Details

analyze175.0ms (1.1%)

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
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
50%	46.8%	3.2%	7
56.2%	37.5%	6.3%	8
62.4%	25.8%	11.8%	9
65.6%	20.3%	14.1%	10
68.7%	13.5%	17.9%	11
70.2%	10.5%	19.2%	12
71.8%	6.9%	21.3%	13
72.6%	5.4%	22%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample21.0ms (0.1%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
0.0ms	11×	body	128	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify71.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

785×	`div-sub_binary64`
608×	`unsub-neg_binary64`
520×	`sub-neg_binary64`
408×	`distribute-neg-frac_binary64`
350×	`neg-mul-1_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	24	16
2	71	16
3	186	16
4	597	16
5	1674	16
6	3076	16
7	4259	16
8	4957	16

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

4.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	4.3b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))

Compiler

Compiled 39 to 30 computations (23.1% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 (-.f64 1 x) (-.f64 3 x))
4.0b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))

rewrite107.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`flip3--_binary64` `flip--_binary64`
11×	`*-un-lft-identity_binary64`
8×	`frac-times_binary64` `associate-/l/_binary64`

Counts

2 → 68

Calls

2 calls:

11.0ms	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))
9.0ms	(*.f64 (-.f64 1 x) (-.f64 3 x))

Compiler

Compiled 1400 to 1024 computations (26.9% saved)

series67.0ms (0.4%)

Error

3.9b

Counts

2 → 21

Calls

2 calls:

36.0ms	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))
14.0ms	(*.f64 (-.f64 1 x) (-.f64 3 x))

Compiler

Compiled 555 to 423 computations (23.8% saved)

simplify85.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

602×	`associate-/r*_binary64`
408×	`associate-*l/_binary64`
319×	`associate-*r/_binary64`
194×	`associate-/l/_binary64`
166×	`times-frac_binary64`

Counts

89 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	166	1589
1	479	1363
2	1929	1315
3	4734	1315
4	4943	1315

prune60.0ms (0.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	69	6	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	6	76

Error

0.0b

Counts

76 → 6

Alt Table

Status	Error	Program
	4.2b	(/.f64 (+.f64 1 (.f64 x (-.f64 (.f64 1/3 x) 4/3))) y)
	41.7b	(.f64 1/3 (.f64 (/.f64 x y) x))
	8.9b	(/.f64 (.f64 (-.f64 1 x) (-.f64 (.f64 3 3) (.f64 x x))) (.f64 (*.f64 y 3) (+.f64 x 3)))
	4.3b	(/.f64 (pow.f64 (.f64 (-.f64 3 x) (-.f64 1 x)) 1) (.f64 y 3))
	4.3b	(/.f64 (/.f64 (*.f64 (-.f64 3 x) (-.f64 1 x)) y) 3)
▶	0.1b	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))

Compiler

Compiled 1024 to 741 computations (27.6% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 3 x) 3)
0.1b	(/.f64 y (/.f64 (-.f64 3 x) 3))
0.1b	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))

rewrite611.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

1218×	`times-frac_binary64`
808×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
461×	`add-cube-cbrt_binary64`
205×	`difference-of-squares_binary64`
142×	`distribute-lft-out--_binary64`

Counts

3 → 592

Calls

3 calls:

25.0ms	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))
8.0ms	(/.f64 y (/.f64 (-.f64 3 x) 3))
6.0ms	(/.f64 (-.f64 3 x) 3)

Compiler

Compiled 12546 to 9075 computations (27.7% saved)

series91.0ms (0.6%)

Error

0.0b

Counts

3 → 33

Calls

3 calls:

37.0ms	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))
26.0ms	(/.f64 y (/.f64 (-.f64 3 x) 3))
8.0ms	(/.f64 (-.f64 3 x) 3)

Compiler

Compiled 992 to 730 computations (26.4% saved)

simplify401.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

554×	`associate-/l/_binary64`
532×	`associate-/r*_binary64`
489×	`associate-/r/_binary64`
395×	`associate-/l*_binary64`
278×	`div-sub_binary64`

