Details

analyze664.0ms (12.1%)

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
49.1%	50.7%	0.2%	9
49.5%	50.3%	0.2%	10
49.7%	50.1%	0.2%	11
50.2%	49.6%	0.2%	12
60.5%	39.3%	0.2%	13
60.6%	37.9%	1.4%	14

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample1.3s (23.3%)

Symmetry

(sort x y)

Results

869.0ms	8256×	body	128	valid
293.0ms	2756×	body	128	invalid

Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify162.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

1491×	`fma-neg_binary64`
579×	`fma-def_binary64`
465×	`distribute-rgt-in_binary64`
419×	`div-sub_binary64`
329×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	21	13
2	45	13
3	70	13
4	138	13
5	257	13
6	498	13
7	922	13
8	1615	13
9	2472	13
10	2435	13
11	2431	13
12	2427	13
13	2428	13
14	2428	13
15	3596	13
16	3260	13
17	3260	13
18	3260	13
19	3140	13

prune2.0ms (0%)

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 (+.f64 x y) z) (*.f64 t 2))

Compiler

Compiled 39 to 27 computations (30.8% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))

series22.0ms (0.4%)

Counts

1 → 48

Calls

1 calls:

22.0ms

(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))

rewrite67.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

444×	`fma-def_binary64`
245×	`fma-neg_binary64`
221×	`expm1-udef_binary64`
221×	`log1p-udef_binary64`
121×	`add-sqr-sqrt_binary64`

Counts

1 → 60

Calls

1 calls:

65.0ms

(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	232	13
2	3405	13
3	4938	13
0	0	0
1	0	0

simplify166.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1151×	`fma-def_binary64`
848×	`fma-neg_binary64`
388×	`div-sub_binary64`
364×	`distribute-rgt-in_binary64`
354×	`unsub-neg_binary64`

Counts

108 → 73

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	930
1	104	735
2	235	696
3	464	579
4	952	579
5	1743	579
6	2112	579
7	2085	579
8	2099	579
9	2102	579
10	2103	579
11	3326	579
12	2878	579
13	2878	579
14	2878	579
15	2782	579

prune47.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	70	4	74

Error

Counts

74 → 4

Alt Table

Status	Error	Program
	33.8b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))) 2)
	34.8b	(.f64 (/.f64 1 (sqrt.f64 (.f64 t 2))) (/.f64 (-.f64 (+.f64 x y) z) (sqrt.f64 (*.f64 t 2))))
▶	0.0b	(-.f64 (/.f64 (+.f64 x y) (.f64 t 2)) (/.f64 z (.f64 t 2)))
✓	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))

Compiler

Compiled 1257 to 646 computations (48.6% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (+.f64 x y) (.f64 t 2)) (/.f64 z (.f64 t 2)))
✓	0.0b	(/.f64 (+.f64 x y) (*.f64 t 2))

series43.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

32.0ms	(-.f64 (/.f64 (+.f64 x y) (.f64 t 2)) (/.f64 z (.f64 t 2)))
11.0ms	(/.f64 (+.f64 x y) (*.f64 t 2))

rewrite88.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

355×	`fma-neg_binary64`
247×	`expm1-udef_binary64`
247×	`log1p-udef_binary64`
135×	`add-sqr-sqrt_binary64`
130×	`egg-rr`

Counts

2 → 130

Calls

2 calls:

85.0ms	(-.f64 (/.f64 (+.f64 x y) (.f64 t 2)) (/.f64 z (.f64 t 2)))
85.0ms	(/.f64 (+.f64 x y) (*.f64 t 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	259	23
2	4036	23
3	5141	23
0	0	0
1	0	0

simplify204.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

1144×	`fma-def_binary64`
852×	`fma-neg_binary64`
409×	`distribute-rgt-in_binary64`
358×	`unsub-neg_binary64`
350×	`distribute-lft-in_binary64`

Counts

214 → 148

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	1371
1	88	1254
2	212	1020
3	441	921
4	892	921
5	1700	921
6	2258	921
7	2078	921
8	2087	921
9	2090	921
10	2091	921
11	2822	921
12	3214	921
13	2878	921
14	2878	921
15	2878	921
16	2782	921

prune87.0ms (1.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	148	4	152

Error

Counts

152 → 4

Alt Table

Status	Error	Program
	34.8b	(/.f64 (/.f64 (-.f64 (+.f64 x y) z) (sqrt.f64 (.f64 t 2))) (sqrt.f64 (.f64 t 2)))
▶	33.8b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))) 2)
✓	0.0b	(-.f64 (/.f64 (+.f64 x y) (.f64 t 2)) (/.f64 z (.f64 t 2)))
✓	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))

Compiler

Compiled 2862 to 1560 computations (45.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))
✓	0.3b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))) 2)
✓	1.5b	(sqrt.f64 (/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2)))

series1.4s (25.7%)

Counts

2 → 24

Calls

2 calls:

