Details

analyze84.0ms (3.8%)

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%	50%	12.6%	6
50%	37.5%	12.6%	7
56.2%	25%	18.8%	8
62.4%	18.7%	18.8%	9
65.6%	12.5%	22%	10
68.7%	9.4%	22%	11
70.2%	6.2%	23.5%	12
71.8%	4.7%	23.5%	13
72.6%	3.1%	24.3%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample757.0ms (34.6%)

Results

712.0ms	8256×	body	128	valid
7.0ms	93×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

15×	`associate-l_binary64`
13×	`associate-r_binary64`
8×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	12	10
2	25	10
3	37	10
4	35	10
5	35	10

prune4.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

10.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	10.7b	(.f64 (.f64 (*.f64 x 3) x) y)

Compiler

Compiled 34 to 22 computations (35.3% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 x 3) x)
✓	10.2b	(.f64 (.f64 (*.f64 x 3) x) y)

series14.0ms (0.6%)

Counts

2 → 36

Calls

2 calls:

9.0ms	(.f64 (.f64 (*.f64 x 3) x) y)
4.0ms	(.f64 (.f64 x 3) x)

rewrite79.0ms (3.6%)

Algorithm

1×	batch-egg-rewrite

Rules

609×	`log1p-expm1-u_binary64`
609×	`expm1-log1p-u_binary64`
370×	`log-prod_binary64`
126×	`expm1-udef_binary64`
126×	`log1p-udef_binary64`

Counts

2 → 36

Calls

2 calls:

78.0ms	(.f64 (.f64 x 3) x)
78.0ms	(.f64 (.f64 (*.f64 x 3) x) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	141	17
2	1620	17
3	4999	17
4	4937	17

simplify154.0ms (7.1%)

Algorithm

1×	egg-herbie

Rules

1104×	`sqr-pow_binary64`
661×	`fabs-mul_binary64`
628×	`pow-sqr_binary64`
611×	`cube-prod_binary64`
323×	`associate-l_binary64`

Counts

72 → 40

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	324
1	19	324
2	39	324
3	80	324
4	191	324
5	540	324
6	636	324
7	873	324
8	898	324
9	1008	324
10	1126	324
11	1293	324
12	1457	324
13	1685	324
14	2019	324
15	2414	324
16	2972	324
17	3656	324
18	3881	324
19	4146	324
20	4238	324
21	4272	324
22	4293	324
23	4976	324

prune42.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	33	7	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	34	7	41

Error

10.5b

Counts

41 → 7

Alt Table

Status	Error	Program
	11.1b	(pow.f64 (cbrt.f64 (.f64 (.f64 x (*.f64 x 3)) y)) 3)
	36.3b	(pow.f64 (pow.f64 (.f64 (.f64 x (*.f64 x 3)) y) 3) 1/3)
▶	10.6b	(.f64 (.f64 3 (pow.f64 x 2)) y)
	10.7b	(.f64 3 (.f64 y (pow.f64 x 2)))
	10.8b	(.f64 (pow.f64 (sqrt.f64 (.f64 x (*.f64 x 3))) 2) y)
	31.5b	(.f64 (cbrt.f64 (pow.f64 (.f64 x (*.f64 x 3)) 3)) y)
	25.3b	(pow.f64 (sqrt.f64 (.f64 (.f64 x (*.f64 x 3)) y)) 2)

Compiler

Compiled 610 to 427 computations (30% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 3 (pow.f64 x 2))
✓	10.2b	(.f64 (.f64 3 (pow.f64 x 2)) y)

series14.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

11.0ms	(.f64 (.f64 3 (pow.f64 x 2)) y)
2.0ms	(*.f64 3 (pow.f64 x 2))

rewrite69.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

627×	`log1p-expm1-u_binary64`
627×	`expm1-log1p-u_binary64`
351×	`log-prod_binary64`
133×	`expm1-udef_binary64`
133×	`log1p-udef_binary64`

Counts

2 → 34

Calls

2 calls:

68.0ms	(*.f64 3 (pow.f64 x 2))
68.0ms	(.f64 (.f64 3 (pow.f64 x 2)) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	164	17
2	1672	17
3	4994	17
4	4895	17

simplify153.0ms (7%)

