 → 10

Compiler

Compiled 2748 to 1047 computations (61.9% saved)

regimes400.0ms (3.9%)

Accuracy

Total 1.7b remaining (7.2%)

Threshold costs 0b (0%)

Compiler

Compiled 3129 to 2203 computations (29.6% saved)

bsearch2.0ms (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	88	162
1	88	162

end0.0ms (0%)

sample6.6s (65%)

Algorithm

1×

intervals

Results

1.5s	2631×	body	1024	valid
1.1s	1442×	body	1024	nan
1.0s	1767×	body	2048	valid
461.0ms	2524×	body	128	overflowed
428.0ms	1151×	body	512	valid
303.0ms	684×	body	512	nan
184.0ms	1879×	body	128	valid
175.0ms	203×	body	1024	invalid
129.0ms	572×	body	256	valid
102.0ms	210×	body	512	invalid
80.0ms	350×	body	256	nan
52.0ms	815×	body	128	nan
41.0ms	139×	body	256	invalid
39.0ms	307×	body	128	invalid
6.0ms	6×	body	2048	nan

Compiler

Compiled 858 to 602 computations (29.8% saved)

Details

analyze1.0s (10.2%)

sample196.0ms (1.9%)

simplify141.0ms (1.4%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite14.0ms (0.1%)

series135.0ms (1.3%)

simplify40.0ms (0.4%)

prune50.0ms (0.5%)

localize9.0ms (0.1%)

rewrite49.0ms (0.5%)

series574.0ms (5.6%)

simplify83.0ms (0.8%)

prune134.0ms (1.3%)

localize14.0ms (0.1%)

rewrite39.0ms (0.4%)

series111.0ms (1.1%)

simplify58.0ms (0.6%)

prune110.0ms (1.1%)

localize17.0ms (0.2%)

rewrite54.0ms (0.5%)

series111.0ms (1.1%)

simplify74.0ms (0.7%)

prune103.0ms (1%)

regimes400.0ms (3.9%)

bsearch2.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample6.6s (65%)

Profiling