Details

analyze1.1s (9.1%)

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)

sample211.0ms (1.8%)

Algorithm

1×

intervals

Results

45.0ms	52×	body	1024	nan
39.0ms	56×	body	2048	valid
38.0ms	79×	body	1024	valid
18.0ms	52×	body	512	valid
15.0ms	83×	body	128	overflowed
12.0ms	20×	body	512	nan
5.0ms	6×	body	1024	invalid
5.0ms	10×	body	512	invalid
5.0ms	50×	body	128	valid
4.0ms	19×	body	256	valid
4.0ms	17×	body	256	nan
3.0ms	30×	body	128	nan
1.0ms	1×	body	2048	nan
1.0ms	5×	body	256	invalid
1.0ms	6×	body	128	invalid

Compiler

Compiled 27 to 25 computations (7.4% saved)

simplify212.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4814	19
1	4814	19

prune3.0ms (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: 34.8b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_100`
30×	`*-un-lft-identity_binary64_78`
26×	`pow-unpow_binary64_155`
21×	`add-cube-cbrt_binary64_113`
20×	`unpow-prod-down_binary64_157`
18×	`times-frac_binary64_84`
9×	`sqr-pow_binary64_50` `difference-of-squares_binary64_47`
7×	`cancel-sign-sub-inv_binary64_44`
5×	`add-log-exp_binary64_117` `add-exp-log_binary64_116` `pow1_binary64_139`
3×	`add-cbrt-cube_binary64_114` `distribute-lft-out--_binary64_30`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `div-inv_binary64_75` `pow-pow_binary64_150` `distribute-lft-out_binary64_29`
1×	`flip3--_binary64_82` `diff-log_binary64_170` `flip--_binary64_53` `sub-neg_binary64_71`

Counts

3 → 85

Calls

3 calls:

12.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
7.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
4.0ms	(pow.f64 x (/.f64 1 n))

series454.0ms (3.8%)

Counts

3 → 9

Calls

3 calls:

262.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
105.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
86.0ms	(pow.f64 x (/.f64 1 n))

simplify96.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4899	1701
1	4899	1701

prune123.0ms (1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	90	4	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	4	95

Merged error: 21.7b

Counts

95 → 4

Compiler

Compiled 1974 to 1361 computations (31.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
0.0b	(exp.f64 (/.f64 (log.f64 x) n))
0.3b	(/.f64 (log.f64 x) n)
2.2b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))

rewrite37.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_100`
34×	`*-un-lft-identity_binary64_78`
33×	`times-frac_binary64_84`
30×	`add-cube-cbrt_binary64_113`
16×	`exp-prod_binary64_130`
13×	`pow-unpow_binary64_155`
12×	`pow1_binary64_139`
7×	`add-log-exp_binary64_117` `add-exp-log_binary64_116` `log-pow_binary64_167`
6×	`add-cbrt-cube_binary64_114`
5×	`unpow-prod-down_binary64_157`
4×	`div-inv_binary64_75` `associate-/l*_binary64_23`
3×	`associate-/r*_binary64_22` `difference-of-squares_binary64_47` `cancel-sign-sub-inv_binary64_44`
2×	`sqr-pow_binary64_50`
1×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `distribute-lft-out--_binary64_30` `flip3--_binary64_82` `diff-log_binary64_170` `rem-exp-log_binary64_118` `frac-2neg_binary64_89` `exp-to-pow_binary64_140` `pow-pow_binary64_150` `flip--_binary64_53` `clear-num_binary64_77` `distribute-lft-out_binary64_29` `sub-neg_binary64_71`

Counts

4 → 102

Calls

4 calls:

11.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))
7.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
5.0ms	(exp.f64 (/.f64 (log.f64 x) n))
4.0ms	(/.f64 (log.f64 x) n)

series529.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

276.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))
107.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
83.0ms	(exp.f64 (/.f64 (log.f64 x) n))
63.0ms	(/.f64 (log.f64 x) n)

simplify96.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4898	1754
1	4898	1754

prune112.0ms (0.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	113	5	118

Merged error: 21.7b

Counts

118 → 5

Compiler

Compiled 2324 to 1187 computations (48.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
0.0b	(exp.f64 (/.f64 (log.f64 x) n))
0.3b	(/.f64 (log.f64 x) n)
2.2b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))

