Details

analyze809.0ms (18.6%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
37.4%	62.4%	0.1%	8
40.6%	56.2%	3.3%	9
46.8%	46%	7.2%	10
58.5%	32.8%	8.7%	11
60.8%	27.9%	11.3%	12
63.8%	22.4%	13.8%	13
69.1%	16.5%	14.4%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample50.0ms (1.1%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
1.0ms	22×	body	128	invalid

Compiler

Compiled 24 to 16 computations (33.3% saved)

simplify15.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`distribute-lft-out_binary64`
1×	`distribute-rgt-out_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	13	7
2	18	7
3	18	7

prune5.0ms (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 d2 d3))
	0.0b	(+.f64 (.f64 d1 d2) (.f64 d1 d3))

Compiler

Compiled 51 to 30 computations (41.2% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series15.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

15.0ms

(*.f64 d1 (+.f64 d2 d3))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 25

Calls

1 calls:

9.0ms

(*.f64 d1 (+.f64 d2 d3))

simplify110.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

935×	`distribute-rgt-in_binary64`
925×	`distribute-lft-in_binary64`
590×	`fma-def_binary64`
549×	`fma-neg_binary64`
280×	`associate-l_binary64`

Counts

49 → 42

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	49	416
1	133	386
2	419	386
3	1050	386
4	3209	386
5	3409	386
6	4244	386
7	4814	386
8	4885	386

prune82.0ms (1.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	42	2	44

Error

0.0b

Counts

44 → 2

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d2 d3))
▶	31.4b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d2 d3))) (sqrt.f64 (+.f64 d2 d3)))

Compiler

Compiled 453 to 133 computations (70.6% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 d2 d3))
✓	0.1b	(*.f64 d1 (sqrt.f64 (+.f64 d2 d3)))
✓	0.2b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d2 d3))) (sqrt.f64 (+.f64 d2 d3)))

series130.0ms (3%)

Counts

3 → 52

Calls

3 calls:

75.0ms	(*.f64 d1 (sqrt.f64 (+.f64 d2 d3)))
40.0ms	(sqrt.f64 (+.f64 d2 d3))
15.0ms	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d2 d3))) (sqrt.f64 (+.f64 d2 d3)))

rewrite46.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`sqrt-div_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
14×	`associate-r_binary64`
13×	`sqrt-prod_binary64`

Counts

3 → 78

Calls

3 calls:

19.0ms	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d2 d3))) (sqrt.f64 (+.f64 d2 d3)))
11.0ms	(*.f64 d1 (sqrt.f64 (+.f64 d2 d3)))
5.0ms	(sqrt.f64 (+.f64 d2 d3))

simplify183.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

787×	`fma-neg_binary64`
544×	`fma-def_binary64`
397×	`*-commutative_binary64`
306×	`cancel-sign-sub-inv_binary64`
303×	`distribute-rgt-in_binary64`

Counts

130 → 126

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	169	1805
1	439	1687
2	1337	1661
3	3094	1651
4	4464	1651
5	4961	1651

prune130.0ms (3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	159	1	160
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	159	3	162

Error

Counts

162 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d2 d3))
✓	31.4b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d2 d3))) (sqrt.f64 (+.f64 d2 d3)))
▶	31.4b	(.f64 (.f64 (*.f64 d1 (sqrt.f64 (+.f64 d2 d3))) (sqrt.f64 (sqrt.f64 (+.f64 d2 d3)))) (sqrt.f64 (sqrt.f64 (+.f64 d2 d3))))

Compiler

Compiled 3302 to 1121 computations (66.1% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (sqrt.f64 (+.f64 d2 d3)))
	0.1b	(*.f64 d1 (sqrt.f64 (+.f64 d2 d3)))
✓	0.2b	(.f64 (.f64 (*.f64 d1 (sqrt.f64 (+.f64 d2 d3))) (sqrt.f64 (sqrt.f64 (+.f64 d2 d3)))) (sqrt.f64 (sqrt.f64 (+.f64 d2 d3))))
✓	0.2b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d2 d3))) (sqrt.f64 (sqrt.f64 (+.f64 d2 d3))))

series797.0ms (18.3%)

