Details

analyze587.0ms (14.9%)

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)

sample1.2s (30%)

Results

838.0ms	7600×	body	128	valid
85.0ms	243×	body	1024	valid
79.0ms	590×	body	128	invalid
66.0ms	244×	body	512	valid
35.0ms	169×	body	256	valid

Compiler

Compiled 50 to 38 computations (24% saved)

simplify223.0ms (5.6%)

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

prune4.0ms (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
▶	0.2b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))

Compiler

Compiled 81 to 56 computations (30.9% saved)

localize6.0ms (0.2%)

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)

series11.0ms (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 (2.7%)

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 → 57

Calls

2 calls:

107.0ms	(fma.f64 z -6 4)
107.0ms	(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

simplify111.0ms (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

105 → 76

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 (1.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	70	6	76
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	71	7	78

Error

0.0b

Counts

78 → 7

Alt Table

Status	Error	Program
	22.8b	(fma.f64 (-.f64 y x) (pow.f64 (pow.f64 (fma.f64 z -6 4) 3) 1/3) x)
	44.8b	(/.f64 (+.f64 (pow.f64 (.f64 (-.f64 y x) (fma.f64 z -6 4)) 3) (pow.f64 x 3)) (fma.f64 (.f64 (-.f64 y x) (fma.f64 z -6 4)) (.f64 (-.f64 y x) (fma.f64 z -6 4)) (-.f64 (.f64 x x) (.f64 (.f64 (-.f64 y x) (fma.f64 z -6 4)) x))))
	34.2b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) 2)
▶	0.2b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	0.2b	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)
	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))

Compiler

Compiled 1312 to 808 computations (38.4% saved)

localize9.0ms (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	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
✓	0.1b	(*.f64 y (fma.f64 z -6 4))

series19.0ms (0.5%)

Counts

3 → 72

Calls

3 calls:

11.0ms	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
5.0ms	(*.f64 y (fma.f64 z -6 4))
2.0ms	(fma.f64 6 z -3)

rewrite52.0ms (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 → 82

Calls

3 calls:

50.0ms	(fma.f64 6 z -3)
50.0ms	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
50.0ms	(*.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

simplify122.0ms (3.1%)

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

154 → 104

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	1014
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

prune110.0ms (2.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	135	7	142

Error

0.0b

Counts

142 → 7

Alt Table

Status	Error	Program
	34.2b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) 2)
✓	0.2b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	27.2b	(fma.f64 x (fma.f64 6 z -3) (sqrt.f64 (pow.f64 (*.f64 y (fma.f64 z -6 4)) 2)))
▶	0.2b	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)
	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
	44.8b	(/.f64 (+.f64 (pow.f64 (.f64 (-.f64 y x) (fma.f64 z -6 4)) 3) (pow.f64 x 3)) (fma.f64 (.f64 (-.f64 y x) (fma.f64 z -6 4)) (.f64 (-.f64 y x) (fma.f64 z -6 4)) (-.f64 (.f64 x x) (.f64 (.f64 (-.f64 y x) (fma.f64 z -6 4)) x))))
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))

Compiler

Compiled 2459 to 1768 computations (28.1% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 4 (*.f64 6 z))
✓	0.1b	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)

series14.0ms (0.4%)

Counts

2 → 39

Calls

2 calls:

10.0ms	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)
4.0ms	(-.f64 4 (*.f64 6 z))

rewrite109.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

544×	`prod-diff_binary64`
396×	`fma-udef_binary64`
288×	`fma-def_binary64`
206×	`expm1-udef_binary64`
206×	`log1p-udef_binary64`

Counts

2 → 71

Calls

2 calls:

107.0ms	(-.f64 4 (*.f64 6 z))
107.0ms	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	228	21
2	2833	17
3	4800	17
4	4754	17
5	4865	17
0	0	0
1	0	0

simplify126.0ms (3.2%)

