Details

analyze899.0ms (20.6%)

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
18.7%	81.1%	0.1%	8
31.2%	68.6%	0.1%	9
35.9%	55.4%	8.7%	10
42.9%	47.6%	9.5%	11
51.5%	38.2%	10.3%	12
55%	30%	15%	13
59.5%	25.3%	15.3%	14

Compiler

Compiled 17 to 13 computations (23.5% saved)

sample1.3s (29.1%)

Results

923.0ms	7601×	body	128	valid
88.0ms	248×	body	1024	valid
72.0ms	628×	body	128	invalid
72.0ms	246×	body	512	valid
34.0ms	161×	body	256	valid

Compiler

Compiled 50 to 38 computations (24% saved)

simplify227.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

5304×	`fma-neg_binary64`
679×	`unsub-neg_binary64`
400×	`sub-neg_binary64`
376×	`fma-def_binary64`
289×	`associate--r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	16
1	23	14
2	59	14
3	157	12
4	438	12
5	1253	12
6	2078	12
7	2563	12
8	2777	12
9	2907	12
10	2949	12
11	2964	12
12	2967	12
13	2967	12
14	2967	12
15	3141	12
16	3015	12
17	3015	12
18	8062	12

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
▶	0.2b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)

Compiler

Compiled 81 to 56 computations (30.9% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z -6 4)
✓	0.1b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)

series12.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
1.0ms	(fma.f64 z -6 4)

rewrite108.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

507×	`fma-def_binary64`
433×	`prod-diff_binary64`
403×	`log-prod_binary64`
298×	`fma-udef_binary64`
175×	`expm1-udef_binary64`

Counts

2 → 55

Calls

2 calls:

106.0ms	(fma.f64 z -6 4)
106.0ms	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	194	17
2	2301	17
3	4847	17
4	4894	17
5	5151	17
0	0	0
1	0	0

simplify123.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1259×	`fma-neg_binary64`
445×	`fma-def_binary64`
152×	`sub-neg_binary64`
121×	`cancel-sign-sub-inv_binary64`
117×	`associate-l_binary64`

Counts

103 → 75

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	819
1	121	721
2	273	643
3	569	562
4	1314	562
5	1413	562
6	1441	562
7	1450	562
8	1459	562
9	1461	562
10	2494	562
11	2494	562
12	2381	562

prune72.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	68	7	75
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	69	8	77

Error

Counts

77 → 8

Alt Table

Status	Error	Program
	0.2b	(+.f64 x (*.f64 (-.f64 y x) (fma.f64 z -6 4)))
▶	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	11.4b	(fma.f64 (-.f64 y x) (/.f64 (+.f64 (pow.f64 (.f64 z -6) 3) 64) (fma.f64 (.f64 z -6) (.f64 z -6) (-.f64 16 (.f64 (*.f64 z -6) 4)))) x)
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
	13.3b	(fma.f64 (-.f64 y x) (expm1.f64 (log1p.f64 (fma.f64 z -6 4))) x)
	32.8b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) 2)
	1.3b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) 3)

Compiler

Compiled 1291 to 808 computations (37.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 z -6 4)
✓	0.1b	(fma.f64 6 z -3)
✓	0.1b	(*.f64 y (fma.f64 z -6 4))
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))

series26.0ms (0.6%)

Counts

3 → 72

Calls

3 calls:

17.0ms	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
7.0ms	(*.f64 y (fma.f64 z -6 4))
1.0ms	(fma.f64 6 z -3)

rewrite58.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

467×	`log-prod_binary64`
207×	`expm1-udef_binary64`
207×	`log1p-udef_binary64`
206×	`pow1/3_binary64`
200×	`pow3_binary64`

Counts

3 → 79

Calls

3 calls:

56.0ms	(fma.f64 6 z -3)
56.0ms	(*.f64 y (fma.f64 z -6 4))
56.0ms	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	244	29
2	2572	29
3	4829	29
0	0	0
1	0	0

simplify128.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

1255×	`fma-neg_binary64`
441×	`fma-def_binary64`
152×	`sub-neg_binary64`
121×	`cancel-sign-sub-inv_binary64`
119×	`associate-l_binary64`

Counts

151 → 101

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	1086
1	122	931
2	271	829
3	575	748
4	1314	748
5	1413	748
6	1441	748
7	1450	748
8	1459	748
9	1461	748
10	2494	748
11	2494	748
12	2381	748

prune128.0ms (2.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	132	8	140

Error

Counts

140 → 8

Alt Table

Status	Error	Program
	0.2b	(+.f64 x (*.f64 (-.f64 y x) (fma.f64 z -6 4)))
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	11.4b	(fma.f64 (-.f64 y x) (/.f64 (+.f64 (pow.f64 (.f64 z -6) 3) 64) (fma.f64 (.f64 z -6) (.f64 z -6) (-.f64 16 (.f64 (*.f64 z -6) 4)))) x)
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
▶	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
	13.3b	(fma.f64 (-.f64 y x) (expm1.f64 (log1p.f64 (fma.f64 z -6 4))) x)
	32.8b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) 2)
	1.3b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) 3)

Compiler

Compiled 2392 to 1734 computations (27.5% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
✓	0.0b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
✓	0.3b	(.f64 6 (.f64 y z))
✓	0.3b	(.f64 6 (.f64 z x))

series42.0ms (1%)

Counts

4 → 18

Calls

4 calls:

13.0ms	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
13.0ms	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
10.0ms	(.f64 6 (.f64 z x))
6.0ms	(.f64 6 (.f64 y z))

rewrite97.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

323×	`log1p-udef_binary64`
177×	`add-sqr-sqrt_binary64`
174×	`log1p-expm1-u_binary64`
174×	`expm1-log1p-u_binary64`
168×	`add-log-exp_binary64`