Counts

625 → 481

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	733	20662
1	1987	20379
2	5112	20379

prune297.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	478	3	481
Fresh	4	1	5
Picked	0	1	1
Done	0	0	0
Total	482	5	487

Error

Counts

487 → 5

Alt Table

Status	Error	Program
	4.2b	(/.f64 (+.f64 1 (.f64 x (-.f64 (.f64 1/3 x) 4/3))) y)
▶	0.2b	(/.f64 (neg.f64 (-.f64 1 x)) (*.f64 (/.f64 y (-.f64 3 x)) -3))
	4.2b	(.f64 (/.f64 1 y) (.f64 (-.f64 1 x) (/.f64 (-.f64 3 x) 3)))
	1.0b	(/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 3)) (/.f64 y (/.f64 (-.f64 3 x) (sqrt.f64 3))))
✓	0.1b	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))

Compiler

Compiled 6913 to 4872 computations (29.5% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 y (-.f64 3 x))
0.1b	(/.f64 (neg.f64 (-.f64 1 x)) (*.f64 (/.f64 y (-.f64 3 x)) -3))
0.2b	(*.f64 (/.f64 y (-.f64 3 x)) -3)

rewrite154.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

60×	`add-sqr-sqrt_binary64`
55×	`*-un-lft-identity_binary64`
47×	`times-frac_binary64`
29×	`add-cube-cbrt_binary64`
21×	`associate-l_binary64`

Counts

3 → 131

Calls

3 calls:

13.0ms	(/.f64 (neg.f64 (-.f64 1 x)) (*.f64 (/.f64 y (-.f64 3 x)) -3))
10.0ms	(*.f64 (/.f64 y (-.f64 3 x)) -3)
5.0ms	(/.f64 y (-.f64 3 x))

Compiler

Compiled 2330 to 1722 computations (26.1% saved)

series110.0ms (0.7%)

Error

Counts

3 → 42

Calls

3 calls:

36.0ms	(/.f64 (neg.f64 (-.f64 1 x)) (*.f64 (/.f64 y (-.f64 3 x)) -3))
26.0ms	(*.f64 (/.f64 y (-.f64 3 x)) -3)
23.0ms	(/.f64 y (-.f64 3 x))

Compiler

Compiled 1447 to 1079 computations (25.4% saved)

simplify103.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

437×	`distribute-rgt-in_binary64`
383×	`distribute-lft-in_binary64`
208×	`div-sub_binary64`
170×	`associate-/l*_binary64`
142×	`distribute-frac-neg_binary64`

Counts

173 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	283	3188
1	712	2830
2	2430	2730
3	5001	2730

prune102.0ms (0.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	134	5	139

Error

Counts

139 → 5

Alt Table

Status	Error	Program
	4.2b	(/.f64 (+.f64 1 (.f64 x (-.f64 (.f64 1/3 x) 4/3))) y)
✓	0.2b	(/.f64 (neg.f64 (-.f64 1 x)) (*.f64 (/.f64 y (-.f64 3 x)) -3))
	4.2b	(.f64 (/.f64 1 y) (.f64 (-.f64 1 x) (/.f64 (-.f64 3 x) 3)))
▶	1.0b	(/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 3)) (/.f64 y (/.f64 (-.f64 3 x) (sqrt.f64 3))))
✓	0.1b	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))

Compiler

Compiled 1807 to 1301 computations (28% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 y (/.f64 (-.f64 3 x) (sqrt.f64 3)))
0.4b	(/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 3)) (/.f64 y (/.f64 (-.f64 3 x) (sqrt.f64 3))))
0.8b	(/.f64 (-.f64 1 x) (sqrt.f64 3))
0.8b	(/.f64 (-.f64 3 x) (sqrt.f64 3))

rewrite6.6s (40.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

16328×	`times-frac_binary64`
9228×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
5725×	`add-cube-cbrt_binary64`
3888×	`sqrt-prod_binary64`
2079×	`difference-of-squares_binary64`

