Details

analyze1.1s (9.4%)

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)

sample226.0ms (1.9%)

Algorithm

1×

intervals

Results

45.0ms	53×	body	1024	nan
40.0ms	81×	body	1024	valid
34.0ms	50×	body	2048	valid
23.0ms	37×	body	512	nan
17.0ms	93×	body	128	overflowed
14.0ms	40×	body	512	valid
8.0ms	8×	body	1024	invalid
8.0ms	14×	body	512	invalid
6.0ms	64×	body	128	valid
5.0ms	21×	body	256	valid
3.0ms	13×	body	256	nan
3.0ms	35×	body	128	nan
1.0ms	5×	body	256	invalid
1.0ms	9×	body	128	invalid

Compiler

Compiled 27 to 25 computations (7.4% saved)

simplify217.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5176	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: 32.8b

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 x (/.f64 1 n))
0.1b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
1.5b	(-.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

31×	`add-sqr-sqrt_binary64_435`
28×	`*-un-lft-identity_binary64_414`
26×	`pow-unpow_binary64_488`
19×	`add-cube-cbrt_binary64_446`
18×	`times-frac_binary64_420`
17×	`unpow-prod-down_binary64_490`
9×	`difference-of-squares_binary64_383`
8×	`sqr-pow_binary64_386`
5×	`pow1_binary64_472` `add-exp-log_binary64_449` `add-log-exp_binary64_450`
3×	`distribute-lft-out--_binary64_368` `add-cbrt-cube_binary64_447`
2×	`div-inv_binary64_411` `pow-pow_binary64_483` `pow-exp_binary64_479` `pow-to-exp_binary64_480` `distribute-lft-out_binary64_367`
1×	`flip3--_binary64_418` `diff-log_binary64_503` `sub-neg_binary64_407` `flip--_binary64_389`

Counts

3 → 78

Calls

3 calls:

11.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
9.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
4.0ms	(pow.f64 x (/.f64 1 n))

series448.0ms (3.9%)

Counts

3 → 9

Calls

3 calls:

261.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
97.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
90.0ms	(pow.f64 x (/.f64 1 n))

simplify91.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4925	1618
1	4925	1618

prune120.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	82	5	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	5	88

Merged error: 23.6b

Counts

88 → 5

Compiler

Compiled 1902 to 1314 computations (30.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
2.7b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (.f64 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 1 n)) (pow.f64 (cbrt.f64 x) (/.f64 1 n))))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64_442`
7×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414` `add-sqr-sqrt_binary64_435`
6×	`add-log-exp_binary64_450`
4×	`pow1_binary64_472` `add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
3×	`pow1/3_binary64_493`
1×	`flip3--_binary64_418` `diff-log_binary64_503` `sub-neg_binary64_407` `flip--_binary64_389`

Counts

4 → 44

Calls

4 calls:

8.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (.f64 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 1 n)) (pow.f64 (cbrt.f64 x) (/.f64 1 n))))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series1.0s (8.6%)

Counts

4 → 12

Calls

4 calls:

561.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (.f64 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 1 n)) (pow.f64 (cbrt.f64 x) (/.f64 1 n))))
149.0ms	(cbrt.f64 x)
146.0ms	(cbrt.f64 x)
145.0ms	(cbrt.f64 x)

simplify57.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4920	1083
1	4920	1083

prune91.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	55	6	61

Merged error: 23.3b

Counts

61 → 6

Compiler

Compiled 1930 to 1181 computations (38.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
8.6b	(log.f64 (exp.f64 (cbrt.f64 x)))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64_442`
10×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414` `add-sqr-sqrt_binary64_435`
7×	`log-pow_binary64_500`
6×	`exp-prod_binary64_463`
5×	`pow1_binary64_472`
4×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447` `add-log-exp_binary64_450`
3×	`log-prod_binary64_497` `pow1/3_binary64_493`
1×	`rem-log-exp_binary64_452`

Counts

4 → 51

Calls

4 calls:

3.0ms	(log.f64 (exp.f64 (cbrt.f64 x)))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series762.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