Counts

4 → 123

Calls

4 calls:

93.0ms	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
93.0ms	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
93.0ms	(.f64 6 (.f64 y z))
93.0ms	(.f64 6 (.f64 z x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	49
1	362	49
2	4865	49
3	5295	49
0	0	0
1	0	0

simplify67.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

856×	`fma-def_binary64`
566×	`fma-neg_binary64`
197×	`cancel-sign-sub-inv_binary64`
144×	`associate-l_binary64`
98×	`distribute-rgt-in_binary64`

Counts

141 → 140

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	35	150
1	107	133
2	227	127
3	434	127
4	805	127
5	1064	127
6	1315	127
7	1383	127
8	1414	127
9	1424	127
10	1424	127
11	1311	127

prune132.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	141	7	148

Error

Counts

148 → 7

Alt Table

Status	Error	Program
	11.4b	(fma.f64 (-.f64 y x) (/.f64 (+.f64 (pow.f64 (.f64 z -6) 3) 64) (fma.f64 (.f64 z -6) (.f64 z -6) (-.f64 16 (.f64 (*.f64 z -6) 4)))) x)
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	13.3b	(fma.f64 (-.f64 y x) (expm1.f64 (log1p.f64 (fma.f64 z -6 4))) x)
	32.8b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) 2)
	1.3b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) 3)
▶	0.1b	(+.f64 (fma.f64 6 (.f64 z x) (.f64 y 4)) (neg.f64 (fma.f64 6 (.f64 z y) (.f64 x 3))))

Compiler

Compiled 4223 to 2593 computations (38.6% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (fma.f64 6 (.f64 z x) (.f64 y 4)) (neg.f64 (fma.f64 6 (.f64 z y) (.f64 x 3))))
✓	0.1b	(fma.f64 6 (.f64 z y) (.f64 x 3))
✓	0.1b	(fma.f64 6 (.f64 z x) (.f64 y 4))

series34.0ms (0.8%)

Counts

3 → 108

Calls

3 calls:

20.0ms	(+.f64 (fma.f64 6 (.f64 z x) (.f64 y 4)) (neg.f64 (fma.f64 6 (.f64 z y) (.f64 x 3))))
7.0ms	(fma.f64 6 (.f64 z x) (.f64 y 4))
7.0ms	(fma.f64 6 (.f64 z y) (.f64 x 3))

rewrite95.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

257×	`expm1-udef_binary64`
257×	`log1p-udef_binary64`
252×	`fma-def_binary64`
218×	`log-pow_binary64`
199×	`fma-neg_binary64`

Counts

3 → 157

Calls

3 calls:

91.0ms	(+.f64 (fma.f64 6 (.f64 z x) (.f64 y 4)) (neg.f64 (fma.f64 6 (.f64 z y) (.f64 x 3))))
91.0ms	(fma.f64 6 (.f64 z y) (.f64 x 3))
91.0ms	(fma.f64 6 (.f64 z x) (.f64 y 4))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	46
1	317	46
2	3443	44
3	4847	44
0	0	0
1	0	0

simplify152.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

1259×	`fma-neg_binary64`
445×	`fma-def_binary64`
152×	`sub-neg_binary64`
121×	`cancel-sign-sub-inv_binary64`
117×	`associate-l_binary64`

Counts

265 → 181

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	38	1437
1	120	1345
2	273	1285
3	569	1204
4	1314	1204
5	1413	1204
6	1441	1204
7	1450	1204
8	1459	1204
9	1461	1204
10	2494	1204
11	2494	1204
12	2381	1204

prune150.0ms (3.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	181	7	188

Error

Counts

188 → 7

Alt Table

Status	Error	Program
	11.4b	(fma.f64 (-.f64 y x) (/.f64 (+.f64 (pow.f64 (.f64 z -6) 3) 64) (fma.f64 (.f64 z -6) (.f64 z -6) (-.f64 16 (.f64 (*.f64 z -6) 4)))) x)
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	13.3b	(fma.f64 (-.f64 y x) (expm1.f64 (log1p.f64 (fma.f64 z -6 4))) x)
	32.8b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) 2)
	1.3b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) 3)
✓	0.1b	(+.f64 (fma.f64 6 (.f64 z x) (.f64 y 4)) (neg.f64 (fma.f64 6 (.f64 z y) (.f64 x 3))))

Compiler

Compiled 4957 to 2960 computations (40.3% saved)

regimes395.0ms (9%)

Accuracy

Total 0.2b remaining (91.4%)

Threshold costs 0.2b (91.4%)

Counts

80 → 1

Compiler

Compiled 6290 to 4572 computations (27.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	24
1	20	24
2	25	24
3	27	24
4	28	24
5	28	24

end113.0ms (2.6%)

Compiler: Compiled 166 to 121 computations (27.1% saved)

Details

analyze899.0ms (20.6%)

sample1.3s (29.1%)

simplify227.0ms (5.2%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series12.0ms (0.3%)

rewrite108.0ms (2.5%)

simplify123.0ms (2.8%)

prune72.0ms (1.6%)

localize8.0ms (0.2%)

series26.0ms (0.6%)

rewrite58.0ms (1.3%)

simplify128.0ms (2.9%)

prune128.0ms (2.9%)

localize11.0ms (0.3%)

series42.0ms (1%)

rewrite97.0ms (2.2%)

simplify67.0ms (1.5%)

prune132.0ms (3%)

localize11.0ms (0.2%)

series34.0ms (0.8%)

rewrite95.0ms (2.2%)

simplify152.0ms (3.5%)

prune150.0ms (3.4%)

regimes395.0ms (9%)

simplify3.0ms (0.1%)

end113.0ms (2.6%)

Profiling