Details

analyze2.9s (20.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.5%	0.5%	0
0%	99.5%	0.5%	1
0%	99.5%	0.5%	2
0%	99.5%	0.5%	3
0%	99.5%	0.5%	4
0%	99.5%	0.5%	5
0%	99.5%	0.5%	6
0%	99.5%	0.5%	7
0%	99.5%	0.5%	8
0%	99.5%	0.5%	9
0%	99.5%	0.5%	10
0%	99.5%	0.5%	11
0%	99.5%	0.5%	12
0%	99.5%	0.5%	13
0%	99.5%	0.5%	14

Compiler

Compiled 42 to 30 computations (28.6% saved)

sample3.9s (28%)

Symmetry

(sort y z)

(sort b c)

(sort j k)

Results

2.0s	8614×	body	128	invalid
1.8s	8256×	body	128	valid

Compiler

Compiled 125 to 89 computations (28.8% saved)

simplify357.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

6437×	`fma-neg_binary64`
684×	`unsub-neg_binary64`
621×	`distribute-rgt-neg-in_binary64`
515×	`distribute-rgt-in_binary64`
434×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	43
1	77	37
2	255	35
3	773	35
4	1711	35
5	2777	35
6	3474	35
7	3470	35
8	3493	35
9	3516	35
10	3534	35
11	3534	35
12	3526	35
13	3549	35
14	3549	35
15	3549	35
16	3639	35
17	4131	35
18	3675	35
19	3675	35
20	3675	35
21	9384	35

prune5.0ms (0%)

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

0.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	6.8b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
▶	6.4b	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (fma.f64 -27 (.f64 j k) (.f64 b c))))

Status

Error

Program

6.8b

(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))

▶

6.4b

(fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))

Compiler

Compiled 218 to 148 computations (32.1% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 18 (.f64 y (.f64 z t)) (*.f64 i -4))
✓	0.1b	(fma.f64 -27 (.f64 j k) (.f64 b c))
✓	3.8b	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (fma.f64 -27 (.f64 j k) (.f64 b c))))
✓	7.2b	(.f64 y (.f64 z t))

series130.0ms (0.9%)

Counts

4 → 252

Calls

4 calls:

97.0ms	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (fma.f64 -27 (.f64 j k) (.f64 b c))))
13.0ms	(fma.f64 18 (.f64 y (.f64 z t)) (*.f64 i -4))
12.0ms	(fma.f64 -27 (.f64 j k) (.f64 b c))
8.0ms	(.f64 y (.f64 z t))

rewrite221.0ms (1.6%)

Algorithm

4×	egg-rewrite

Rules

60×	`egg`
50×	`egg`
23×	`egg`
20×	`egg`

Counts

4 → 153

Calls

4 calls:

68.0ms	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (fma.f64 -27 (.f64 j k) (.f64 b c))))
52.0ms	(.f64 y (.f64 z t))
51.0ms	(fma.f64 18 (.f64 y (.f64 z t)) (*.f64 i -4))
46.0ms	(fma.f64 -27 (.f64 j k) (.f64 b c))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	119	7
2	1412	7
3	5368	7
0	24	35
1	479	35
2	4893	35
3	5039	35
0	9	11
1	178	11
2	2003	11
3	5001	11
0	11	14
1	221	14
2	2477	14
3	4957	14

simplify703.0ms (5%)

Algorithm

1×	egg-herbie

Rules

6691×	`fma-neg_binary64`
864×	`unsub-neg_binary64`
611×	`sub-neg_binary64`
523×	`distribute-rgt-neg-in_binary64`
518×	`cancel-sign-sub-inv_binary64`

Counts

405 → 192

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	5548
1	191	5103
2	549	4906
3	1453	4904
4	2957	4904
5	3527	4904
6	3850	4904
7	3739	4904
8	3756	4904
9	3758	4904
10	3803	4904
11	3923	4904
12	3993	4904
13	3999	4904
14	3999	4904
15	4093	4904
16	4685	4904
17	4157	4904
18	4157	4904
19	4157	4904
20	4157	4904
21	9832	4904

prune232.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	188	4	192
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	188	6	194

Error

0.0b

Counts

194 → 6

Alt Table

Status	Error	Program
	6.8b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	10.4b	(fma.f64 k (.f64 j -27) (fma.f64 -4 (fma.f64 t a (.f64 x i)) (*.f64 c b)))
	44.9b	(.f64 (-.f64 (.f64 18 (.f64 y (.f64 z x))) (*.f64 4 a)) t)
	6.9b	(fma.f64 x (fma.f64 (.f64 18 (.f64 y z)) t (.f64 i -4)) (fma.f64 a (.f64 t -4) (fma.f64 -27 (.f64 j k) (.f64 b c))))
▶	5.1b	(fma.f64 -4 (fma.f64 t a (.f64 x i)) (fma.f64 y (.f64 18 (.f64 t (.f64 z x))) (fma.f64 c b (.f64 (.f64 k j) -27))))
✓	6.4b	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (fma.f64 -27 (.f64 j k) (.f64 b c))))

