Details

analyze155.0ms (4.3%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	31.2%	6.3%	6
68.7%	21.9%	9.5%	7
68.7%	17.2%	14.1%	8
71.8%	11.7%	16.5%	9
71.8%	9%	19.2%	10
73.4%	6%	20.6%	11
73.4%	4.6%	22%	12
74.1%	3.1%	22.8%	13
74.1%	2.3%	23.5%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample51.0ms (1.4%)

Algorithm

1×

intervals

Results

14.0ms	41×	body	2048	valid
9.0ms	52×	body	1024	valid
8.0ms	61×	body	512	valid
3.0ms	86×	body	128	valid
1.0ms	16×	body	256	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 19 to 15 computations (21.1% saved)

simplify61.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

467×	`cancel-sign-sub-inv_binary64`
455×	`*-commutative_binary64`
440×	`unswap-sqr_binary64`
344×	`associate-l_binary64`
274×	`associate-+l+_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	15	9
2	22	9
3	33	9
4	65	9
5	149	9
6	403	9
7	1433	9
8	3314	9
9	4997	9
10	4875	9

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

32.9b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	32.9b	(-.f64 (exp.f64 (*.f64 a x)) 1)

Compiler

Compiled 16 to 12 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

2.6b	(-.f64 (exp.f64 (*.f64 a x)) 1)

rewrite25.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

32.9b

Rules

6×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
3×	`cancel-sign-sub-inv_binary64`
3×	`add-log-exp_binary64`
2×	`difference-of-squares_binary64`

Counts

1 → 18

Calls

1 calls:

3.0ms

(-.f64 (exp.f64 (*.f64 a x)) 1)

Compiler

Compiled 226 to 112 computations (50.4% saved)

series19.0ms (0.5%)

Error

0.3b

Counts

1 → 12

Calls

1 calls:

13.0ms

(-.f64 (exp.f64 (*.f64 a x)) 1)

Compiler

Compiled 304 to 222 computations (27% saved)

simplify83.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

421×	`*-commutative_binary64`
330×	`unswap-sqr_binary64`
284×	`distribute-rgt-out_binary64`
238×	`exp-prod_binary64`
218×	`cancel-sign-sub-inv_binary64`

Counts

30 → 17

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	58	507
1	124	482
2	310	464
3	998	452
4	1907	446
5	2847	446
6	4639	446
7	5089	446

prune15.0ms (0.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	13	4	17
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	14	4	18

Error

0.0b

Counts

18 → 4

Alt Table

Status	Error	Program
	32.9b	(/.f64 (+.f64 (pow.f64 (exp.f64 (.f64 a x)) 2) -1) (+.f64 (exp.f64 (.f64 a x)) 1))
	32.9b	(cbrt.f64 (pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3))
▶	18.9b	(+.f64 (.f64 a x) (+.f64 (+.f64 (.f64 1/2 (pow.f64 (.f64 a x) 2)) (.f64 1/6 (pow.f64 (.f64 a x) 3))) (.f64 1/24 (pow.f64 (*.f64 a x) 4))))
	33.0b	(.f64 (+.f64 1 (sqrt.f64 (exp.f64 (.f64 a x)))) (+.f64 -1 (sqrt.f64 (exp.f64 (*.f64 a x)))))

Compiler

Compiled 282 to 164 computations (41.8% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (*.f64 a x) 2)
3.8b	(+.f64 (.f64 a x) (+.f64 (+.f64 (.f64 1/2 (pow.f64 (.f64 a x) 2)) (.f64 1/6 (pow.f64 (.f64 a x) 3))) (.f64 1/24 (pow.f64 (*.f64 a x) 4))))
9.3b	(+.f64 (.f64 1/2 (pow.f64 (.f64 a x) 2)) (.f64 1/6 (pow.f64 (.f64 a x) 3)))
10.0b	(+.f64 (+.f64 (.f64 1/2 (pow.f64 (.f64 a x) 2)) (.f64 1/6 (pow.f64 (.f64 a x) 3))) (.f64 1/24 (pow.f64 (.f64 a x) 4)))

rewrite84.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

20×	`add-log-exp_binary64`
10×	`sum-log_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`