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

110 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	756
1	121	658
2	273	598
3	569	517
4	1314	517
5	1413	517
6	1441	517
7	1450	517
8	1459	517
9	1461	517
10	2494	517
11	2494	517
12	2381	517

prune57.0ms (1.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	89	7	96

Error

0.0b

Counts

96 → 7

Alt Table

Status	Error	Program
	34.2b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) 2)
✓	0.2b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	27.2b	(fma.f64 x (fma.f64 6 z -3) (sqrt.f64 (pow.f64 (*.f64 y (fma.f64 z -6 4)) 2)))
✓	0.2b	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)
▶	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
	44.8b	(/.f64 (+.f64 (pow.f64 (.f64 (-.f64 y x) (fma.f64 z -6 4)) 3) (pow.f64 x 3)) (fma.f64 (.f64 (-.f64 y x) (fma.f64 z -6 4)) (.f64 (-.f64 y x) (fma.f64 z -6 4)) (-.f64 (.f64 x x) (.f64 (.f64 (-.f64 y x) (fma.f64 z -6 4)) x))))
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))

Compiler

Compiled 1487 to 908 computations (38.9% 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 z x))
✓	0.3b	(.f64 6 (.f64 y z))

series79.0ms (2%)

Counts

4 → 18

Calls

4 calls:

42.0ms	(.f64 6 (.f64 y z))
26.0ms	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
7.0ms	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
4.0ms	(.f64 6 (.f64 z x))

rewrite112.0ms (2.8%)

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 → 126

Calls

4 calls:

109.0ms	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
109.0ms	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
109.0ms	(.f64 6 (.f64 z x))
109.0ms	(.f64 6 (.f64 y z))

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

simplify63.0ms (1.6%)

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

144 → 142

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

prune142.0ms (3.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	139	3	142
Fresh	3	1	4
Picked	1	0	1
Done	0	2	2
Total	143	6	149

Error

Counts

149 → 6

Alt Table

Status	Error	Program
	34.2b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) 2)
✓	0.2b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
✓	0.2b	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)
	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (fma.f64 x 3 (.f64 6 (*.f64 y z))))
	0.2b	(-.f64 (fma.f64 6 (.f64 z x) (.f64 y 4)) (fma.f64 6 (.f64 y z) (.f64 x 3)))
	23.8b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (/.f64 (-.f64 (.f64 36 (pow.f64 (.f64 y z) 2)) (.f64 (.f64 x x) 9)) (-.f64 (.f64 6 (.f64 y z)) (.f64 x 3))))

Compiler

Compiled 4142 to 2523 computations (39.1% saved)

regimes499.0ms (12.7%)

Accuracy

Total 0.1b remaining (88.7%)

Threshold costs 0.1b (88.7%)

Counts

97 → 1

Compiler

Compiled 8950 to 6482 computations (27.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`distribute-lft-neg-in_binary64`
4×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	22	21
2	30	21
3	40	21
4	47	21
5	52	21
6	54	21
7	53	21

end102.0ms (2.6%)

Compiler: Compiled 156 to 111 computations (28.8% saved)

Details

analyze587.0ms (14.9%)

sample1.2s (30%)

simplify223.0ms (5.6%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

series11.0ms (0.3%)

rewrite108.0ms (2.7%)

simplify111.0ms (2.8%)

prune72.0ms (1.8%)

localize9.0ms (0.2%)

series19.0ms (0.5%)

rewrite52.0ms (1.3%)

simplify122.0ms (3.1%)

prune110.0ms (2.8%)

localize6.0ms (0.2%)

series14.0ms (0.4%)

rewrite109.0ms (2.8%)

simplify126.0ms (3.2%)

prune57.0ms (1.4%)

localize11.0ms (0.3%)

series79.0ms (2%)

rewrite112.0ms (2.8%)

simplify63.0ms (1.6%)

prune142.0ms (3.6%)

regimes499.0ms (12.7%)

simplify3.0ms (0.1%)

end102.0ms (2.6%)

Profiling