1.0s	(pow.f64 (sqrt.f64 (/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))) 2)
363.0ms	(sqrt.f64 (/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2)))

rewrite71.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

455×	`fma-def_binary64`
248×	`fma-neg_binary64`
234×	`expm1-udef_binary64`
234×	`log1p-udef_binary64`
129×	`add-sqr-sqrt_binary64`

Counts

2 → 116

Calls

2 calls:

69.0ms	(pow.f64 (sqrt.f64 (/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))) 2)
69.0ms	(sqrt.f64 (/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	258	28
2	3635	28
3	4979	28
0	0	0
1	0	0

simplify70.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

804×	`fma-neg_binary64`
525×	`associate-r_binary64`
490×	`associate-l_binary64`
382×	`fma-def_binary64`
263×	`*-commutative_binary64`

Counts

140 → 146

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	1055
1	356	843
2	995	791
3	3624	789
4	4931	789
5	4977	789

prune112.0ms (2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	219	0	219
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	219	4	223

Error

Counts

223 → 4

Alt Table

Status	Error	Program
▶	34.8b	(/.f64 (/.f64 (-.f64 (+.f64 x y) z) (sqrt.f64 (.f64 t 2))) (sqrt.f64 (.f64 t 2)))
✓	33.8b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))) 2)
✓	0.0b	(-.f64 (/.f64 (+.f64 x y) (.f64 t 2)) (/.f64 z (.f64 t 2)))
✓	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))

Compiler

Compiled 4455 to 2412 computations (45.9% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (+.f64 x y) z) (sqrt.f64 (*.f64 t 2)))
✓	0.2b	(/.f64 (/.f64 (-.f64 (+.f64 x y) z) (sqrt.f64 (.f64 t 2))) (sqrt.f64 (.f64 t 2)))

series195.0ms (3.5%)

Counts

2 → 80

Calls

2 calls:

128.0ms	(/.f64 (/.f64 (-.f64 (+.f64 x y) z) (sqrt.f64 (.f64 t 2))) (sqrt.f64 (.f64 t 2)))
67.0ms	(/.f64 (-.f64 (+.f64 x y) z) (sqrt.f64 (*.f64 t 2)))

rewrite82.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

256×	`fma-neg_binary64`
254×	`expm1-udef_binary64`
254×	`log1p-udef_binary64`
140×	`add-sqr-sqrt_binary64`
135×	`log1p-expm1-u_binary64`

Counts

2 → 110

Calls

2 calls:

79.0ms	(/.f64 (-.f64 (+.f64 x y) z) (sqrt.f64 (*.f64 t 2)))
79.0ms	(/.f64 (/.f64 (-.f64 (+.f64 x y) z) (sqrt.f64 (.f64 t 2))) (sqrt.f64 (.f64 t 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	275	28
2	4006	28
3	4995	28
0	0	0
1	0	0

simplify108.0ms (2%)

Algorithm

1×	egg-herbie

Rules

452×	`associate-/l/_binary64`
421×	`fma-neg_binary64`
389×	`neg-mul-1_binary64`
372×	`fma-def_binary64`
365×	`times-frac_binary64`

Counts

190 → 137

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	42	2463
1	111	1713
2	241	1551
3	511	1416
4	1398	1206
5	3611	1206
6	4863	1206
7	5090	1206

prune77.0ms (1.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	137	4	141

Error

Counts

141 → 4

Alt Table

Status	Error	Program
✓	34.8b	(/.f64 (/.f64 (-.f64 (+.f64 x y) z) (sqrt.f64 (.f64 t 2))) (sqrt.f64 (.f64 t 2)))
✓	33.8b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))) 2)
✓	0.0b	(-.f64 (/.f64 (+.f64 x y) (.f64 t 2)) (/.f64 z (.f64 t 2)))
✓	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))

Compiler

Compiled 2733 to 1584 computations (42% saved)

regimes440.0ms (8%)

Accuracy

Total 0.1b remaining (62.7%)

Threshold costs 0.1b (62.7%)

Counts

51 → 1

Compiler

Compiled 6305 to 4688 computations (25.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	14	16
2	21	16
3	25	16
4	28	16
5	29	16
6	29	16

end69.0ms (1.3%)

Remove: (sort x y)
Compiler: Compiled 125 to 87 computations (30.4% saved)

Details

analyze664.0ms (12.1%)

sample1.3s (23.3%)

simplify162.0ms (2.9%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series22.0ms (0.4%)

rewrite67.0ms (1.2%)

simplify166.0ms (3%)

prune47.0ms (0.9%)

localize8.0ms (0.2%)

series43.0ms (0.8%)

rewrite88.0ms (1.6%)

simplify204.0ms (3.7%)

prune87.0ms (1.6%)

localize8.0ms (0.1%)

series1.4s (25.7%)

rewrite71.0ms (1.3%)

simplify70.0ms (1.3%)

prune112.0ms (2%)

localize9.0ms (0.2%)

series195.0ms (3.5%)

rewrite82.0ms (1.5%)

simplify108.0ms (2%)

prune77.0ms (1.4%)

regimes440.0ms (8%)

simplify2.0ms (0%)

end69.0ms (1.3%)

Profiling