Counts

3 → 96

Calls

3 calls:

737.0ms

(*.f64 (*.f64 d1 (sqrt.f64 (+.f64 d2 d3))) (sqrt.f64 (sqrt.f64 (+.f64 d2 d3))))

44.0ms

(sqrt.f64 (sqrt.f64 (+.f64 d2 d3)))

14.0ms

(*.f64 (*.f64 (*.f64 d1 (sqrt.f64 (+.f64 d2 d3))) (sqrt.f64 (sqrt.f64 (+.f64 d2 d3)))) (sqrt.f64 (sqrt.f64 (+.f64 d2 d3))))

rewrite101.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`sqrt-div_binary64`
34×	`sqrt-prod_binary64`
34×	`flip-+_binary64`
34×	`associate-*r/_binary64`
34×	`flip3-+_binary64`

Counts

3 → 115

Calls

3 calls:

35.0ms

(*.f64 (*.f64 (*.f64 d1 (sqrt.f64 (+.f64 d2 d3))) (sqrt.f64 (sqrt.f64 (+.f64 d2 d3)))) (sqrt.f64 (sqrt.f64 (+.f64 d2 d3))))

22.0ms

(*.f64 (*.f64 d1 (sqrt.f64 (+.f64 d2 d3))) (sqrt.f64 (sqrt.f64 (+.f64 d2 d3))))

8.0ms

(sqrt.f64 (sqrt.f64 (+.f64 d2 d3)))

simplify259.0ms (6%)

Algorithm

1×	egg-herbie

Rules

987×	`times-frac_binary64`
717×	`fma-def_binary64`
507×	`associate-l_binary64`
392×	`associate-r_binary64`
252×	`*-commutative_binary64`

Counts

211 → 222

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	345	5963
1	970	5151
2	3073	4941
3	5234	4941

prune317.0ms (7.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	319	0	319
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	319	3	322

Error

Counts

322 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d2 d3))
✓	31.4b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d2 d3))) (sqrt.f64 (+.f64 d2 d3)))
✓	31.4b	(.f64 (.f64 (*.f64 d1 (sqrt.f64 (+.f64 d2 d3))) (sqrt.f64 (sqrt.f64 (+.f64 d2 d3)))) (sqrt.f64 (sqrt.f64 (+.f64 d2 d3))))

Compiler

Compiled 10622 to 3954 computations (62.8% saved)

regimes131.0ms (3%)

Accuracy

Total 0.0b remaining (21.2%)

Threshold costs 0.0b (21.2%)

Counts

16 → 1

Compiler

Compiled 964 to 522 computations (45.9% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	8	7
2	8	7

end12.0ms (0.3%)

Remove: (sort d2 d3)
Compiler: Compiled 24 to 15 computations (37.5% saved)

sample1.1s (25.2%)

Algorithm

1×

intervals

Results

472.0ms	8000×	body	128	valid
43.0ms	722×	body	128	invalid

Compiler

Compiled 65 to 36 computations (44.6% saved)

Details

analyze809.0ms (18.6%)

sample50.0ms (1.1%)

simplify15.0ms (0.3%)

prune5.0ms (0.1%)

localize7.0ms (0.2%)

series15.0ms (0.3%)

rewrite11.0ms (0.3%)

simplify110.0ms (2.5%)

prune82.0ms (1.9%)

localize11.0ms (0.3%)

series130.0ms (3%)

rewrite46.0ms (1.1%)

simplify183.0ms (4.2%)

prune130.0ms (3%)

localize17.0ms (0.4%)

series797.0ms (18.3%)

rewrite101.0ms (2.3%)

simplify259.0ms (6%)

prune317.0ms (7.3%)

regimes131.0ms (3%)

simplify8.0ms (0.2%)

end12.0ms (0.3%)

sample1.1s (25.2%)

Profiling