Compiler

Compiled 5861 to 2704 computations (53.9% saved)

localize38.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 18 (.f64 t (*.f64 z x)))
✓	0.3b	(.f64 (.f64 k j) -27)
✓	2.3b	(fma.f64 y (.f64 18 (.f64 t (.f64 z x))) (fma.f64 c b (.f64 (*.f64 k j) -27)))
✓	4.5b	(.f64 t (.f64 z x))

series91.0ms (0.7%)

Counts

4 → 120

Calls

4 calls:

50.0ms	(fma.f64 y (.f64 18 (.f64 t (.f64 z x))) (fma.f64 c b (.f64 (*.f64 k j) -27)))
22.0ms	(.f64 (.f64 k j) -27)
10.0ms	(.f64 18 (.f64 t (*.f64 z x)))
8.0ms	(.f64 t (.f64 z x))

rewrite245.0ms (1.8%)

Algorithm

4×	egg-rewrite

Rules

60×	`egg`
54×	`egg`
34×	`egg`
24×	`egg`

Counts

4 → 172

Calls

4 calls:

83.0ms	(.f64 t (.f64 z x))
68.0ms	(fma.f64 y (.f64 18 (.f64 t (.f64 z x))) (fma.f64 c b (.f64 (*.f64 k j) -27)))
47.0ms	(.f64 18 (.f64 t (*.f64 z x)))
44.0ms	(.f64 (.f64 k j) -27)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	119	7
2	1412	7
3	5368	7
0	18	24
1	362	24
2	4179	24
3	5232	24
0	6	7
1	121	7
2	1358	7
3	5050	7
0	8	10
1	162	10
2	1882	10
3	4966	10

simplify389.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1453×	`fma-def_binary64`
895×	`fma-neg_binary64`
532×	`distribute-rgt-neg-in_binary64`
338×	`unsub-neg_binary64`
314×	`cancel-sign-sub-inv_binary64`

Counts

292 → 183

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	2318
1	55	2162
2	125	2162
3	307	2162
4	560	2162
5	1021	2162
6	1519	2162
7	2385	2162
8	2357	2162
9	2411	2162
10	2405	2162
11	2405	2162
12	3434	2162
13	3367	2162
14	3443	2162
15	3453	2162
16	3453	2162
17	3453	2162
18	3453	2162
19	3453	2162
20	3453	2162
21	3292	2162

prune291.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	179	4	183
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	181	8	189

Error

0.0b

Counts

189 → 8

Alt Table

Status	Error	Program
	20.3b	(fma.f64 -4 (fma.f64 t a (.f64 x i)) (fma.f64 y (.f64 18 (.f64 t (.f64 z x))) (fma.f64 c b (cbrt.f64 (.f64 (pow.f64 (.f64 k j) 3) -19683)))))
	5.3b	(fma.f64 -4 (fma.f64 t a (.f64 x i)) (fma.f64 y (.f64 18 (.f64 t (.f64 z x))) (fma.f64 c b (.f64 (.f64 -27 (pow.f64 (cbrt.f64 (.f64 k j)) 2)) (cbrt.f64 (.f64 k j))))))
	44.9b	(.f64 (-.f64 (.f64 18 (.f64 y (.f64 z x))) (*.f64 4 a)) t)
	6.9b	(fma.f64 x (fma.f64 (.f64 18 (.f64 y z)) t (.f64 i -4)) (fma.f64 a (.f64 t -4) (fma.f64 -27 (.f64 j k) (.f64 b c))))
	10.4b	(fma.f64 k (.f64 j -27) (fma.f64 -4 (fma.f64 t a (.f64 x i)) (*.f64 c b)))
▶	4.9b	(fma.f64 -4 (fma.f64 t a (.f64 x i)) (fma.f64 y (.f64 18 (.f64 x (.f64 t z))) (fma.f64 c b (.f64 (.f64 k j) -27))))
	5.1b	(fma.f64 -4 (fma.f64 t a (.f64 x i)) (fma.f64 y (.f64 18 (.f64 t (.f64 z x))) (fma.f64 c b (.f64 j (.f64 k -27)))))
✓	6.4b	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (fma.f64 -27 (.f64 j k) (.f64 b c))))

