Details

analyze1.4s (8.9%)

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)

sample313.0ms (2%)

Algorithm

1×

intervals

Results

66.0ms	90×	body	1024	valid
63.0ms	49×	body	1024	nan
59.0ms	53×	body	2048	valid
25.0ms	91×	body	128	overflowed
24.0ms	38×	body	512	nan
20.0ms	39×	body	512	valid
7.0ms	23×	body	256	valid
7.0ms	51×	body	128	valid
6.0ms	4×	body	1024	invalid
6.0ms	8×	body	512	invalid
4.0ms	7×	body	256	invalid
3.0ms	9×	body	256	nan
2.0ms	21×	body	128	nan
1.0ms	6×	body	128	invalid

Compiler

Compiled 27 to 25 computations (7.4% saved)

simplify263.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4814	19
1	4814	19

prune5.0ms (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: 34.1b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize16.0ms (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))
2.8b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite43.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_441`
30×	`*-un-lft-identity_binary64_419`
26×	`pow-unpow_binary64_496`
21×	`add-cube-cbrt_binary64_454`
20×	`unpow-prod-down_binary64_498`
18×	`times-frac_binary64_425`
9×	`difference-of-squares_binary64_388` `sqr-pow_binary64_391`
7×	`cancel-sign-sub-inv_binary64_385`
5×	`add-log-exp_binary64_458` `add-exp-log_binary64_457` `pow1_binary64_480`
3×	`distribute-lft-out--_binary64_371` `add-cbrt-cube_binary64_455`
2×	`div-inv_binary64_416` `pow-exp_binary64_487` `distribute-lft-out_binary64_370` `pow-to-exp_binary64_488` `pow-pow_binary64_491`
1×	`sub-neg_binary64_412` `flip3--_binary64_423` `diff-log_binary64_511` `flip--_binary64_394`

Counts

3 → 85

Calls

3 calls:

12.0ms	(-.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))

series532.0ms (3.3%)

Counts

3 → 9

Calls

3 calls:

279.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
139.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
113.0ms	(pow.f64 x (/.f64 1 n))

simplify107.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4899	1701
1	4899	1701

prune156.0ms (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: 22.8b

Counts

95 → 4

Compiler

Compiled 1959 to 1350 computations (31.1% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
0.0b	(pow.f64 x (/.f64 1 n))
0.0b	(pow.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) 3)
2.8b	(-.f64 (cbrt.f64 (pow.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) 3)) (pow.f64 x (/.f64 1 n)))

rewrite70.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`add-sqr-sqrt_binary64_441`
50×	`unpow-prod-down_binary64_498`
35×	`*-un-lft-identity_binary64_419`
29×	`pow-unpow_binary64_496`
27×	`difference-of-squares_binary64_388` `add-cube-cbrt_binary64_454`
24×	`cbrt-prod_binary64_450` `sqr-pow_binary64_391`
18×	`times-frac_binary64_425`
17×	`cube-prod_binary64_447`
8×	`add-exp-log_binary64_457`
7×	`cancel-sign-sub-inv_binary64_385`
6×	`add-log-exp_binary64_458` `pow-exp_binary64_487` `pow1_binary64_480`
5×	`add-cbrt-cube_binary64_455`
4×	`pow-to-exp_binary64_488`
3×	`distribute-lft-out_binary64_370` `pow-pow_binary64_491`
2×	`div-inv_binary64_416`
1×	`sub-neg_binary64_412` `unpow3_binary64_485` `cube-mult_binary64_449` `rem-cube-cbrt_binary64_442` `flip3--_binary64_423` `distribute-lft-out--_binary64_371` `diff-log_binary64_511` `flip--_binary64_394`

Counts

4 → 136

Calls

4 calls:

25.0ms	(-.f64 (cbrt.f64 (pow.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) 3)) (pow.f64 x (/.f64 1 n)))
12.0ms	(pow.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) 3)
11.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
7.0ms	(pow.f64 x (/.f64 1 n))

series1.1s (6.8%)

Counts

4 → 12

Calls

4 calls:

472.0ms	(pow.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) 3)
312.0ms	(-.f64 (cbrt.f64 (pow.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) 3)) (pow.f64 x (/.f64 1 n)))
149.0ms	(pow.f64 x (/.f64 1 n))
148.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))

simplify133.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4941	3170
1	4941	3170

prune274.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	147	5	152

Merged error: 22.7b

Counts

152 → 5

Compiler

Compiled 3528 to 2577 computations (27% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.9b	(/.f64 1/2 (.f64 x (.f64 x n)))
1.3b	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
3.0b	(-.f64 (/.f64 1 (.f64 x n)) (/.f64 1/2 (.f64 x (*.f64 x n))))
8.6b	(.f64 x (.f64 n n))

rewrite51.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
16×	`*-un-lft-identity_binary64_419`
14×	`add-sqr-sqrt_binary64_441`
12×	`times-frac_binary64_425`
11×	`add-cube-cbrt_binary64_454` `pow1_binary64_480`
9×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
7×	`cancel-sign-sub-inv_binary64_385` `associate-/l*_binary64_364`
6×	`add-log-exp_binary64_458` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
4×	`div-inv_binary64_416`
3×	`pow-prod-down_binary64_490` `distribute-lft-out--_binary64_371` `associate-l_binary64_360`
2×	`clear-num_binary64_418` `log-pow_binary64_508` `frac-2neg_binary64_430` `associate-/r*_binary64_363`
1×	`sub-neg_binary64_412` `difference-of-squares_binary64_388` `associate-r_binary64_359` `unswap-sqr_binary64_387` `flip3--_binary64_423` `*-commutative_binary64_350` `diff-log_binary64_511` `flip--_binary64_394` `frac-sub_binary64_428`