Counts

4 → 56

Calls

4 calls:

11.0ms	(+.f64 (+.f64 (.f64 1/2 (pow.f64 (.f64 a x) 2)) (.f64 1/6 (pow.f64 (.f64 a x) 3))) (.f64 1/24 (pow.f64 (.f64 a x) 4)))
7.0ms	(+.f64 (.f64 a x) (+.f64 (+.f64 (.f64 1/2 (pow.f64 (.f64 a x) 2)) (.f64 1/6 (pow.f64 (.f64 a x) 3))) (.f64 1/24 (pow.f64 (*.f64 a x) 4))))
4.0ms	(+.f64 (.f64 1/2 (pow.f64 (.f64 a x) 2)) (.f64 1/6 (pow.f64 (.f64 a x) 3)))
3.0ms	(pow.f64 (*.f64 a x) 2)

Compiler

Compiled 2294 to 1354 computations (41% saved)

series144.0ms (4%)

Error

0.0b

Counts

4 → 52

Calls

4 calls:

42.0ms	(+.f64 (.f64 1/2 (pow.f64 (.f64 a x) 2)) (.f64 1/6 (pow.f64 (.f64 a x) 3)))
38.0ms	(+.f64 (.f64 a x) (+.f64 (+.f64 (.f64 1/2 (pow.f64 (.f64 a x) 2)) (.f64 1/6 (pow.f64 (.f64 a x) 3))) (.f64 1/24 (pow.f64 (*.f64 a x) 4))))
35.0ms	(+.f64 (+.f64 (.f64 1/2 (pow.f64 (.f64 a x) 2)) (.f64 1/6 (pow.f64 (.f64 a x) 3))) (.f64 1/24 (pow.f64 (.f64 a x) 4)))
17.0ms	(pow.f64 (*.f64 a x) 2)

Compiler

Compiled 2171 to 1586 computations (26.9% saved)

simplify114.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

744×	`distribute-rgt-in_binary64`
418×	`cancel-sign-sub-inv_binary64`
266×	`exp-prod_binary64`
262×	`distribute-rgt-neg-in_binary64`
246×	`distribute-lft-neg-in_binary64`

Counts

108 → 90

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	122	3014
1	373	2825
2	1557	2600
3	4831	2600
4	5129	2600

prune48.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	89	5	94

Error

0.0b

Counts

94 → 5

Alt Table

Status	Error	Program
▶	32.9b	(/.f64 (+.f64 (pow.f64 (exp.f64 (.f64 a x)) 2) -1) (+.f64 (exp.f64 (.f64 a x)) 1))
	32.9b	(cbrt.f64 (pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3))
✓	18.9b	(+.f64 (.f64 a x) (+.f64 (+.f64 (.f64 1/2 (pow.f64 (.f64 a x) 2)) (.f64 1/6 (pow.f64 (.f64 a x) 3))) (.f64 1/24 (pow.f64 (*.f64 a x) 4))))
	48.1b	(/.f64 (+.f64 (pow.f64 (.f64 a x) 3) (pow.f64 (+.f64 (.f64 (pow.f64 (.f64 a x) 2) (+.f64 1/2 (.f64 1/6 (.f64 a x)))) (.f64 1/24 (pow.f64 (.f64 a x) 4))) 3)) (+.f64 (pow.f64 (.f64 a x) 2) (.f64 (+.f64 (.f64 (pow.f64 (.f64 a x) 2) (+.f64 1/2 (.f64 1/6 (.f64 a x)))) (.f64 1/24 (pow.f64 (.f64 a x) 4))) (-.f64 (+.f64 (.f64 (pow.f64 (.f64 a x) 2) (+.f64 1/2 (.f64 1/6 (.f64 a x)))) (.f64 1/24 (pow.f64 (.f64 a x) 4))) (.f64 a x)))))
	33.0b	(.f64 (+.f64 1 (sqrt.f64 (exp.f64 (.f64 a x)))) (+.f64 -1 (sqrt.f64 (exp.f64 (*.f64 a x)))))