Compiler

Compiled 6037 to 2451 computations (59.4% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 18 (.f64 x (*.f64 t z)))
	0.3b	(.f64 (.f64 k j) -27)
✓	2.3b	(fma.f64 y (.f64 18 (.f64 x (.f64 t z))) (fma.f64 c b (.f64 (*.f64 k j) -27)))
✓	4.6b	(.f64 x (.f64 t z))

series208.0ms (1.5%)

Counts

3 → 168

Calls

3 calls:

146.0ms	(fma.f64 y (.f64 18 (.f64 x (.f64 t z))) (fma.f64 c b (.f64 (*.f64 k j) -27)))
54.0ms	(.f64 18 (.f64 x (*.f64 t z)))
8.0ms	(.f64 x (.f64 t z))

rewrite167.0ms (1.2%)

Algorithm

3×	egg-rewrite

Rules

60×	`egg`
34×	`egg`
24×	`egg`

Counts

3 → 118

Calls

3 calls:

67.0ms	(fma.f64 y (.f64 18 (.f64 x (.f64 t z))) (fma.f64 c b (.f64 (*.f64 k j) -27)))
51.0ms	(.f64 18 (.f64 x (*.f64 t z)))
46.0ms	(.f64 x (.f64 t z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	119	7
2	1412	7
3	5368	7
0	18	24
1	362	24
2	4179	24
3	5232	24
0	8	10
1	162	10
2	1882	10
3	4966	10

simplify414.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1455×	`fma-def_binary64`
892×	`fma-neg_binary64`
530×	`distribute-rgt-neg-in_binary64`
346×	`unsub-neg_binary64`
301×	`cancel-sign-sub-inv_binary64`

Counts

286 → 133

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	2762
1	59	2606
2	140	2606
3	324	2606
4	565	2606
5	1029	2606
6	1521	2606
7	2399	2606
8	2358	2606
9	2411	2606
10	2405	2606
11	2405	2606
12	3434	2606
13	3367	2606
14	3443	2606
15	3453	2606
16	3453	2606
17	3453	2606
18	3453	2606
19	3453	2606
20	3453	2606
21	3292	2606

prune267.0ms (1.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	186	8	194

Error

0.0b

Counts

194 → 8

Alt Table

Status	Error	Program
	20.3b	(fma.f64 -4 (fma.f64 t a (.f64 x i)) (fma.f64 y (.f64 18 (.f64 t (.f64 z x))) (fma.f64 c b (cbrt.f64 (.f64 (pow.f64 (.f64 k j) 3) -19683)))))
	5.3b	(fma.f64 -4 (fma.f64 t a (.f64 x i)) (fma.f64 y (.f64 18 (.f64 t (.f64 z x))) (fma.f64 c b (.f64 (.f64 -27 (pow.f64 (cbrt.f64 (.f64 k j)) 2)) (cbrt.f64 (.f64 k j))))))
	44.9b	(.f64 (-.f64 (.f64 18 (.f64 y (.f64 z x))) (*.f64 4 a)) t)
	6.9b	(fma.f64 x (fma.f64 (.f64 18 (.f64 y z)) t (.f64 i -4)) (fma.f64 a (.f64 t -4) (fma.f64 -27 (.f64 j k) (.f64 b c))))
	10.4b	(fma.f64 k (.f64 j -27) (fma.f64 -4 (fma.f64 t a (.f64 x i)) (*.f64 c b)))
✓	4.9b	(fma.f64 -4 (fma.f64 t a (.f64 x i)) (fma.f64 y (.f64 18 (.f64 x (.f64 t z))) (fma.f64 c b (.f64 (.f64 k j) -27))))
▶	5.1b	(fma.f64 -4 (fma.f64 t a (.f64 x i)) (fma.f64 y (.f64 18 (.f64 t (.f64 z x))) (fma.f64 c b (.f64 j (.f64 k -27)))))
✓	6.4b	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (fma.f64 -27 (.f64 j k) (.f64 b c))))

Compiler

Compiled 6069 to 2451 computations (59.6% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 18 (.f64 t (*.f64 z x)))
✓	0.2b	(.f64 j (.f64 k -27))
✓	2.3b	(fma.f64 y (.f64 18 (.f64 t (.f64 z x))) (fma.f64 c b (.f64 j (*.f64 k -27))))
	4.5b	(.f64 t (.f64 z x))

series58.0ms (0.4%)

Counts

2 → 120

Calls

2 calls:

53.0ms	(fma.f64 y (.f64 18 (.f64 t (.f64 z x))) (fma.f64 c b (.f64 j (*.f64 k -27))))
4.0ms	(.f64 j (.f64 k -27))

rewrite122.0ms (0.9%)

Algorithm

2×	egg-rewrite

Rules

56×	`egg`
24×	`egg`

Counts

2 → 80

Calls

2 calls:

