Details

analyze897.0ms (16%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
28.1%	68.6%	3.3%	10
29.6%	65.5%	4.9%	11
32%	61.7%	6.3%	12
35.5%	56.9%	7.6%	13
48%	38.7%	13.4%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample253.0ms (4.5%)

Algorithm

1×

intervals

Symmetry

(sort d2 d4)

Results

13.0ms	256×	body	128	valid
3.0ms	65×	body	128	invalid

Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify100.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1400×	`fma-neg_binary64`
654×	`fma-def_binary64`
233×	`sub-neg_binary64`
210×	`unsub-neg_binary64`
158×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	32	14
2	94	13
3	263	13
4	655	13
5	1556	13
6	1691	13
7	1500	13
8	1500	13
9	2739	13
10	2707	13
11	2707	13
12	2632	13

prune3.0ms (0.1%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
▶	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))

Compiler

Compiled 92 to 53 computations (42.4% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (*.f64 d4 d1))
✓	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
✓	0.0b	(-.f64 (.f64 d1 d2) (.f64 d1 d3))

series46.0ms (0.8%)

Counts

3 → 132

Calls

3 calls:

26.0ms	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
13.0ms	(+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (*.f64 d4 d1))
7.0ms	(-.f64 (.f64 d1 d2) (.f64 d1 d3))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-log-exp_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`
6×	`diff-log_binary64`

Counts

3 → 64

Calls

3 calls:

7.0ms	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
5.0ms	(+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (*.f64 d4 d1))
3.0ms	(-.f64 (.f64 d1 d2) (.f64 d1 d3))

simplify96.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

713×	`associate-l_binary64`
685×	`fma-def_binary64`
488×	`fma-neg_binary64`
459×	`distribute-rgt-in_binary64`
440×	`distribute-lft-in_binary64`

Counts

196 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	2558
1	361	2139
2	1230	2096
3	4966	2096
4	5229	2096

prune83.0ms (1.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	125	3	128

Error

0.0b

Counts

128 → 3

Alt Table

Status	Error	Program
	32.5b	(.f64 (+.f64 d1 (sqrt.f64 (.f64 d1 (+.f64 d4 (-.f64 d2 d3))))) (-.f64 (sqrt.f64 (*.f64 d1 (+.f64 d4 (-.f64 d2 d3)))) d1))
✓	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
▶	0.0b	(-.f64 (.f64 d1 d2) (.f64 d1 (-.f64 d3 (-.f64 d4 d1))))

Compiler

Compiled 2607 to 506 computations (80.6% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 d1 d2) (.f64 d1 (-.f64 d3 (-.f64 d4 d1))))
✓	0.0b	(*.f64 d1 (-.f64 d3 (-.f64 d4 d1)))

series32.0ms (0.6%)

Counts

2 → 84

Calls

2 calls:

22.0ms	(-.f64 (.f64 d1 d2) (.f64 d1 (-.f64 d3 (-.f64 d4 d1))))
10.0ms	(*.f64 d1 (-.f64 d3 (-.f64 d4 d1)))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64`
76×	`add-sqr-sqrt_binary64`
61×	`prod-diff_binary64`
44×	`associate--r+_binary64`
44×	`distribute-lft-in_binary64`

Counts

2 → 130

Calls

2 calls:

10.0ms	(*.f64 d1 (-.f64 d3 (-.f64 d4 d1)))
8.0ms	(-.f64 (.f64 d1 d2) (.f64 d1 (-.f64 d3 (-.f64 d4 d1))))

simplify90.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

762×	`fma-def_binary64`
746×	`distribute-rgt-in_binary64`
682×	`distribute-lft-in_binary64`
221×	`cancel-sign-sub-inv_binary64`
196×	`fma-neg_binary64`

Counts

214 → 189

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	220	3706
1	497	3014
2	1460	2743
3	5389	2743

prune122.0ms (2.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	189	3	192

Error

0.0b

Counts

192 → 3

Alt Table

Status	Error	Program
▶	32.5b	(.f64 (+.f64 d1 (sqrt.f64 (.f64 d1 (+.f64 d4 (-.f64 d2 d3))))) (-.f64 (sqrt.f64 (*.f64 d1 (+.f64 d4 (-.f64 d2 d3)))) d1))
✓	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
✓	0.0b	(-.f64 (.f64 d1 d2) (.f64 d1 (-.f64 d3 (-.f64 d4 d1))))

Compiler

Compiled 4715 to 793 computations (83.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 d1 (sqrt.f64 (*.f64 d1 (+.f64 d4 (-.f64 d2 d3)))))
✓	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 d2 d3)))
✓	0.2b	(.f64 (+.f64 d1 (sqrt.f64 (.f64 d1 (+.f64 d4 (-.f64 d2 d3))))) (-.f64 (sqrt.f64 (*.f64 d1 (+.f64 d4 (-.f64 d2 d3)))) d1))
✓	2.0b	(sqrt.f64 (*.f64 d1 (+.f64 d4 (-.f64 d2 d3))))

series1.9s (33.2%)

