Details

analyze345.0ms (15.9%)

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
21.8%	78%	0.1%	7
26.5%	73.3%	0.1%	8
36.7%	63.2%	0.1%	9
41.3%	49.9%	8.7%	10
47.2%	43.3%	9.5%	11
54.4%	35.5%	10.1%	12
57.9%	27.4%	14.7%	13
61.7%	23.2%	15.1%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample48.0ms (2.2%)

Algorithm

1×

intervals

Symmetry

(sort x y)

Results

7.0ms	256×	body	128	valid
0.0ms	14×	body	128	invalid

Compiler

Compiled 24 to 18 computations (25% saved)

simplify12.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

186×	`fma-def_binary64`
33×	`distribute-rgt-in_binary64`
26×	`associate-+l+_binary64`
22×	`associate-+r+_binary64`
21×	`distribute-lft-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	19	10
2	45	10
3	88	10
4	170	10
5	254	10
6	256	10
7	258	10
8	252	10

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))

Compiler

Compiled 30 to 21 computations (30% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))

series7.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

7.0ms

(*.f64 (+.f64 x y) (+.f64 z 1))

rewrite8.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
6×	`flip-+_binary64`
6×	`flip3-+_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`associate-r_binary64`

Counts

1 → 32

Calls

1 calls:

7.0ms

(*.f64 (+.f64 x y) (+.f64 z 1))

simplify69.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

759×	`distribute-rgt-in_binary64`
724×	`distribute-lft-in_binary64`
449×	`fma-def_binary64`
414×	`fma-neg_binary64`
258×	`unsub-neg_binary64`

Counts

68 → 61

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	83	908
1	269	804
2	911	798
3	3385	798
4	4092	798
5	5126	798

prune35.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	58	3	61
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	58	4	62

Error

Counts

62 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))
	12.2b	(.f64 (.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (+.f64 z 1)))
▶	0.0b	(+.f64 y (+.f64 (.f64 y z) (+.f64 (.f64 z x) x)))
	34.3b	(fma.f64 y z y)

Compiler

Compiled 982 to 502 computations (48.9% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 y (+.f64 (.f64 y z) (+.f64 (.f64 z x) x)))
✓	0.0b	(+.f64 (*.f64 z x) x)
✓	0.0b	(+.f64 (.f64 y z) (+.f64 (.f64 z x) x))

series20.0ms (0.9%)

Counts

3 → 33

Calls

3 calls:

9.0ms	(+.f64 y (+.f64 (.f64 y z) (+.f64 (.f64 z x) x)))
7.0ms	(+.f64 (.f64 y z) (+.f64 (.f64 z x) x))
4.0ms	(+.f64 (*.f64 z x) x)

rewrite16.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-log-exp_binary64`
10×	`sum-log_binary64`
7×	`*-un-lft-identity_binary64`
5×	`fma-def_binary64`
4×	`add-sqr-sqrt_binary64`

Counts

3 → 52

Calls

3 calls:

6.0ms	(+.f64 y (+.f64 (.f64 y z) (+.f64 (.f64 z x) x)))
5.0ms	(+.f64 (.f64 y z) (+.f64 (.f64 z x) x))
3.0ms	(+.f64 (*.f64 z x) x)

simplify56.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

661×	`distribute-rgt-in_binary64`
623×	`fma-def_binary64`
605×	`fma-neg_binary64`
593×	`distribute-lft-in_binary64`
396×	`associate-l_binary64`

Counts

85 → 94

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	839
1	270	770
2	983	748
3	4469	747
4	5002	747

prune48.0ms (2.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	95	3	98

Error

Counts

98 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))
	12.2b	(.f64 (.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (+.f64 z 1)))
▶	0.0b	(+.f64 (fma.f64 z y y) (+.f64 (*.f64 z x) x))

Compiler

Compiled 1545 to 418 computations (72.9% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (*.f64 z x) x)
✓	0.0b	(+.f64 (fma.f64 z y y) (+.f64 (*.f64 z x) x))

series11.0ms (0.5%)

Counts

1 → 36

Calls

1 calls:

11.0ms

(+.f64 (fma.f64 z y y) (+.f64 (*.f64 z x) x))

rewrite6.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-log-exp_binary64`
4×	`*-un-lft-identity_binary64`
3×	`sum-log_binary64`
3×	`fma-def_binary64`
2×	`add-sqr-sqrt_binary64`

Counts

1 → 20

Calls

1 calls:

5.0ms

(+.f64 (fma.f64 z y y) (+.f64 (*.f64 z x) x))

simplify61.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

749×	`sub-neg_binary64`
581×	`distribute-rgt-in_binary64`
559×	`distribute-lft-in_binary64`
399×	`cancel-sign-sub-inv_binary64`
341×	`fma-neg_binary64`

Counts

56 → 42

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	47	692
1	137	618
2	568	570
3	2931	570
4	4505	569
5	5336	569

prune36.0ms (1.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	67	3	70

Error

Counts

70 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))
▶	12.2b	(.f64 (.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (+.f64 z 1)))
✓	0.0b	(+.f64 (fma.f64 z y y) (+.f64 (*.f64 z x) x))

Compiler

Compiled 1021 to 296 computations (71% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 z 1))
✓	0.1b	(*.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1)))
✓	0.1b	(.f64 (.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (+.f64 z 1)))

series76.0ms (3.5%)

Counts

3 → 68

Calls

3 calls:

38.0ms	(.f64 (.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (+.f64 z 1)))
30.0ms	(*.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1)))
8.0ms	(sqrt.f64 (+.f64 z 1))

rewrite31.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`sqrt-div_binary64`
34×	`flip-+_binary64`
34×	`flip3-+_binary64`
32×	`frac-times_binary64`
18×	`*-un-lft-identity_binary64`

Counts

3 → 104

Calls

3 calls:

12.0ms	(.f64 (.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (+.f64 z 1)))
7.0ms	(*.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1)))
4.0ms	(sqrt.f64 (+.f64 z 1))

simplify128.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

769×	`fma-def_binary64`
725×	`associate--l+_binary64`
625×	`fma-neg_binary64`
373×	`*-commutative_binary64`
341×	`cancel-sign-sub-inv_binary64`

Counts

172 → 191

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	192	2970
1	515	2690
2	1569	2658
3	3339	2639
4	4913	2639
5	5177	2639

prune134.0ms (6.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	227	0	227
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	227	3	230

Error

Counts

230 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))
✓	12.2b	(.f64 (.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (+.f64 z 1)))
✓	0.0b	(+.f64 (fma.f64 z y y) (+.f64 (*.f64 z x) x))

Compiler

Compiled 5091 to 3148 computations (38.2% saved)

regimes156.0ms (7.2%)

Accuracy

Total 0.0b remaining (78.7%)

Threshold costs 0.0b (78.7%)

Counts

27 → 1

Compiler

Compiled 1904 to 1220 computations (35.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	11	14
2	11	14

end9.0ms (0.4%)

Compiler: Compiled 39 to 21 computations (46.2% saved)

sample830.0ms (38.2%)

Algorithm

1×

intervals

Results

235.0ms	7998×	body	128	valid
15.0ms	557×	body	128	invalid
0.0ms	2×	body	1024	valid

Compiler

Compiled 66 to 44 computations (33.3% saved)

Details

analyze345.0ms (15.9%)

sample48.0ms (2.2%)

simplify12.0ms (0.6%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series7.0ms (0.3%)

rewrite8.0ms (0.4%)

simplify69.0ms (3.2%)

prune35.0ms (1.6%)

localize7.0ms (0.3%)

series20.0ms (0.9%)

rewrite16.0ms (0.7%)

simplify56.0ms (2.6%)

prune48.0ms (2.2%)

localize7.0ms (0.3%)

series11.0ms (0.5%)

rewrite6.0ms (0.3%)

simplify61.0ms (2.8%)

prune36.0ms (1.6%)

localize7.0ms (0.3%)

series76.0ms (3.5%)

rewrite31.0ms (1.4%)

simplify128.0ms (5.9%)

prune134.0ms (6.2%)

regimes156.0ms (7.2%)

simplify2.0ms (0.1%)

end9.0ms (0.4%)

sample830.0ms (38.2%)

Profiling