Counts

4 → 4725

Calls

4 calls:

140.0ms	(/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 3)) (/.f64 y (/.f64 (-.f64 3 x) (sqrt.f64 3))))
11.0ms	(/.f64 y (/.f64 (-.f64 3 x) (sqrt.f64 3)))
7.0ms	(/.f64 (-.f64 3 x) (sqrt.f64 3))
7.0ms	(/.f64 (-.f64 1 x) (sqrt.f64 3))

Compiler

Compiled 101985 to 80351 computations (21.2% saved)

series152.0ms (0.9%)

Error

Counts

4 → 39

Calls

4 calls:

61.0ms	(/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 3)) (/.f64 y (/.f64 (-.f64 3 x) (sqrt.f64 3))))
35.0ms	(/.f64 y (/.f64 (-.f64 3 x) (sqrt.f64 3)))
17.0ms	(/.f64 (-.f64 1 x) (sqrt.f64 3))
16.0ms	(/.f64 (-.f64 3 x) (sqrt.f64 3))

Compiler

Compiled 1713 to 1427 computations (16.7% saved)

simplify3.6s (22.5%)

Algorithm

1×	egg-herbie

Rules

2030×	`associate-/l/_binary64`
83×	`div-sub_binary64`
29×	`/-rgt-identity_binary64`
21×	`remove-double-div_binary64`
20×	`sub-neg_binary64`

Counts

4764 → 3530

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2774	262735
1	5600	262735

prune1.7s (10.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	3530	0	3530
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	3530	5	3535

Error

Counts

3535 → 5

Alt Table

Status	Error	Program
	4.2b	(/.f64 (+.f64 1 (.f64 x (-.f64 (.f64 1/3 x) 4/3))) y)
	0.2b	(/.f64 (neg.f64 (-.f64 1 x)) (*.f64 (/.f64 y (-.f64 3 x)) -3))
	4.2b	(.f64 (/.f64 1 y) (.f64 (-.f64 1 x) (/.f64 (-.f64 3 x) 3)))
	1.0b	(/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 3)) (/.f64 y (/.f64 (-.f64 3 x) (sqrt.f64 3))))
	0.1b	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))

Compiler

Compiled 36235 to 28103 computations (22.4% saved)

regimes937.0ms (5.8%)

Accuracy

Total 0.1b remaining (81.9%)

Threshold costs 0.1b (81.9%)

Compiler

Compiled 12636 to 9803 computations (22.4% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	16	16
2	21	16
3	23	16
4	24	16
5	23	16

end1.0ms (0%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

sample630.0ms (3.9%)

Algorithm

1×

intervals

Results

275.0ms	8000×	body	128	valid
10.0ms	320×	body	128	invalid

Compiler

Compiled 101 to 80 computations (20.8% saved)

Details

analyze175.0ms (1.1%)

sample21.0ms (0.1%)

simplify71.0ms (0.4%)

prune3.0ms (0%)

localize7.0ms (0%)

rewrite107.0ms (0.7%)

series67.0ms (0.4%)

simplify85.0ms (0.5%)

prune60.0ms (0.4%)

localize7.0ms (0%)

rewrite611.0ms (3.8%)

series91.0ms (0.6%)

simplify401.0ms (2.5%)

prune297.0ms (1.8%)

localize8.0ms (0%)

rewrite154.0ms (1%)

series110.0ms (0.7%)

simplify103.0ms (0.6%)

prune102.0ms (0.6%)

localize9.0ms (0.1%)

rewrite6.6s (40.7%)

series152.0ms (0.9%)

simplify3.6s (22.5%)

prune1.7s (10.7%)

regimes937.0ms (5.8%)

simplify4.0ms (0%)

end1.0ms (0%)

sample630.0ms (3.9%)

Profiling