Counts

4 → 90

Calls

4 calls:

15.0ms	(-.f64 (/.f64 1 (.f64 x n)) (/.f64 1/2 (.f64 x (*.f64 x n))))
12.0ms	(.f64 x (.f64 n n))
8.0ms	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
7.0ms	(/.f64 1/2 (.f64 x (.f64 x n)))

series249.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

109.0ms	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
58.0ms	(-.f64 (/.f64 1 (.f64 x n)) (/.f64 1/2 (.f64 x (*.f64 x n))))
49.0ms	(.f64 x (.f64 n n))
33.0ms	(/.f64 1/2 (.f64 x (.f64 x n)))

simplify71.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4980	1498
1	4980	1498

prune172.0ms (1.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	96	6	102
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	97	10	107

Merged error: 22.3b

Counts

107 → 10

Compiler

Compiled 2903 to 1090 computations (62.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (/.f64 1 x) (-.f64 (/.f64 1 n) (/.f64 1/2 (.f64 x n))))
0.5b	(/.f64 1/2 (*.f64 x n))
1.3b	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
8.6b	(.f64 x (.f64 n n))

rewrite80.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64_441`
32×	`add-exp-log_binary64_457`
28×	`add-cbrt-cube_binary64_455`
26×	`*-un-lft-identity_binary64_419` `times-frac_binary64_425`
21×	`add-cube-cbrt_binary64_454`
16×	`associate-l_binary64_360`
14×	`cancel-sign-sub-inv_binary64_385`
13×	`pow1_binary64_480`
11×	`prod-exp_binary64_468`
9×	`associate-r_binary64_359` `cbrt-unprod_binary64_452`
8×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
7×	`div-exp_binary64_470` `associate-/l*_binary64_364`
6×	`div-inv_binary64_416` `cbrt-undiv_binary64_453`
4×	`pow-prod-down_binary64_490` `add-log-exp_binary64_458` `unswap-sqr_binary64_387`
3×	`difference-of-squares_binary64_388` `frac-times_binary64_429` `associate-*r/_binary64_361`
2×	`clear-num_binary64_418` `sub-neg_binary64_412` `flip3--_binary64_423` `distribute-lft-out--_binary64_371` `log-pow_binary64_508` `-commutative_binary64_350` `frac-2neg_binary64_430` `flip--_binary64_394` `associate-/r_binary64_363` `frac-sub_binary64_428`
1×	`associate-*l/_binary64_362` `1-exp_binary64_463` `rec-exp_binary64_469`

Counts

4 → 127

Calls

4 calls:

22.0ms	(.f64 (/.f64 1 x) (-.f64 (/.f64 1 n) (/.f64 1/2 (.f64 x n))))
15.0ms	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
10.0ms	(.f64 x (.f64 n n))
8.0ms	(/.f64 1/2 (*.f64 x n))

series307.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

135.0ms	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
76.0ms	(.f64 (/.f64 1 x) (-.f64 (/.f64 1 n) (/.f64 1/2 (.f64 x n))))
60.0ms	(.f64 x (.f64 n n))
36.0ms	(/.f64 1/2 (*.f64 x n))

simplify69.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5126	2087

prune210.0ms (1.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	133	6	139
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	136	13	149

Merged error: 22.2b

Counts

149 → 13

Compiler

Compiled 3616 to 1611 computations (55.4% saved)

regimes753.0ms (4.7%)

Compiler: Compiled 4145 to 2896 computations (30.1% saved)

bsearch165.0ms (1%)

Steps

Iters	Range		Point
8	141.0477585752277	818178.149409701	601298.5732088129
9	-4.0357611379939435e+45	-3.388323043908295e+39	-3.4419418499706947e+39

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	75	103
1	75	103

end0.0ms (0%)

sample9.3s (58.7%)

Algorithm

1×

intervals

Results

1.8s	2710×	body	1024	valid
1.7s	1459×	body	1024	nan
1.6s	1721×	body	2048	valid
655.0ms	2606×	body	128	overflowed
545.0ms	1175×	body	512	valid
511.0ms	756×	body	512	nan
238.0ms	181×	body	1024	invalid
235.0ms	1787×	body	128	valid
165.0ms	607×	body	256	valid
156.0ms	240×	body	512	invalid
113.0ms	330×	body	256	nan
75.0ms	790×	body	128	nan
55.0ms	153×	body	256	invalid
50.0ms	242×	body	128	invalid
10.0ms	6×	body	2048	nan

Compiler

Compiled 1058 to 729 computations (31.1% saved)

Details

analyze1.4s (8.9%)

sample313.0ms (2%)

simplify263.0ms (1.6%)

prune5.0ms (0%)

localize16.0ms (0.1%)

rewrite43.0ms (0.3%)

series532.0ms (3.3%)

simplify107.0ms (0.7%)

prune156.0ms (1%)

localize16.0ms (0.1%)

rewrite70.0ms (0.4%)

series1.1s (6.8%)

simplify133.0ms (0.8%)

prune274.0ms (1.7%)

localize14.0ms (0.1%)

rewrite51.0ms (0.3%)

series249.0ms (1.6%)

simplify71.0ms (0.4%)

prune172.0ms (1.1%)

localize15.0ms (0.1%)

rewrite80.0ms (0.5%)

series307.0ms (1.9%)

simplify69.0ms (0.4%)

prune210.0ms (1.3%)

regimes753.0ms (4.7%)

bsearch165.0ms (1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample9.3s (58.7%)

Profiling