rewrite38.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_100`
34×	`*-un-lft-identity_binary64_78`
33×	`times-frac_binary64_84`
30×	`add-cube-cbrt_binary64_113`
16×	`exp-prod_binary64_130`
13×	`pow-unpow_binary64_155`
12×	`pow1_binary64_139`
7×	`add-log-exp_binary64_117` `add-exp-log_binary64_116` `log-pow_binary64_167`
6×	`add-cbrt-cube_binary64_114`
5×	`unpow-prod-down_binary64_157`
4×	`div-inv_binary64_75` `associate-/l*_binary64_23`
3×	`associate-/r*_binary64_22` `difference-of-squares_binary64_47` `cancel-sign-sub-inv_binary64_44`
2×	`sqr-pow_binary64_50`
1×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `distribute-lft-out--_binary64_30` `flip3--_binary64_82` `diff-log_binary64_170` `rem-exp-log_binary64_118` `frac-2neg_binary64_89` `exp-to-pow_binary64_140` `pow-pow_binary64_150` `flip--_binary64_53` `clear-num_binary64_77` `distribute-lft-out_binary64_29` `sub-neg_binary64_71`

Counts

4 → 102

Calls

4 calls:

12.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))
7.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
5.0ms	(exp.f64 (/.f64 (log.f64 x) n))
4.0ms	(/.f64 (log.f64 x) n)

series503.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

263.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))
101.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
81.0ms	(exp.f64 (/.f64 (log.f64 x) n))
57.0ms	(/.f64 (log.f64 x) n)

simplify91.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4898	1754
1	4898	1754

prune136.0ms (1.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	111	8	119

Merged error: 21.7b

Counts

119 → 8

Compiler

Compiled 2747 to 1582 computations (42.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1 (*.f64 x n))
0.7b	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
2.0b	(-.f64 (/.f64 1 (.f64 x n)) (/.f64 1/2 (.f64 x (*.f64 x n))))
8.5b	(.f64 x (.f64 n n))

rewrite43.0ms (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))))
8.0ms	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
6.0ms	(.f64 x (.f64 n n))
5.0ms	(/.f64 1 (*.f64 x n))

series209.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

90.0ms	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
54.0ms	(-.f64 (/.f64 1 (.f64 x n)) (/.f64 1/2 (.f64 x (*.f64 x n))))
47.0ms	(.f64 x (.f64 n n))
18.0ms	(/.f64 1 (*.f64 x n))

simplify57.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4930	1417
1	4930	1417

prune108.0ms (0.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	102	5	107
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	103	12	115

Merged error: 21.4b

Counts

115 → 12

Compiler

Compiled 2739 to 924 computations (66.3% saved)

regimes428.0ms (3.6%)

Compiler: Compiled 3914 to 2836 computations (27.5% saved)

bsearch114.0ms (1%)

Steps

Iters	Range		Point
7	0.14960664165121668	8.621168846379732	8.437394065986364
8	-15431541351.58284	-1569999.7168058404	-124899201.97469188

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	73	125
1	73	125

end0.0ms (0%)

sample7.3s (60.3%)

Algorithm

1×

intervals

Results

1.4s	2635×	body	1024	valid
1.3s	1482×	body	1024	nan
1.2s	1707×	body	2048	valid
480.0ms	2570×	body	128	overflowed
434.0ms	1220×	body	512	valid
387.0ms	751×	body	512	nan
181.0ms	1885×	body	128	valid
166.0ms	174×	body	1024	invalid
128.0ms	252×	body	512	invalid
118.0ms	553×	body	256	valid
91.0ms	368×	body	256	nan
62.0ms	813×	body	128	nan
46.0ms	168×	body	256	invalid
37.0ms	260×	body	128	invalid
10.0ms	7×	body	2048	nan

Compiler

Compiled 1002 to 710 computations (29.1% saved)

Details

analyze1.1s (9.1%)

sample211.0ms (1.8%)

simplify212.0ms (1.8%)

prune3.0ms (0%)

localize8.0ms (0.1%)

rewrite32.0ms (0.3%)

series454.0ms (3.8%)

simplify96.0ms (0.8%)

prune123.0ms (1%)

localize11.0ms (0.1%)

rewrite37.0ms (0.3%)

series529.0ms (4.4%)

simplify96.0ms (0.8%)

prune112.0ms (0.9%)

localize15.0ms (0.1%)

rewrite38.0ms (0.3%)

series503.0ms (4.2%)

simplify91.0ms (0.8%)

prune136.0ms (1.1%)

localize14.0ms (0.1%)

rewrite43.0ms (0.4%)

series209.0ms (1.7%)

simplify57.0ms (0.5%)

prune108.0ms (0.9%)

regimes428.0ms (3.6%)

bsearch114.0ms (1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample7.3s (60.3%)

Profiling