Compiler

Compiled 1672 to 950 computations (43.2% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (exp.f64 (*.f64 a x)) 1)
0.0b	(/.f64 (+.f64 (pow.f64 (exp.f64 (.f64 a x)) 2) -1) (+.f64 (exp.f64 (.f64 a x)) 1))
0.0b	(pow.f64 (exp.f64 (*.f64 a x)) 2)
2.6b	(+.f64 (pow.f64 (exp.f64 (*.f64 a x)) 2) -1)

rewrite100.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

52×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
32×	`add-sqr-sqrt_binary64`
24×	`difference-of-sqr--1_binary64`
20×	`add-cube-cbrt_binary64`

Counts

4 → 108

Calls

4 calls:

12.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 (.f64 a x)) 2) -1) (+.f64 (exp.f64 (.f64 a x)) 1))
4.0ms	(+.f64 (pow.f64 (exp.f64 (*.f64 a x)) 2) -1)
3.0ms	(+.f64 (exp.f64 (*.f64 a x)) 1)
2.0ms	(pow.f64 (exp.f64 (*.f64 a x)) 2)

Compiler

Compiled 2459 to 1279 computations (48% saved)

series103.0ms (2.9%)

Error

0.0b

Counts

4 → 48

Calls

4 calls:

33.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 (.f64 a x)) 2) -1) (+.f64 (exp.f64 (.f64 a x)) 1))
23.0ms	(+.f64 (pow.f64 (exp.f64 (*.f64 a x)) 2) -1)
18.0ms	(+.f64 (exp.f64 (*.f64 a x)) 1)
16.0ms	(pow.f64 (exp.f64 (*.f64 a x)) 2)

Compiler

Compiled 1720 to 1176 computations (31.6% saved)

simplify173.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

574×	`associate-l_binary64`
500×	`associate-r_binary64`
258×	`times-frac_binary64`
244×	`associate-/l*_binary64`
206×	`exp-prod_binary64`

Counts

156 → 117

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	195	3946
1	424	3577
2	1081	3280
3	4421	3279
4	4987	3279
5	4963	3279

prune54.0ms (1.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	117	5	122

Error

0.0b

Counts

122 → 5

Alt Table

Status	Error	Program
▶	19.1b	(.f64 x (+.f64 a (.f64 1/2 (.f64 a (.f64 a x)))))
✓	18.9b	(+.f64 (.f64 a x) (+.f64 (+.f64 (.f64 1/2 (pow.f64 (.f64 a x) 2)) (.f64 1/6 (pow.f64 (.f64 a x) 3))) (.f64 1/24 (pow.f64 (*.f64 a x) 4))))
	32.9b	(/.f64 (/.f64 (+.f64 -1 (pow.f64 (exp.f64 (.f64 a x)) 4)) (+.f64 (pow.f64 (exp.f64 (.f64 a x)) 2) 1)) (+.f64 (exp.f64 (*.f64 a x)) 1))
	32.9b	(/.f64 (log.f64 (exp.f64 (-.f64 (pow.f64 (exp.f64 (.f64 a x)) 2) 1))) (+.f64 (exp.f64 (.f64 a x)) 1))
	33.0b	(.f64 (+.f64 1 (sqrt.f64 (exp.f64 (.f64 a x)))) (+.f64 -1 (sqrt.f64 (exp.f64 (*.f64 a x)))))

Compiler

Compiled 1780 to 934 computations (47.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(.f64 a (.f64 a x))
0.2b	(.f64 1/2 (.f64 a (*.f64 a x)))
2.3b	(.f64 x (+.f64 a (.f64 1/2 (.f64 a (.f64 a x)))))

rewrite47.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

19×	`add-cbrt-cube_binary64`
19×	`add-exp-log_binary64`
19×	`pow1_binary64`
10×	`cbrt-unprod_binary64`
10×	`prod-exp_binary64`

Counts

3 → 61

Calls

3 calls:

5.0ms	(.f64 1/2 (.f64 a (*.f64 a x)))
4.0ms	(.f64 x (+.f64 a (.f64 1/2 (.f64 a (.f64 a x)))))
4.0ms	(.f64 a (.f64 a x))

