Details

analyze7.0ms (0.2%)

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 29 to 19 computations (34.5% saved)

sample1.4s (51.7%)

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 84 to 55 computations (34.5% saved)

simplify57.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

581×	`associate-/r*_binary64`
510×	`distribute-rgt-in_binary64`
489×	`distribute-lft-in_binary64`
463×	`fma-neg_binary64`
415×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	40	26
2	185	17
3	915	13
4	2340	13
5	4455	13
6	4958	13
7	5077	13

prune5.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	47.8b	(/.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 107 to 73 computations (31.8% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 4 (/.f64 1 (*.f64 i i)))
✓	0.3b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
✓	0.5b	(/.f64 1 (*.f64 i i))

series8.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
3.0ms	(/.f64 1 (*.f64 i i))
2.0ms	(-.f64 4 (/.f64 1 (*.f64 i i)))

rewrite24.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-sqr-sqrt_binary64`
54×	`*-un-lft-identity_binary64`
49×	`times-frac_binary64`
34×	`add-cube-cbrt_binary64`
21×	`prod-diff_binary64`

Counts

3 → 134

Calls

3 calls:

6.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
5.0ms	(-.f64 4 (/.f64 1 (*.f64 i i)))
5.0ms	(/.f64 1 (*.f64 i i))

simplify140.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

817×	`fma-neg_binary64`
446×	`unswap-sqr_binary64`
408×	`associate-l_binary64`
361×	`fma-def_binary64`
294×	`associate-r_binary64`

Counts

170 → 196

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	203	2573
1	382	2324
2	977	2089
3	3418	2089
4	4641	2081
5	4949	2081
6	4780	2081

prune153.0ms (5.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	195	3	198

Error

Counts

198 → 3

Alt Table

Status	Error	Program
	0.3b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
	34.6b	(*.f64 -1/4 (pow.f64 i 2))
▶	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))

Compiler

Compiled 3688 to 2738 computations (25.8% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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)))

series9.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
3.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
3.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))

rewrite52.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 167

Calls

3 calls:

25.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
7.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
7.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))

simplify134.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

499×	`associate-/l*_binary64`
456×	`fma-def_binary64`
288×	`associate-/l/_binary64`
277×	`fma-neg_binary64`
200×	`associate-/r*_binary64`

Counts

203 → 242

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	259	4188
1	697	3891
2	2091	3770
3	4611	3768
4	5010	3768

prune198.0ms (7.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	242	0	242
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	242	3	245

Error

Counts

245 → 3

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
	34.6b	(*.f64 -1/4 (pow.f64 i 2))
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))

Compiler

Compiled 5804 to 5016 computations (13.6% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 4 (pow.f64 i -2))
✓	0.3b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))

series6.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
2.0ms	(-.f64 4 (pow.f64 i -2))

rewrite16.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
30×	`add-cube-cbrt_binary64`
21×	`prod-diff_binary64`
21×	`times-frac_binary64`

Counts

2 → 95

Calls

2 calls:

5.0ms	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
4.0ms	(-.f64 4 (pow.f64 i -2))

simplify107.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

841×	`times-frac_binary64`
658×	`fma-neg_binary64`
467×	`associate-l_binary64`
386×	`fma-def_binary64`
334×	`associate-r_binary64`

Counts

119 → 144

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	2626
1	389	2113
2	1019	1527
3	3058	1527
4	4965	1527
5	4787	1527

prune111.0ms (4.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	144	3	147

Error

Counts

147 → 3

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
▶	34.6b	(*.f64 -1/4 (pow.f64 i 2))
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))

Compiler

Compiled 2661 to 2205 computations (17.1% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 -1/4 (pow.f64 i 2))

series3.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

3.0ms

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

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
6×	`add-exp-log_binary64`
4×	`unswap-sqr_binary64`
4×	`unpow-prod-down_binary64`

Counts

1 → 29

Calls

1 calls:

4.0ms

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

simplify75.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

964×	`fma-def_binary64`
644×	`unswap-sqr_binary64`
397×	`log-prod_binary64`
394×	`sqr-pow_binary64`
337×	`*-commutative_binary64`

Counts

29 → 45

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	321
1	97	249
2	198	239
3	636	233
4	1071	233
5	2844	233
6	3957	233
7	4846	233
8	4880	233

prune26.0ms (0.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	45	0	45
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	45	3	48

Error

Counts

48 → 3

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
✓	34.6b	(*.f64 -1/4 (pow.f64 i 2))
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))

Compiler

Compiled 490 to 377 computations (23.1% saved)

regimes66.0ms (2.4%)

Accuracy

Total 0.1b remaining (94.5%)

Threshold costs 0.1b (94.5%)

Counts

31 → 1

Compiler

Compiled 886 to 695 computations (21.6% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_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

end87.0ms (3.2%)

Compiler: Compiled 62 to 54 computations (12.9% saved)

Details

analyze7.0ms (0.2%)

sample1.4s (51.7%)

simplify57.0ms (2.1%)

prune5.0ms (0.2%)

localize6.0ms (0.2%)

series8.0ms (0.3%)

rewrite24.0ms (0.9%)

simplify140.0ms (5.1%)

prune153.0ms (5.6%)

localize9.0ms (0.3%)

series9.0ms (0.3%)

rewrite52.0ms (1.9%)

simplify134.0ms (4.9%)

prune198.0ms (7.3%)

localize4.0ms (0.1%)

series6.0ms (0.2%)

rewrite16.0ms (0.6%)

simplify107.0ms (3.9%)

prune111.0ms (4.1%)

localize5.0ms (0.2%)

series3.0ms (0.1%)

rewrite5.0ms (0.2%)

simplify75.0ms (2.7%)

prune26.0ms (0.9%)

regimes66.0ms (2.4%)

simplify6.0ms (0.2%)

end87.0ms (3.2%)

Profiling