Details

analyze65.0ms (2.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
0%	50%	50%	3
37.5%	12.5%	50%	4
43.7%	6.2%	50%	5
46.9%	3.1%	50%	6
48.4%	1.6%	50%	7
49.2%	0.8%	50%	8
49.6%	0.4%	50%	9
49.8%	0.2%	50%	10
49.9%	0.1%	50%	11
49.9%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 30 to 20 computations (33.3% saved)

sample33.0ms (1.4%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 57 to 38 computations (33.3% saved)

simplify49.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

581×	`associate-/r*_binary64`
516×	`cancel-sign-sub-inv_binary64`
510×	`distribute-rgt-in_binary64`
489×	`distribute-lft-in_binary64`
415×	`associate-/r/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	39	28
2	177	19
3	904	13
4	2320	13
5	4069	13
6	5047	13

prune6.0ms (0.2%)

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

0.3b

Counts

2 → 2

Alt Table

Status	Error	Program
	47.4b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
▶	0.3b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

Compiler

Compiled 82 to 58 computations (29.3% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.4b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
0.4b	(/.f64 1 (*.f64 i i))

rewrite96.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

37×	`add-sqr-sqrt_binary64`
35×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64`

Counts

2 → 81

Calls

2 calls:

7.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
5.0ms	(/.f64 1 (*.f64 i i))

Compiler

Compiled 1183 to 881 computations (25.5% saved)

series33.0ms (1.4%)

Error

0.0b

Counts

2 → 15

Calls

2 calls:

16.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
6.0ms	(/.f64 1 (*.f64 i i))

Compiler

Compiled 344 to 299 computations (13.1% saved)

simplify96.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

463×	`associate-/l*_binary64`
430×	`cancel-sign-sub-inv_binary64`
308×	`div-sub_binary64`
300×	`associate-/r/_binary64`
262×	`associate-/l/_binary64`

Counts

96 → 74

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	154	1565
1	300	1472
2	669	1369
3	1640	1369
4	4435	1309
5	4852	1309

prune38.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	71	3	74
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	73	3	76

Error

Counts

76 → 3

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
	0.4b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
	31.2b	(.f64 (.f64 i i) -1/4)

Compiler

Compiled 547 to 415 computations (24.1% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
0.1b	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
0.1b	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))

rewrite209.0ms (8.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

108×	`add-sqr-sqrt_binary64`
96×	`times-frac_binary64` `*-un-lft-identity_binary64`
47×	`add-cube-cbrt_binary64`
30×	`associate-r_binary64`
21×	`difference-of-squares_binary64` `associate-l_binary64`

Counts

3 → 161

Calls

3 calls:

33.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
9.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
8.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))

Compiler

Compiled 3456 to 3034 computations (12.2% saved)

series68.0ms (2.9%)

Error

Counts

3 → 36

Calls

3 calls:

17.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
14.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
14.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))

Compiler

Compiled 1069 to 915 computations (14.4% saved)

simplify179.0ms (7.6%)

Algorithm

1×	egg-herbie

Rules

573×	`associate-*l/_binary64`
499×	`associate-/l*_binary64`
288×	`associate-/l/_binary64`
200×	`associate-/r*_binary64`
190×	`times-frac_binary64`

Counts

197 → 138

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	253	4122
1	677	3817
2	1992	3696
3	4594	3696
4	4978	3696
5	4928	3696

prune93.0ms (4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	138	3	141

Error

Counts

141 → 3

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
▶	0.4b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
	31.2b	(.f64 (.f64 i i) -1/4)

Compiler

Compiled 1949 to 1643 computations (15.7% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.4b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))

rewrite54.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

33×	`add-sqr-sqrt_binary64`
21×	`times-frac_binary64` `*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`
7×	`associate-/r*_binary64`

Counts

1 → 45

Calls

1 calls:

7.0ms

(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))

Compiler

Compiled 712 to 629 computations (11.7% saved)

series23.0ms (1%)

