Details

analyze753.0ms (27.6%)

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
12.5%	87.3%	0.2%	10
15.6%	80.3%	4.1%	11
31.2%	63.9%	4.9%	12
39%	50.9%	10.1%	13
44.8%	44.4%	10.7%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.0s (37.8%)

Symmetry

(sort x y)

(sort z t)

Results

833.0ms	8256×	body	128	valid
135.0ms	1313×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify15.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

171×	`fma-def_binary64`
87×	`fma-neg_binary64`
36×	`cancel-sign-sub-inv_binary64`
23×	`distribute-rgt-neg-in_binary64`
20×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	16	10
2	27	10
3	44	10
4	66	10
5	100	10
6	152	10
7	213	10
8	257	10
9	279	10
10	299	10
11	305	10
12	274	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 t))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x y) (.f64 z t))

series9.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

8.0ms

(-.f64 (*.f64 x y) (*.f64 z t))

rewrite56.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

890×	`log1p-expm1-u_binary64`
890×	`expm1-log1p-u_binary64`
92×	`add-sqr-sqrt_binary64`
85×	`add-log-exp_binary64`
84×	`add-cube-cbrt_binary64`

Counts

1 → 50

Calls

1 calls:

54.0ms

(-.f64 (*.f64 x y) (*.f64 z t))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	175	10
2	2254	10
3	5413	10
0	0	0
1	0	0

simplify40.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

172×	`fma-def_binary64`
87×	`fma-neg_binary64`
36×	`cancel-sign-sub-inv_binary64`
23×	`distribute-rgt-neg-in_binary64`
20×	`sub-neg_binary64`

Counts

98 → 54

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	420
1	21	420
2	33	420
3	44	420
4	66	420
5	100	420
6	152	420
7	213	420
8	257	420
9	279	420
10	299	420
11	305	420
12	274	420

prune24.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	53	2	55

Error

Counts

55 → 2

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (.f64 x y) (.f64 z t))
▶	32.2b	(pow.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) 2)

Compiler

Compiled 936 to 243 computations (74% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (.f64 x y) (.f64 z t))
✓	0.2b	(pow.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) 2)
✓	1.5b	(sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))

series365.0ms (13.4%)

Counts

2 → 32

Calls

2 calls:

300.0ms	(pow.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) 2)
65.0ms	(sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))

rewrite80.0ms (2.9%)

Algorithm

2×	batch-egg-rewrite

Rules

532×	`log-prod_binary64`
414×	`fma-def_binary64`
231×	`egg-rr`
194×	`expm1-udef_binary64`
194×	`log1p-udef_binary64`

Counts

2 → 231

Calls

2 calls:

75.0ms	(pow.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) 2)
75.0ms	(sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	220	22
2	2626	22
3	4982	22
0	0	0
1	0	0

simplify52.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

536×	`fma-neg_binary64`
477×	`unswap-sqr_binary64`
421×	`associate-r_binary64`
371×	`associate-l_binary64`
321×	`times-frac_binary64`

Counts

263 → 251

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	900
1	206	818
2	645	806
3	3537	806
4	5103	806

prune137.0ms (5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	305	0	305
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	305	2	307

Error

Counts

307 → 2

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (.f64 x y) (.f64 z t))
✓	32.2b	(pow.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) 2)

Compiler

Compiled 6341 to 1560 computations (75.4% saved)

regimes93.0ms (3.4%)

Accuracy

Total -0.0b remaining (-70.9%)

Threshold costs -0.0b (-70.9%)

Counts

12 → 1

Compiler

Compiled 1194 to 778 computations (34.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	13	10
2	15	10
3	16	10
4	16	10

end56.0ms (2.1%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 91 to 59 computations (35.2% saved)

Iter	Nodes	Cost
0	8	10
1	16	10
2	27	10
3	44	10
4	66	10
5	100	10
6	152	10
7	213	10
8	257	10
9	279	10
10	299	10
11	305	10
12	274	10

Iter	Nodes	Cost
0	10	420
1	21	420
2	33	420
3	44	420
4	66	420
5	100	420
6	152	420
7	213	420
8	257	420
9	279	420
10	299	420
11	305	420
12	274	420

Iter	Nodes	Cost
0	8	10
1	16	10
2	27	10
3	44	10
4	66	10
5	100	10
6	152	10
7	213	10
8	257	10
9	279	10
10	299	10
11	305	10
12	274	10

Iter	Nodes	Cost
0	10	420
1	21	420
2	33	420
3	44	420
4	66	420
5	100	420
6	152	420
7	213	420
8	257	420
9	279	420
10	299	420
11	305	420
12	274	420

Details

analyze753.0ms (27.6%)

sample1.0s (37.8%)

simplify15.0ms (0.6%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series9.0ms (0.3%)

rewrite56.0ms (2%)

simplify40.0ms (1.5%)

prune24.0ms (0.9%)

localize7.0ms (0.2%)

series365.0ms (13.4%)

rewrite80.0ms (2.9%)

simplify52.0ms (1.9%)

prune137.0ms (5%)

regimes93.0ms (3.4%)

simplify2.0ms (0.1%)

end56.0ms (2.1%)

Profiling

Iter	Nodes	Cost
0	8	10
1	16	10
2	27	10
3	44	10
4	66	10
5	100	10
6	152	10
7	213	10
8	257	10
9	279	10
10	299	10
11	305	10
12	274	10

Iter	Nodes	Cost
0	10	420
1	21	420
2	33	420
3	44	420
4	66	420
5	100	420
6	152	420
7	213	420
8	257	420
9	279	420
10	299	420
11	305	420
12	274	420