Details

analyze721.0ms (13.4%)

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
12.5%	87.4%	0.1%	7
25%	74.9%	0.1%	8
31.2%	64%	4.8%	9
31.2%	42.1%	26.7%	10
35.9%	37.1%	27.1%	11
38.2%	32.2%	29.6%	12
47.8%	21.6%	30.6%	13
50.2%	19%	30.8%	14

Compiler

Compiled 19 to 9 computations (52.6% saved)

sample1.9s (35.1%)

Symmetry

(sort x y)

Results

1.5s	8256×	body	128	valid
301.0ms	493×	body	128	invalid

Compiler

Compiled 56 to 26 computations (53.6% saved)

simplify15.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

32×	`fma-def_binary64`
5×	`*-commutative_binary64`
4×	`associate-+l+_binary64`
4×	`associate-r_binary64`
3×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	17	15
2	34	11
3	54	11
4	68	11
5	72	11
6	70	11

prune7.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
▶	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))

Compiler

Compiled 84 to 41 computations (51.2% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series61.0ms (1.1%)

Counts

3 → 108

Calls

3 calls:

23.0ms	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))
21.0ms	(+.f64 (+.f64 (.f64 x y) (.f64 z z)) (*.f64 z z))
16.0ms	(+.f64 (.f64 x y) (.f64 z z))

rewrite123.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

853×	`fma-def_binary64`
351×	`fma-neg_binary64`
237×	`egg-rr`
197×	`expm1-udef_binary64`
197×	`log1p-udef_binary64`

Counts

3 → 237

Calls

3 calls:

113.0ms	(+.f64 (+.f64 (.f64 x y) (.f64 z z)) (*.f64 z z))
113.0ms	(+.f64 (.f64 x y) (.f64 z z))
113.0ms	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	42
1	210	34
2	2947	34
3	4975	34
0	0	0
1	0	0

simplify304.0ms (5.6%)

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

345 → 250

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	942
1	27	942
2	49	942
3	80	942
4	154	942
5	367	942
6	484	942
7	724	942
8	759	942
9	869	942
10	987	942
11	1152	942
12	1312	942
13	1539	942
14	1872	942
15	2266	942
16	2824	942
17	3508	942
18	3733	942
19	3998	942
20	4090	942
21	4124	942
22	4145	942
23	4828	942

prune250.0ms (4.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	248	2	250
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	249	3	252

Error

Counts

252 → 3

Alt Table

Status	Error	Program
	1.2b	(pow.f64 (cbrt.f64 (fma.f64 x y (fma.f64 z z (.f64 (.f64 z z) 2)))) 3)
	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
▶	0.0b	(fma.f64 z z (fma.f64 x y (.f64 (.f64 z z) 2)))

Compiler

Compiled 4972 to 1707 computations (65.7% saved)

localize14.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 z z) 2)
✓	0.0b	(fma.f64 z z (fma.f64 x y (.f64 (.f64 z z) 2)))

series30.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

26.0ms	(fma.f64 z z (fma.f64 x y (.f64 (.f64 z z) 2)))
4.0ms	(.f64 (.f64 z z) 2)

rewrite84.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

749×	`log1p-expm1-u_binary64`
749×	`expm1-log1p-u_binary64`
263×	`prod-diff_binary64`
89×	`add-sqr-sqrt_binary64`
83×	`add-log-exp_binary64`

Counts

2 → 36

Calls

2 calls:

83.0ms	(.f64 (.f64 z z) 2)
83.0ms	(fma.f64 z z (fma.f64 x y (.f64 (.f64 z z) 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	180	22
2	1968	22
3	5087	22
0	0	0
1	0	0

simplify206.0ms (3.8%)

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

84 → 43

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	429
1	21	429
2	38	429
3	67	429
4	137	429
5	344	429
6	449	429
7	686	429
8	711	429
9	821	429
10	939	429
11	1106	429
12	1270	429
13	1498	429
14	1832	429
15	2227	429
16	2785	429
17	3469	429
18	3694	429
19	3959	429
20	4051	429
21	4085	429
22	4106	429
23	4789	429

prune63.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	42	1	43
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	43	3	46

Error

Counts

46 → 3

Alt Table

Status	Error	Program
	0.3b	(fma.f64 z z (fma.f64 x y (pow.f64 (*.f64 z (sqrt.f64 2)) 2)))
▶	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
✓	0.0b	(fma.f64 z z (fma.f64 x y (.f64 (.f64 z z) 2)))

Compiler

Compiled 689 to 349 computations (49.3% saved)

localize10.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))

series139.0ms (2.6%)

Counts

1 → 36

Calls

1 calls:

139.0ms

(fma.f64 z (*.f64 z 3) (*.f64 x y))

rewrite180.0ms (3.3%)

Algorithm

2×	batch-egg-rewrite

Rules

678×	`log1p-expm1-u_binary64`
678×	`expm1-log1p-u_binary64`
191×	`prod-diff_binary64`
144×	`expm1-udef_binary64`
144×	`log1p-udef_binary64`