Counts

4 → 88

Calls

4 calls:

1.3s	(.f64 (+.f64 d1 (sqrt.f64 (.f64 d1 (+.f64 d4 (-.f64 d2 d3))))) (-.f64 (sqrt.f64 (*.f64 d1 (+.f64 d4 (-.f64 d2 d3)))) d1))
262.0ms	(sqrt.f64 (*.f64 d1 (+.f64 d4 (-.f64 d2 d3))))
235.0ms	(+.f64 d1 (sqrt.f64 (*.f64 d1 (+.f64 d4 (-.f64 d2 d3)))))
11.0ms	(*.f64 d1 (+.f64 d4 (-.f64 d2 d3)))

rewrite45.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64`
34×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
24×	`prod-diff_binary64`
17×	`distribute-lft-in_binary64`

Counts

4 → 124

Calls

4 calls:

14.0ms	(.f64 (+.f64 d1 (sqrt.f64 (.f64 d1 (+.f64 d4 (-.f64 d2 d3))))) (-.f64 (sqrt.f64 (*.f64 d1 (+.f64 d4 (-.f64 d2 d3)))) d1))
12.0ms	(*.f64 d1 (+.f64 d4 (-.f64 d2 d3)))
6.0ms	(sqrt.f64 (*.f64 d1 (+.f64 d4 (-.f64 d2 d3))))
3.0ms	(+.f64 d1 (sqrt.f64 (*.f64 d1 (+.f64 d4 (-.f64 d2 d3)))))

simplify186.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

588×	`fma-neg_binary64`
417×	`times-frac_binary64`
395×	`exp-prod_binary64`
328×	`associate-l_binary64`
319×	`associate-r_binary64`

Counts

212 → 250

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	318	5099
1	785	4714
2	3377	4642
3	4332	4640
4	4860	4640
5	4963	4640

prune158.0ms (2.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	347	0	347
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	347	3	350

Error

0.0b

Counts

350 → 3

Alt Table

Status	Error	Program
✓	32.5b	(.f64 (+.f64 d1 (sqrt.f64 (.f64 d1 (+.f64 d4 (-.f64 d2 d3))))) (-.f64 (sqrt.f64 (*.f64 d1 (+.f64 d4 (-.f64 d2 d3)))) d1))
✓	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
✓	0.0b	(-.f64 (.f64 d1 d2) (.f64 d1 (-.f64 d3 (-.f64 d4 d1))))

Compiler

Compiled 11578 to 1940 computations (83.2% saved)

regimes395.0ms (7.1%)

Accuracy

Total 0.0b remaining (49.7%)

Threshold costs 0.0b (49.7%)

Counts

83 → 1

Compiler

Compiled 6948 to 4104 computations (40.9% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

42×	`distribute-rgt-neg-in_binary64`
40×	`cancel-sign-sub-inv_binary64`
28×	`distribute-lft-neg-in_binary64`
24×	`distribute-neg-in_binary64`
24×	`neg-sub0_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	26	19
2	46	19
3	80	19
4	118	19
5	154	19
6	186	19
7	204	19
8	216	19
9	220	19
10	216	19

end5.0ms (0.1%)

Compiler: Compiled 51 to 30 computations (41.2% saved)

sample1.1s (20.2%)

Algorithm

1×

intervals

Results

438.0ms	8000×	body	128	valid
137.0ms	2383×	body	128	invalid

Compiler

Compiled 100 to 57 computations (43% saved)

Iter	Nodes	Cost
0	12	21
1	26	19
2	46	19
3	80	19
4	118	19
5	154	19
6	186	19
7	204	19
8	216	19
9	220	19
10	216	19

Iter	Nodes	Cost
0	12	21
1	26	19
2	46	19
3	80	19
4	118	19
5	154	19
6	186	19
7	204	19
8	216	19
9	220	19
10	216	19

Details

analyze897.0ms (16%)

sample253.0ms (4.5%)

simplify100.0ms (1.8%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series46.0ms (0.8%)

rewrite22.0ms (0.4%)

simplify96.0ms (1.7%)

prune83.0ms (1.5%)

localize8.0ms (0.1%)

series32.0ms (0.6%)

rewrite32.0ms (0.6%)

simplify90.0ms (1.6%)

prune122.0ms (2.2%)

localize10.0ms (0.2%)

series1.9s (33.2%)

rewrite45.0ms (0.8%)

simplify186.0ms (3.3%)

prune158.0ms (2.8%)

regimes395.0ms (7.1%)

simplify7.0ms (0.1%)

end5.0ms (0.1%)

sample1.1s (20.2%)

Profiling

Iter	Nodes	Cost
0	12	21
1	26	19
2	46	19
3	80	19
4	118	19
5	154	19
6	186	19
7	204	19
8	216	19
9	220	19
10	216	19