Details

analyze11.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
25%	25%	50%	2
25%	25%	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)

sample1.2s (39.1%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 84 to 55 computations (34.5% saved)

simplify60.0ms (2%)

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

0.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
	47.5b	(/.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))

Compiler

Compiled 107 to 73 computations (31.8% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 4 (/.f64 1 (*.f64 i i)))
✓	0.5b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
✓	0.6b	(/.f64 1 (*.f64 i i))

series16.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

6.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
6.0ms	(/.f64 1 (*.f64 i i))
4.0ms	(-.f64 4 (/.f64 1 (*.f64 i i)))

rewrite109.0ms (3.6%)

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:

68.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
11.0ms	(-.f64 4 (/.f64 1 (*.f64 i i)))
9.0ms	(/.f64 1 (*.f64 i i))

simplify165.0ms (5.4%)

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

prune180.0ms (5.9%)

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
	15.4b	(exp.f64 (log.f64 (/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))))
▶	0.5b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
	30.5b	(*.f64 -1/4 (pow.f64 i 2))

Compiler

Compiled 3680 to 2730 computations (25.8% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 4 (pow.f64 i -2))
✓	0.5b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))

series11.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
4.0ms	(-.f64 4 (pow.f64 i -2))

rewrite32.0ms (1.1%)

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:

10.0ms	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
9.0ms	(-.f64 4 (pow.f64 i -2))

simplify214.0ms (7%)

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

prune214.0ms (7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	144	3	147

Error

Counts

147 → 3

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
▶	15.4b	(exp.f64 (log.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))
	30.5b	(*.f64 -1/4 (pow.f64 i 2))

Compiler

Compiled 2665 to 2209 computations (17.1% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 4 (pow.f64 i -2))
✓	0.0b	(exp.f64 (log.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))
	0.5b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
✓	17.2b	(log.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))

series16.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

9.0ms	(exp.f64 (log.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))
7.0ms	(log.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))

rewrite38.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
54×	`log-prod_binary64`
42×	`times-frac_binary64`
37×	`*-un-lft-identity_binary64`
27×	`exp-sum_binary64`

Counts

2 → 82

Calls

2 calls:

14.0ms	(exp.f64 (log.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))
10.0ms	(log.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))

simplify228.0ms (7.4%)

Algorithm

1×	egg-herbie

Rules

494×	`fma-neg_binary64`
415×	`cancel-sign-sub-inv_binary64`
323×	`times-frac_binary64`
296×	`fma-def_binary64`
218×	`sub-neg_binary64`

Counts

106 → 143

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	253	2193
1	474	2114
2	1037	2021
3	2419	1937
4	4198	1927
5	4569	1903
6	4936	1903
7	4878	1903

prune258.0ms (8.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	287	0	287
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	287	3	290

Error

Counts

290 → 3

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
✓	15.4b	(exp.f64 (log.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))
▶	30.5b	(*.f64 -1/4 (pow.f64 i 2))

Compiler

Compiled 5517 to 4759 computations (13.7% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(*.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))

simplify85.0ms (2.8%)

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

prune24.0ms (0.8%)

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
✓	0.5b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
✓	15.4b	(exp.f64 (log.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))
✓	30.5b	(*.f64 -1/4 (pow.f64 i 2))

Compiler

Compiled 484 to 372 computations (23.1% saved)

regimes90.0ms (2.9%)

Accuracy

Total 0.3b remaining (97.8%)

Threshold costs 0.3b (97.8%)

Counts

19 → 1

Compiler

Compiled 518 to 411 computations (20.7% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	13	13
2	19	13
3	21	13
4	22	13
5	20	13

end64.0ms (2.1%)

Compiler: Compiled 44 to 37 computations (15.9% saved)

Details

analyze11.0ms (0.3%)

sample1.2s (39.1%)

simplify60.0ms (2%)

prune5.0ms (0.2%)

localize7.0ms (0.2%)

series16.0ms (0.5%)

rewrite109.0ms (3.6%)

simplify165.0ms (5.4%)

prune180.0ms (5.9%)

localize9.0ms (0.3%)

series11.0ms (0.3%)

rewrite32.0ms (1.1%)

simplify214.0ms (7%)

prune214.0ms (7%)

localize15.0ms (0.5%)

series16.0ms (0.5%)

rewrite38.0ms (1.2%)

simplify228.0ms (7.4%)

prune258.0ms (8.4%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite5.0ms (0.2%)

simplify85.0ms (2.8%)

prune24.0ms (0.8%)

regimes90.0ms (2.9%)

simplify5.0ms (0.2%)

end64.0ms (2.1%)

Profiling