74.0ms	(fma.f64 y (.f64 18 (.f64 t (.f64 z x))) (fma.f64 c b (.f64 j (*.f64 k -27))))
46.0ms	(.f64 j (.f64 k -27))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	24
1	362	24
2	4185	24
3	5286	24
0	6	7
1	121	7
2	1364	7
3	5047	7

simplify367.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1453×	`fma-def_binary64`
895×	`fma-neg_binary64`
532×	`distribute-rgt-neg-in_binary64`
338×	`unsub-neg_binary64`
314×	`cancel-sign-sub-inv_binary64`

Counts

200 → 92

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	2318
1	55	2162
2	125	2162
3	307	2162
4	560	2162
5	1021	2162
6	1519	2162
7	2385	2162
8	2357	2162
9	2411	2162
10	2405	2162
11	2405	2162
12	3434	2162
13	3367	2162
14	3443	2162
15	3453	2162
16	3453	2162
17	3453	2162
18	3453	2162
19	3453	2162
20	3453	2162
21	3292	2162

prune268.0ms (1.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	186	8	194

Error

0.0b

Counts

194 → 8

Alt Table

Status	Error	Program
	20.3b	(fma.f64 -4 (fma.f64 t a (.f64 x i)) (fma.f64 y (.f64 18 (.f64 t (.f64 z x))) (fma.f64 c b (cbrt.f64 (.f64 (pow.f64 (.f64 k j) 3) -19683)))))
	5.3b	(fma.f64 -4 (fma.f64 t a (.f64 x i)) (fma.f64 y (.f64 18 (.f64 t (.f64 z x))) (fma.f64 c b (.f64 (.f64 -27 (pow.f64 (cbrt.f64 (.f64 k j)) 2)) (cbrt.f64 (.f64 k j))))))
	44.9b	(.f64 (-.f64 (.f64 18 (.f64 y (.f64 z x))) (*.f64 4 a)) t)
	6.9b	(fma.f64 x (fma.f64 (.f64 18 (.f64 y z)) t (.f64 i -4)) (fma.f64 a (.f64 t -4) (fma.f64 -27 (.f64 j k) (.f64 b c))))
	10.4b	(fma.f64 k (.f64 j -27) (fma.f64 -4 (fma.f64 t a (.f64 x i)) (*.f64 c b)))
✓	4.9b	(fma.f64 -4 (fma.f64 t a (.f64 x i)) (fma.f64 y (.f64 18 (.f64 x (.f64 t z))) (fma.f64 c b (.f64 (.f64 k j) -27))))
✓	5.1b	(fma.f64 -4 (fma.f64 t a (.f64 x i)) (fma.f64 y (.f64 18 (.f64 t (.f64 z x))) (fma.f64 c b (.f64 j (.f64 k -27)))))
✓	6.4b	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (fma.f64 -27 (.f64 j k) (.f64 b c))))

Compiler

Compiled 5895 to 2509 computations (57.4% saved)

regimes2.1s (15%)

Accuracy

Total 0.9b remaining (96.7%)

Threshold costs 0.9b (96.7%)

Counts

66 → 3

Compiler

Compiled 34395 to 24562 computations (28.6% saved)

bsearch3.0ms (0%)

Compiler: Compiled 41 to 29 computations (29.3% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

29×	`*-commutative_binary64`
16×	`+-commutative_binary64`
15×	`sub-neg_binary64`
12×	`distribute-rgt-neg-in_binary64`
12×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	218
1	81	218
2	124	218
3	148	218
4	166	218
5	172	218
6	170	218

end417.0ms (3%)

Remove

(sort b c)

(sort y z)

Compiler

Compiled 1860 to 1103 computations (40.7% saved)

Details

analyze2.9s (20.7%)

sample3.9s (28%)

simplify357.0ms (2.6%)

prune5.0ms (0%)

localize19.0ms (0.1%)

series130.0ms (0.9%)

rewrite221.0ms (1.6%)

simplify703.0ms (5%)

prune232.0ms (1.7%)

localize38.0ms (0.3%)

series91.0ms (0.7%)

rewrite245.0ms (1.8%)

simplify389.0ms (2.8%)

prune291.0ms (2.1%)

localize20.0ms (0.1%)

series208.0ms (1.5%)

rewrite167.0ms (1.2%)

simplify414.0ms (3%)

prune267.0ms (1.9%)

localize19.0ms (0.1%)

series58.0ms (0.4%)

rewrite122.0ms (0.9%)

simplify367.0ms (2.6%)

prune268.0ms (1.9%)

regimes2.1s (15%)

bsearch3.0ms (0%)

simplify9.0ms (0.1%)

end417.0ms (3%)

Profiling