Details

analyze665.0ms (19.2%)

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)

sample920.0ms (26.6%)

Symmetry

(sort x y)

Results

837.0ms	8256×	body	128	valid
48.0ms	500×	body	128	invalid

Compiler

Compiled 56 to 26 computations (53.6% saved)

simplify7.0ms (0.2%)

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

prune3.0ms (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)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series32.0ms (0.9%)

Counts

3 → 108

Calls

3 calls:

15.0ms	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))
10.0ms	(+.f64 (+.f64 (.f64 x y) (.f64 z z)) (*.f64 z z))
7.0ms	(+.f64 (.f64 x y) (.f64 z z))

rewrite79.0ms (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:

74.0ms	(+.f64 (.f64 x y) (.f64 z z))
74.0ms	(+.f64 (+.f64 (.f64 x y) (.f64 z z)) (*.f64 z z))
74.0ms	(+.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

simplify193.0ms (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

prune182.0ms (5.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	245	5	250
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	246	6	252

Error

Counts

252 → 6

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 x y (fma.f64 z z (.f64 (.f64 z z) 2)))
	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
	0.2b	(fma.f64 (hypot.f64 z z) (hypot.f64 z z) (fma.f64 x y (*.f64 z z)))
	1.1b	(fma.f64 (cbrt.f64 (fma.f64 x y (.f64 (.f64 z z) 2))) (pow.f64 (cbrt.f64 (fma.f64 x y (.f64 (.f64 z z) 2))) 2) (*.f64 z z))
	11.7b	(fma.f64 (pow.f64 (cbrt.f64 z) 2) (+.f64 (cbrt.f64 (pow.f64 z 4)) (cbrt.f64 (pow.f64 z 4))) (fma.f64 x y (*.f64 z z)))
	29.5b	(pow.f64 (hypot.f64 z (hypot.f64 z (hypot.f64 z (sqrt.f64 (*.f64 x y))))) 2)

Compiler

Compiled 5100 to 1781 computations (65.1% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (fma.f64 z z (.f64 (.f64 z z) 2)))
✓	0.1b	(fma.f64 z z (.f64 (.f64 z z) 2))

series15.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(fma.f64 x y (fma.f64 z z (.f64 (.f64 z z) 2)))
3.0ms	(fma.f64 z z (.f64 (.f64 z z) 2))

rewrite49.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

2 → 50

Calls

2 calls:

48.0ms	(fma.f64 x y (fma.f64 z z (.f64 (.f64 z z) 2)))
48.0ms	(fma.f64 z z (.f64 (.f64 z z) 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	180	18
2	1971	18
3	5220	18
0	0	0
1	0	0

simplify184.0ms (5.3%)

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

98 → 54

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	429
1	19	429
2	32	429
3	53	429
4	101	429
5	238	429
6	718	429
7	1143	429
8	1145	429
9	1293	429
10	1463	429
11	1645	429
12	1868	429
13	2153	429
14	2572	429
15	3137	429
16	3823	429
17	4041	429
18	4285	429
19	4367	429
20	4400	429
21	4421	429
22	4990	429

prune49.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	51	3	54
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	54	6	60

Error

Counts

60 → 6

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 x y (fma.f64 z z (.f64 (.f64 z z) 2)))
	0.5b	(fma.f64 x y (.f64 (cbrt.f64 (.f64 (.f64 z z) 3)) (pow.f64 (cbrt.f64 (.f64 (*.f64 z z) 3)) 2)))
▶	0.1b	(fma.f64 x y (.f64 z (+.f64 z (.f64 z 2))))
	0.2b	(fma.f64 (hypot.f64 z z) (hypot.f64 z z) (fma.f64 x y (*.f64 z z)))
	1.1b	(fma.f64 (cbrt.f64 (fma.f64 x y (.f64 (.f64 z z) 2))) (pow.f64 (cbrt.f64 (fma.f64 x y (.f64 (.f64 z z) 2))) 2) (*.f64 z z))
	0.3b	(fma.f64 x y (pow.f64 (hypot.f64 z (*.f64 z (sqrt.f64 2))) 2))

Compiler

Compiled 886 to 466 computations (47.4% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (.f64 z (+.f64 z (.f64 z 2))))
✓	0.2b	(.f64 z (+.f64 z (.f64 z 2)))

series12.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(fma.f64 x y (.f64 z (+.f64 z (.f64 z 2))))
2.0ms	(.f64 z (+.f64 z (.f64 z 2)))

rewrite60.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

467×	`log-prod_binary64`
333×	`fma-def_binary64`
253×	`pow2_binary64`
177×	`pow1/3_binary64`
175×	`expm1-udef_binary64`

Counts

2 → 87

Calls

2 calls:

58.0ms	(fma.f64 x y (.f64 z (+.f64 z (.f64 z 2))))
58.0ms	(.f64 z (+.f64 z (.f64 z 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	193	18
2	2390	18
3	4955	18
0	0	0
1	0	0

simplify173.0ms (5%)