299.0ms	(log.f64 (exp.f64 (cbrt.f64 x)))
172.0ms	(cbrt.f64 x)
147.0ms	(cbrt.f64 x)
143.0ms	(cbrt.f64 x)

simplify69.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4996	387
1	4996	387

prune84.0ms (0.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	63	6	69

Merged error: 23.3b

Counts

69 → 6

Compiler

Compiled 1973 to 1090 computations (44.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1 (*.f64 x n))
1.1b	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
2.8b	(-.f64 (/.f64 1 (.f64 x n)) (/.f64 1/2 (.f64 x (*.f64 x n))))
8.5b	(.f64 x (.f64 n n))

rewrite37.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-exp-log_binary64_449`
23×	`add-cbrt-cube_binary64_447`
14×	`pow1_binary64_472` `*-un-lft-identity_binary64_414`
12×	`add-sqr-sqrt_binary64_435`
9×	`times-frac_binary64_420` `add-cube-cbrt_binary64_446` `prod-exp_binary64_460`
7×	`associate-/l*_binary64_361` `cbrt-unprod_binary64_444` `div-exp_binary64_462`
6×	`add-log-exp_binary64_450`
5×	`cbrt-undiv_binary64_445`
4×	`pow-prod-down_binary64_482`
3×	`distribute-lft-out--_binary64_368` `div-inv_binary64_411` `associate-l_binary64_357`
2×	`1-exp_binary64_455` `clear-num_binary64_413` `log-pow_binary64_500` `pow-flip_binary64_485` `rec-exp_binary64_461` `frac-2neg_binary64_425` `associate-/r*_binary64_360`
1×	`flip3--_binary64_418` `difference-of-squares_binary64_383` `inv-pow_binary64_496` `diff-log_binary64_503` `-commutative_binary64_347` `frac-sub_binary64_423` `sub-neg_binary64_407` `associate-r*_binary64_356` `flip--_binary64_389` `unswap-sqr_binary64_382`

Counts

4 → 88

Calls

4 calls:

11.0ms	(-.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))
5.0ms	(/.f64 1 (*.f64 x n))

series200.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

81.0ms	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
56.0ms	(-.f64 (/.f64 1 (.f64 x n)) (/.f64 1/2 (.f64 x (*.f64 x n))))
44.0ms	(.f64 x (.f64 n n))
18.0ms	(/.f64 1 (*.f64 x n))

simplify57.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5277	1324

prune97.0ms (0.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	94	6	100
Fresh	0	3	3
Picked	1	0	1
Done	1	1	2
Total	96	10	106

Merged error: 23.0b

Counts

106 → 10

Compiler

Compiled 2572 to 868 computations (66.3% saved)

regimes270.0ms (2.3%)

Compiler: Compiled 961 to 673 computations (30% 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	97	132
1	97	132

end0.0ms (0%)

sample6.6s (56.6%)

Algorithm

1×

intervals

Results

1.4s	2657×	body	1024	valid
1.2s	1408×	body	1024	nan
1.2s	1752×	body	2048	valid
477.0ms	2576×	body	128	overflowed
414.0ms	1161×	body	512	valid
379.0ms	730×	body	512	nan
182.0ms	1850×	body	128	valid
181.0ms	194×	body	1024	invalid
128.0ms	240×	body	512	invalid
121.0ms	580×	body	256	valid
91.0ms	371×	body	256	nan
58.0ms	782×	body	128	nan
38.0ms	268×	body	128	invalid
34.0ms	127×	body	256	invalid
8.0ms	6×	body	2048	nan

Compiler

Compiled 418 to 295 computations (29.4% saved)

Details

analyze1.1s (9.4%)

sample226.0ms (1.9%)

simplify217.0ms (1.9%)

prune3.0ms (0%)

localize8.0ms (0.1%)

rewrite31.0ms (0.3%)

series448.0ms (3.9%)

simplify91.0ms (0.8%)

prune120.0ms (1%)

localize14.0ms (0.1%)

rewrite16.0ms (0.1%)

series1.0s (8.6%)

simplify57.0ms (0.5%)

prune91.0ms (0.8%)

localize16.0ms (0.1%)

rewrite11.0ms (0.1%)

series762.0ms (6.6%)

simplify69.0ms (0.6%)

prune84.0ms (0.7%)

localize13.0ms (0.1%)

rewrite37.0ms (0.3%)

series200.0ms (1.7%)

simplify57.0ms (0.5%)

prune97.0ms (0.8%)

regimes270.0ms (2.3%)

bsearch2.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample6.6s (56.6%)

Profiling