Algorithm

1×	egg-herbie

Rules

1104×	`sqr-pow_binary64`
661×	`fabs-mul_binary64`
628×	`pow-sqr_binary64`
611×	`cube-prod_binary64`
310×	`cube-mult_binary64`

Counts

58 → 36

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	240
1	17	240
2	35	240
3	70	240
4	167	240
5	475	240
6	586	240
7	823	240
8	848	240
9	958	240
10	1076	240
11	1243	240
12	1407	240
13	1635	240
14	1969	240
15	2364	240
16	2922	240
17	3606	240
18	3831	240
19	4096	240
20	4188	240
21	4222	240
22	4243	240
23	4926	240

prune34.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	33	3	36
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	36	7	43

Error

4.5b

Counts

43 → 7

Alt Table

Status	Error	Program
	29.4b	(pow.f64 (.f64 (.f64 x (sqrt.f64 3)) (sqrt.f64 y)) 2)
✓	10.6b	(.f64 (.f64 3 (pow.f64 x 2)) y)
	11.1b	(pow.f64 (cbrt.f64 (.f64 (.f64 x (*.f64 x 3)) y)) 3)
	10.8b	(.f64 (pow.f64 (.f64 x (sqrt.f64 3)) 2) y)
▶	10.7b	(.f64 3 (.f64 y (pow.f64 x 2)))
	23.9b	(.f64 (sqrt.f64 (.f64 9 (pow.f64 x 4))) y)
	25.3b	(pow.f64 (sqrt.f64 (.f64 (.f64 x (*.f64 x 3)) y)) 2)

Compiler

Compiled 546 to 361 computations (33.9% saved)

localize20.0ms (0.9%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 3 (.f64 y (pow.f64 x 2)))
✓	10.2b	(*.f64 y (pow.f64 x 2))

series18.0ms (0.8%)

Counts

2 → 0

Calls

2 calls:

11.0ms	(.f64 3 (.f64 y (pow.f64 x 2)))
7.0ms	(*.f64 y (pow.f64 x 2))

rewrite72.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

625×	`log1p-expm1-u_binary64`
625×	`expm1-log1p-u_binary64`
352×	`log-prod_binary64`
133×	`expm1-udef_binary64`
133×	`log1p-udef_binary64`

Counts

2 → 34

Calls

2 calls:

72.0ms	(.f64 3 (.f64 y (pow.f64 x 2)))
72.0ms	(*.f64 y (pow.f64 x 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	164	17
2	1668	17
3	4980	17
4	4939	17

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune37.0ms (1.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	31	3	34
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	32	9	41

Error

4.4b

Counts

41 → 9

Alt Table

Status	Error	Program
	29.4b	(pow.f64 (.f64 (.f64 x (sqrt.f64 3)) (sqrt.f64 y)) 2)
✓	10.6b	(.f64 (.f64 3 (pow.f64 x 2)) y)
	29.3b	(pow.f64 (.f64 (sqrt.f64 (.f64 y 3)) x) 2)
	23.9b	(.f64 (sqrt.f64 (.f64 9 (pow.f64 x 4))) y)
	11.1b	(pow.f64 (cbrt.f64 (.f64 (.f64 x (*.f64 x 3)) y)) 3)
▶	10.8b	(.f64 (pow.f64 (.f64 x (sqrt.f64 3)) 2) y)
✓	10.7b	(.f64 3 (.f64 y (pow.f64 x 2)))
	41.7b	(.f64 3 (log.f64 (pow.f64 (exp.f64 y) (.f64 x x))))
	29.3b	(.f64 3 (pow.f64 (.f64 x (sqrt.f64 y)) 2))

Compiler

Compiled 562 to 322 computations (42.7% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (*.f64 x (sqrt.f64 3)) 2)
✓	0.3b	(*.f64 x (sqrt.f64 3))
✓	10.2b	(.f64 (pow.f64 (.f64 x (sqrt.f64 3)) 2) y)

series33.0ms (1.5%)

Counts

3 → 48

Calls

3 calls:

25.0ms	(.f64 (pow.f64 (.f64 x (sqrt.f64 3)) 2) y)
5.0ms	(pow.f64 (*.f64 x (sqrt.f64 3)) 2)
3.0ms	(*.f64 x (sqrt.f64 3))

rewrite71.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

684×	`log1p-expm1-u_binary64`
684×	`expm1-log1p-u_binary64`
376×	`log-prod_binary64`
144×	`expm1-udef_binary64`
144×	`log1p-udef_binary64`

Counts

3 → 65

Calls

3 calls:

70.0ms	(pow.f64 (*.f64 x (sqrt.f64 3)) 2)
70.0ms	(*.f64 x (sqrt.f64 3))
70.0ms	(.f64 (pow.f64 (.f64 x (sqrt.f64 3)) 2) y)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	184	23
2	1827	23
3	5292	23

simplify181.0ms (8.3%)

Algorithm

1×	egg-herbie

Rules

806×	`fabs-mul_binary64`
785×	`sqr-pow_binary64`
759×	`cube-prod_binary64`
666×	`pow-sqr_binary64`
617×	`unswap-sqr_binary64`

Counts

113 → 69

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	576
1	24	396
2	50	396
3	135	396
4	489	396
5	680	396
6	1160	396
7	1254	396
8	1393	396
9	1537	396
10	1703	396
11	1879	396
12	1914	396
13	2150	396
14	2578	396
15	3104	396
16	3805	396
17	4080	396
18	4393	396
19	4641	396
20	4734	396
21	4752	396
22	4957	396

prune65.0ms (3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	69	9	78

Error

4.4b

Counts

78 → 9

Alt Table

Status	Error	Program
	29.4b	(pow.f64 (.f64 (.f64 x (sqrt.f64 3)) (sqrt.f64 y)) 2)
✓	10.6b	(.f64 (.f64 3 (pow.f64 x 2)) y)
	29.3b	(pow.f64 (.f64 (sqrt.f64 (.f64 y 3)) x) 2)
	23.9b	(.f64 (sqrt.f64 (.f64 9 (pow.f64 x 4))) y)
	11.1b	(pow.f64 (cbrt.f64 (.f64 (.f64 x (*.f64 x 3)) y)) 3)
✓	10.8b	(.f64 (pow.f64 (.f64 x (sqrt.f64 3)) 2) y)
✓	10.7b	(.f64 3 (.f64 y (pow.f64 x 2)))
	41.7b	(.f64 3 (log.f64 (pow.f64 (exp.f64 y) (.f64 x x))))
	29.3b	(.f64 3 (pow.f64 (.f64 x (sqrt.f64 y)) 2))

Compiler

Compiled 920 to 630 computations (31.5% saved)

regimes120.0ms (5.5%)

Accuracy

Total 0.5b remaining (9.1%)

Threshold costs 0.5b (9.1%)

Counts

19 → 2

Compiler

Compiled 976 to 674 computations (30.9% saved)

bsearch12.0ms (0.6%)

Steps

Iters	Range		Point
6	1.8341727165077139e-299	1.6919668269795723e-298	3.271832721285948e-299

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	28
1	20	28
2	20	28

end122.0ms (5.6%)

Compiler: Compiled 134 to 104 computations (22.4% saved)

Details

analyze84.0ms (3.8%)

sample757.0ms (34.6%)

simplify7.0ms (0.3%)

prune4.0ms (0.2%)

localize4.0ms (0.2%)

series14.0ms (0.6%)

rewrite79.0ms (3.6%)

simplify154.0ms (7.1%)

prune42.0ms (1.9%)

localize4.0ms (0.2%)

series14.0ms (0.6%)

rewrite69.0ms (3.2%)

simplify153.0ms (7%)

prune34.0ms (1.6%)

localize20.0ms (0.9%)

series18.0ms (0.8%)

rewrite72.0ms (3.3%)

simplify6.0ms (0.3%)

prune37.0ms (1.7%)

localize6.0ms (0.3%)

series33.0ms (1.5%)

rewrite71.0ms (3.3%)

simplify181.0ms (8.3%)

prune65.0ms (3%)

regimes120.0ms (5.5%)

bsearch12.0ms (0.6%)

simplify3.0ms (0.1%)

end122.0ms (5.6%)

Profiling