Compiler

Compiled 1014 to 422 computations (58.4% saved)

series51.0ms (1.4%)

Error

0.0b

Counts

3 → 24

Calls

3 calls:

25.0ms	(.f64 x (+.f64 a (.f64 1/2 (.f64 a (.f64 a x)))))
13.0ms	(.f64 1/2 (.f64 a (*.f64 a x)))
11.0ms	(.f64 a (.f64 a x))

Compiler

Compiled 584 to 415 computations (28.9% saved)

simplify106.0ms (3%)

Algorithm

1×	egg-herbie

Rules

480×	`unswap-sqr_binary64`
453×	`*-commutative_binary64`
253×	`distribute-rgt-neg-in_binary64`
250×	`distribute-rgt-in_binary64`
245×	`distribute-lft-in_binary64`

Counts

85 → 56

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	100	1197
1	262	1083
2	1041	1079
3	2272	1075
4	4747	1075
5	4982	1075
6	4984	1075

prune20.0ms (0.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	56	5	61

Error

0.0b

Counts

61 → 5

Alt Table

Status	Error	Program
	19.1b	(.f64 x (+.f64 a (.f64 1/2 (.f64 a (.f64 a x)))))
	18.9b	(+.f64 (.f64 a x) (+.f64 (+.f64 (.f64 1/2 (pow.f64 (.f64 a x) 2)) (.f64 1/6 (pow.f64 (.f64 a x) 3))) (.f64 1/24 (pow.f64 (*.f64 a x) 4))))
	32.9b	(/.f64 (/.f64 (+.f64 -1 (pow.f64 (exp.f64 (.f64 a x)) 4)) (+.f64 (pow.f64 (exp.f64 (.f64 a x)) 2) 1)) (+.f64 (exp.f64 (*.f64 a x)) 1))
	32.9b	(/.f64 (log.f64 (exp.f64 (-.f64 (pow.f64 (exp.f64 (.f64 a x)) 2) 1))) (+.f64 (exp.f64 (.f64 a x)) 1))
	33.0b	(.f64 (+.f64 1 (sqrt.f64 (exp.f64 (.f64 a x)))) (+.f64 -1 (sqrt.f64 (exp.f64 (*.f64 a x)))))

Compiler

Compiled 496 to 255 computations (48.6% saved)

regimes523.0ms (14.6%)

Accuracy

Total 0.2b remaining (87.7%)

Threshold costs 0.2b (87.7%)

Compiler

Compiled 6409 to 4232 computations (34% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 5 to 3 computations (40% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	73
1	42	73
2	43	73
3	41	73

end8.0ms (0.2%)

Remove: (sort a x)
Compiler: Compiled 150 to 87 computations (42% saved)

sample1.5s (43.3%)

Algorithm

1×

intervals

Results

595.0ms	1431×	body	2048	valid
321.0ms	1756×	body	1024	valid
115.0ms	1102×	body	512	valid
109.0ms	3086×	body	128	valid
46.0ms	625×	body	256	valid
5.0ms	158×	body	128	invalid

Compiler

Compiled 165 to 103 computations (37.6% saved)

Details

analyze155.0ms (4.3%)

sample51.0ms (1.4%)

simplify61.0ms (1.7%)

prune1.0ms (0%)

localize5.0ms (0.1%)

rewrite25.0ms (0.7%)

series19.0ms (0.5%)

simplify83.0ms (2.3%)

prune15.0ms (0.4%)

localize15.0ms (0.4%)

rewrite84.0ms (2.3%)

series144.0ms (4%)

simplify114.0ms (3.2%)

prune48.0ms (1.3%)

localize11.0ms (0.3%)

rewrite100.0ms (2.8%)

series103.0ms (2.9%)

simplify173.0ms (4.8%)

prune54.0ms (1.5%)

localize6.0ms (0.2%)

rewrite47.0ms (1.3%)

series51.0ms (1.4%)

simplify106.0ms (3%)

prune20.0ms (0.6%)

regimes523.0ms (14.6%)

bsearch2.0ms (0.1%)

simplify5.0ms (0.1%)

end8.0ms (0.2%)

sample1.5s (43.3%)

Profiling