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

135 → 92

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	429
1	19	429
2	32	429
3	53	429
4	101	429
5	238	429
6	718	429
7	1143	429
8	1145	429
9	1293	429
10	1463	429
11	1645	429
12	1868	429
13	2153	429
14	2572	429
15	3137	429
16	3823	429
17	4041	429
18	4285	429
19	4367	429
20	4400	429
21	4421	429
22	4990	429

prune83.0ms (2.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	92	6	98

Error

Counts

98 → 6

Alt Table

Status	Error	Program
	7.8b	(fma.f64 x y (/.f64 (.f64 (.f64 (.f64 z 3) (.f64 z -1)) z) (*.f64 z -1)))
▶	0.2b	(fma.f64 (hypot.f64 z z) (hypot.f64 z z) (fma.f64 x y (*.f64 z z)))
✓	0.0b	(fma.f64 x y (fma.f64 z z (.f64 (.f64 z z) 2)))
✓	0.1b	(fma.f64 x y (.f64 z (+.f64 z (.f64 z 2))))
	0.4b	(fma.f64 x y (fma.f64 (pow.f64 (cbrt.f64 (.f64 z (+.f64 z z))) 2) (cbrt.f64 (.f64 z (+.f64 z z))) (*.f64 z z)))
	0.3b	(fma.f64 x y (pow.f64 (hypot.f64 z (*.f64 z (sqrt.f64 2))) 2))

Compiler

Compiled 1500 to 687 computations (54.2% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series36.0ms (1%)

Counts

3 → 84

Calls

3 calls:

26.0ms	(fma.f64 (hypot.f64 z z) (hypot.f64 z z) (fma.f64 x y (*.f64 z z)))
7.0ms	(fma.f64 x y (*.f64 z z))
3.0ms	(hypot.f64 z z)

rewrite51.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

676×	`log1p-expm1-u_binary64`
676×	`expm1-log1p-u_binary64`
308×	`prod-diff_binary64`
142×	`expm1-udef_binary64`
142×	`log1p-udef_binary64`

Counts

3 → 68

Calls

3 calls:

50.0ms	(fma.f64 x y (*.f64 z z))
50.0ms	(hypot.f64 z z)
50.0ms	(fma.f64 (hypot.f64 z z) (hypot.f64 z z) (fma.f64 x y (*.f64 z z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	30
1	159	29
2	1769	29
3	5112	29
0	0	0
1	0	0

simplify120.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

940×	`fma-def_binary64`
617×	`unswap-sqr_binary64`
538×	`fma-neg_binary64`
313×	`distribute-rgt-in_binary64`
308×	`distribute-rgt-neg-in_binary64`

Counts

152 → 82

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	925
1	43	677
2	94	677
3	204	677
4	548	677
5	918	677
6	1619	677
7	2233	677
8	3117	677
9	3784	677
10	4301	677
11	4791	677
12	4795	677

prune75.0ms (2.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	106	6	112

Error

Counts

112 → 6

Alt Table

Status	Error	Program
	7.8b	(fma.f64 x y (/.f64 (.f64 (.f64 (.f64 z 3) (.f64 z -1)) z) (*.f64 z -1)))
✓	0.2b	(fma.f64 (hypot.f64 z z) (hypot.f64 z z) (fma.f64 x y (*.f64 z z)))
✓	0.0b	(fma.f64 x y (fma.f64 z z (.f64 (.f64 z z) 2)))
✓	0.1b	(fma.f64 x y (.f64 z (+.f64 z (.f64 z 2))))
	0.4b	(fma.f64 x y (fma.f64 (pow.f64 (cbrt.f64 (.f64 z (+.f64 z z))) 2) (cbrt.f64 (.f64 z (+.f64 z z))) (*.f64 z z)))
	0.3b	(fma.f64 x y (pow.f64 (hypot.f64 z (*.f64 z (sqrt.f64 2))) 2))

Compiler

Compiled 1841 to 431 computations (76.6% saved)

regimes351.0ms (10.1%)

Accuracy

Total 0.0b remaining (85.2%)

Threshold costs 0.0b (85.2%)

Counts

57 → 1

Compiler

Compiled 5714 to 3584 computations (37.3% 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

end84.0ms (2.4%)

Remove: (sort x y)
Compiler: Compiled 156 to 89 computations (42.9% saved)

Details

analyze665.0ms (19.2%)

sample920.0ms (26.6%)

simplify7.0ms (0.2%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series32.0ms (0.9%)

rewrite79.0ms (2.3%)

simplify193.0ms (5.6%)

prune182.0ms (5.3%)

localize7.0ms (0.2%)

series15.0ms (0.4%)

rewrite49.0ms (1.4%)

simplify184.0ms (5.3%)

prune49.0ms (1.4%)

localize6.0ms (0.2%)

series12.0ms (0.4%)

rewrite60.0ms (1.7%)

simplify173.0ms (5%)

prune83.0ms (2.4%)

localize10.0ms (0.3%)

series36.0ms (1%)

rewrite51.0ms (1.5%)

simplify120.0ms (3.5%)

prune75.0ms (2.2%)

regimes351.0ms (10.1%)

simplify4.0ms (0.1%)

end84.0ms (2.4%)

Profiling