Error

Counts

1 → 12

Calls

1 calls:

16.0ms

(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))

Compiler

Compiled 275 to 237 computations (13.8% saved)

simplify130.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

390×	`times-frac_binary64`
378×	`cancel-sign-sub-inv_binary64`
288×	`associate-/l*_binary64`
269×	`associate-/r*_binary64`
244×	`div-sub_binary64`

Counts

57 → 41

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	136	1041
1	272	995
2	594	991
3	1407	949
4	4206	949
5	4650	949
6	4973	949
7	4925	949

prune25.0ms (1.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	41	3	44

Error

Counts

44 → 3

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
✓	0.4b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
▶	31.2b	(.f64 (.f64 i i) -1/4)

Compiler

Compiled 387 to 317 computations (18.1% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(.f64 (.f64 i i) -1/4)

rewrite20.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

6×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `add-sqr-sqrt_binary64` `associate-r_binary64`
2×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
1×	`add-log-exp_binary64` `unswap-sqr_binary64` `associate-l_binary64` `*-commutative_binary64`

Counts

1 → 19

Calls

1 calls:

5.0ms

(*.f64 (*.f64 i i) -1/4)

Compiler

Compiled 180 to 105 computations (41.7% saved)

series8.0ms (0.4%)

Error

Counts

1 → 3

Calls

1 calls:

7.0ms

(*.f64 (*.f64 i i) -1/4)

Compiler

Compiled 42 to 35 computations (16.7% saved)

simplify82.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

673×	`associate-/l*_binary64`
380×	`distribute-rgt-in_binary64`
324×	`distribute-lft-in_binary64`
293×	`log-div_binary64`
248×	`associate-l_binary64`

Counts

22 → 17

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	227
1	85	191
2	236	182
3	540	182
4	781	182
5	1253	182
6	2268	182
7	4594	182
8	4980	182
9	4803	182

prune9.0ms (0.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	17	0	17
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	17	3	20

Error

Counts

20 → 3

Alt Table

Status	Error	Program
	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
	0.4b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
	31.2b	(.f64 (.f64 i i) -1/4)

Compiler

Compiled 115 to 76 computations (33.9% saved)

regimes111.0ms (4.7%)

Accuracy

Total 0.1b remaining (95.4%)

Threshold costs 0.1b (95.4%)

Compiler

Compiled 1232 to 999 computations (18.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`sub-neg_binary64` `*-commutative_binary64`
1×	`1-exp_binary64` `neg-mul-1_binary64` `neg-sub0_binary64` `distribute-neg-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	17	22
2	23	22
3	25	22
4	26	22
5	24	22

end1.0ms (0%)

Compiler: Compiled 16 to 14 computations (12.5% saved)

sample883.0ms (37.8%)

Algorithm

1×

intervals

Results

431.0ms	8000×	body	128	valid
104.0ms	8000×	pre	128	true

Compiler

Compiled 77 to 60 computations (22.1% saved)

Details

analyze65.0ms (2.8%)

sample33.0ms (1.4%)

simplify49.0ms (2.1%)

prune6.0ms (0.2%)

localize6.0ms (0.3%)

rewrite96.0ms (4.1%)

series33.0ms (1.4%)

simplify96.0ms (4.1%)

prune38.0ms (1.6%)

localize8.0ms (0.4%)

rewrite209.0ms (8.9%)

series68.0ms (2.9%)

simplify179.0ms (7.6%)

prune93.0ms (4%)

localize5.0ms (0.2%)

rewrite54.0ms (2.3%)

series23.0ms (1%)

simplify130.0ms (5.6%)

prune25.0ms (1.1%)

localize3.0ms (0.1%)

rewrite20.0ms (0.9%)

series8.0ms (0.4%)

simplify82.0ms (3.5%)

prune9.0ms (0.4%)

regimes111.0ms (4.7%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample883.0ms (37.8%)

Profiling