Counts

1 → 23

Calls

1 calls:

179.0ms

(fma.f64 z (*.f64 z 3) (*.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	159	11
2	1785	11
3	4975	11
0	0	0
1	0	0

simplify224.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
573×	`fabs-mul_binary64`
560×	`cube-prod_binary64`
536×	`pow-sqr_binary64`
454×	`associate-l_binary64`

Counts

59 → 28

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	345
1	19	345
2	32	345
3	53	345
4	101	345
5	238	345
6	718	345
7	1143	345
8	1145	345
9	1293	345
10	1463	345
11	1645	345
12	1868	345
13	2153	345
14	2572	345
15	3137	345
16	3823	345
17	4041	345
18	4285	345
19	4367	345
20	4400	345
21	4421	345
22	4990	345

prune31.0ms (0.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	28	3	31

Error

Counts

31 → 3

Alt Table

Status	Error	Program
▶	0.3b	(fma.f64 z z (fma.f64 x y (pow.f64 (*.f64 z (sqrt.f64 2)) 2)))
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
✓	0.0b	(fma.f64 z z (fma.f64 x y (.f64 (.f64 z z) 2)))

Compiler

Compiled 408 to 226 computations (44.6% saved)

localize14.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z z (fma.f64 x y (pow.f64 (*.f64 z (sqrt.f64 2)) 2)))
✓	0.4b	(pow.f64 (*.f64 z (sqrt.f64 2)) 2)
✓	0.5b	(*.f64 z (sqrt.f64 2))

series106.0ms (2%)

Counts

3 → 60

Calls

3 calls:

57.0ms	(*.f64 z (sqrt.f64 2))
40.0ms	(fma.f64 z z (fma.f64 x y (pow.f64 (*.f64 z (sqrt.f64 2)) 2)))
9.0ms	(pow.f64 (*.f64 z (sqrt.f64 2)) 2)

rewrite84.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

813×	`log1p-expm1-u_binary64`
813×	`expm1-log1p-u_binary64`
224×	`prod-diff_binary64`
96×	`add-sqr-sqrt_binary64`
90×	`add-log-exp_binary64`

Counts

3 → 65

Calls

3 calls:

81.0ms	(fma.f64 z z (fma.f64 x y (pow.f64 (*.f64 z (sqrt.f64 2)) 2)))
81.0ms	(pow.f64 (*.f64 z (sqrt.f64 2)) 2)
81.0ms	(*.f64 z (sqrt.f64 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	32
1	203	28
2	2132	28
3	5382	28
0	0	0
1	0	0

simplify274.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

790×	`fabs-mul_binary64`
763×	`sqr-pow_binary64`
742×	`cube-prod_binary64`
617×	`unswap-sqr_binary64`
466×	`fma-def_binary64`

Counts

125 → 73

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	809
1	35	501
2	75	501
3	164	501
4	431	501
5	706	501
6	1229	501
7	1275	501
8	1400	501
9	1530	501
10	1688	501
11	1849	501
12	2055	501
13	2290	501
14	2718	501
15	3244	501
16	3945	501
17	4220	501
18	4533	501
19	4781	501
20	4863	501

prune93.0ms (1.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	73	3	76

Error

Counts

76 → 3

Alt Table

Status	Error	Program
✓	0.3b	(fma.f64 z z (fma.f64 x y (pow.f64 (*.f64 z (sqrt.f64 2)) 2)))
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
✓	0.0b	(fma.f64 z z (fma.f64 x y (.f64 (.f64 z z) 2)))

Compiler

Compiled 1168 to 648 computations (44.5% saved)

regimes328.0ms (6.1%)

Accuracy

Total 0.0b remaining (74.9%)

Threshold costs 0.0b (74.9%)

Counts

26 → 1

Compiler

Compiled 2384 to 1515 computations (36.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	10	15
2	10	15

end119.0ms (2.2%)

Remove: (sort x y)
Compiler: Compiled 96 to 57 computations (40.6% saved)

Details

analyze721.0ms (13.4%)

sample1.9s (35.1%)

simplify15.0ms (0.3%)

prune7.0ms (0.1%)

localize12.0ms (0.2%)

series61.0ms (1.1%)

rewrite123.0ms (2.3%)

simplify304.0ms (5.6%)

prune250.0ms (4.6%)

localize14.0ms (0.3%)

series30.0ms (0.6%)

rewrite84.0ms (1.6%)

simplify206.0ms (3.8%)

prune63.0ms (1.2%)

localize10.0ms (0.2%)

series139.0ms (2.6%)

rewrite180.0ms (3.3%)

simplify224.0ms (4.2%)

prune31.0ms (0.6%)

localize14.0ms (0.3%)

series106.0ms (2%)

rewrite84.0ms (1.6%)

simplify274.0ms (5.1%)

prune93.0ms (1.7%)

regimes328.0ms (6.1%)

simplify4.0ms (0.1%)

end119.0ms (2.2%)

Profiling