Details

analyze2.0s (17.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
1.6%	98.1%	0.3%	13
2.3%	97.4%	0.3%	14

Compiler

Compiled 24 to 18 computations (25% saved)

sample2.0s (17.1%)

Symmetry

(sort y z t)

(sort a b)

Results

1.3s	8256×	body	128	valid
447.0ms	3140×	body	128	invalid

Compiler

Compiled 71 to 53 computations (25.4% saved)

simplify75.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-neg_binary64`
641×	`fma-def_binary64`
213×	`cancel-sign-sub-inv_binary64`
172×	`distribute-rgt-neg-in_binary64`
157×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	25
1	39	23
2	115	21
3	308	21
4	552	21
5	902	21
6	1201	21
7	1433	21
8	1672	21
9	1787	21
10	1791	21
11	1791	21
12	1791	21
13	1674	21

prune4.0ms (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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	3.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	3.2b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

Compiler

Compiled 126 to 90 computations (28.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t))
✓	0.2b	(.f64 (.f64 y 9) z)
✓	0.2b	(.f64 (.f64 a 27) b)
✓	7.3b	(.f64 (.f64 (*.f64 y 9) z) t)

series34.0ms (0.3%)

Counts

4 → 132

Calls

4 calls:

13.0ms	(-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t))
10.0ms	(.f64 (.f64 (*.f64 y 9) z) t)
7.0ms	(.f64 (.f64 a 27) b)
4.0ms	(.f64 (.f64 y 9) z)

rewrite236.0ms (2.1%)

Algorithm

4×	egg-rewrite

Rules

175×	`egg`
58×	`egg`
58×	`egg`
39×	`egg`

Counts

4 → 330

Calls

4 calls:

83.0ms	(-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t))
56.0ms	(.f64 (.f64 (*.f64 y 9) z) t)
45.0ms	(.f64 (.f64 a 27) b)
44.0ms	(.f64 (.f64 y 9) z)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	163	10
2	1878	10
3	4934	10
0	6	7
1	121	7
2	1356	7
3	5047	7
0	6	7
1	122	7
2	1356	7
3	5006	7
0	12	16
1	261	16
2	3190	16
3	5968	16

simplify114.0ms (1%)

Algorithm

1×	egg-herbie

Rules

760×	`fma-def_binary64`
290×	`fma-neg_binary64`
132×	`distribute-rgt-neg-in_binary64`
130×	`cancel-sign-sub-inv_binary64`
110×	`associate-l_binary64`

Counts

462 → 335

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	1362
1	44	1290
2	97	1290
3	207	1290
4	322	1290
5	390	1290
6	528	1290
7	663	1290
8	841	1290
9	973	1290
10	1066	1290
11	1096	1290
12	1096	1290
13	1007	1290

prune542.0ms (4.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	327	8	335
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	329	8	337

Error

0.0b

Counts

337 → 8

Alt Table

Status	Error	Program
▶	3.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 a (.f64 27 b)))
	21.9b	(+.f64 (-.f64 (.f64 x 2) (pow.f64 (sqrt.f64 (.f64 (.f64 (.f64 y 9) z) t)) 2)) (.f64 (.f64 a 27) b))
	3.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t)) (.f64 (.f64 a 27) b))
	3.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 27 (.f64 a b)))
	3.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 9 (.f64 y (.f64 t z)))) (.f64 (.f64 a 27) b))
	4.4b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 t y) (.f64 9 z))) (.f64 (.f64 a 27) b))
	4.9b	(+.f64 (-.f64 (.f64 x 2) (.f64 z (.f64 (.f64 y 9) t))) (.f64 (.f64 a 27) b))
	3.2b	(+.f64 (+.f64 (-.f64 (+.f64 x x) (.f64 (.f64 (.f64 y 9) z) t)) (+.f64 (fma.f64 (.f64 (.f64 y 9) z) (neg.f64 t) (.f64 (.f64 (.f64 y 9) z) t)) (fma.f64 (.f64 (.f64 y 9) z) (neg.f64 t) (.f64 (.f64 (.f64 y 9) z) t)))) (.f64 (*.f64 a 27) b))

Compiler

Compiled 10332 to 6345 computations (38.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t))
	0.2b	(.f64 (.f64 y 9) z)
✓	0.2b	(.f64 a (.f64 27 b))
	7.3b	(.f64 (.f64 (*.f64 y 9) z) t)

series4.0ms (0%)

Counts

1 → 24

Calls

1 calls:

4.0ms

(*.f64 a (*.f64 27 b))

rewrite46.0ms (0.4%)

Algorithm

1×	egg-rewrite

Rules

60× egg

Counts

1 → 60

Calls

1 calls:

45.0ms

(*.f64 a (*.f64 27 b))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	121	7
2	1358	7
3	5055	7

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`

Counts

84 → 61

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	10	168
2	16	168
3	16	168
4	16	168

prune750.0ms (6.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	336	2	338
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	340	6	346

Error

0.0b

Counts

346 → 6

Alt Table

Status	Error	Program
	3.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t)) (.f64 (.f64 a 27) b))
	3.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 27 (.f64 a b)))
	4.4b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 t y) (.f64 9 z))) (.f64 (.f64 a 27) b))
	4.9b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 t (.f64 y 9)) z)) (.f64 a (.f64 27 b)))
▶	3.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 y (.f64 9 (.f64 z t)))) (.f64 a (.f64 27 b)))
	3.2b	(+.f64 (+.f64 (-.f64 (+.f64 x x) (.f64 (.f64 (.f64 y 9) z) t)) (+.f64 (fma.f64 (.f64 (.f64 y 9) z) (neg.f64 t) (.f64 (.f64 (.f64 y 9) z) t)) (fma.f64 (.f64 (.f64 y 9) z) (neg.f64 t) (.f64 (.f64 (.f64 y 9) z) t)))) (.f64 (*.f64 a 27) b))

Compiler

Compiled 10291 to 6308 computations (38.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x 2) (.f64 y (.f64 9 (.f64 z t))))
	0.2b	(.f64 a (.f64 27 b))
✓	0.2b	(.f64 9 (.f64 z t))
✓	8.1b	(.f64 y (.f64 9 (*.f64 z t)))

series28.0ms (0.2%)

Counts

3 → 108

Calls

3 calls:

13.0ms	(-.f64 (.f64 x 2) (.f64 y (.f64 9 (.f64 z t))))
11.0ms	(.f64 y (.f64 9 (*.f64 z t)))
4.0ms	(.f64 9 (.f64 z t))

rewrite222.0ms (1.9%)

Algorithm

3×	egg-rewrite

Rules

178×	`egg`
54×	`egg`
40×	`egg`

Counts

3 → 272

Calls

3 calls:

84.0ms	(-.f64 (.f64 x 2) (.f64 y (.f64 9 (.f64 z t))))
83.0ms	(.f64 y (.f64 9 (*.f64 z t)))
45.0ms	(.f64 9 (.f64 z t))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	163	10
2	1872	10
3	4996	10
4	4920	10
0	6	7
1	122	7
2	1358	7
3	5014	7
0	12	16
1	261	14
2	3191	14
3	5972	14

simplify104.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

758×	`fma-def_binary64`
291×	`fma-neg_binary64`
132×	`cancel-sign-sub-inv_binary64`
131×	`distribute-rgt-neg-in_binary64`
108×	`associate-l_binary64`

Counts

380 → 278

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	1194
1	34	1122
2	83	1122
3	193	1122
4	306	1122
5	374	1122
6	512	1122
7	647	1122
8	825	1122
9	958	1122
10	1051	1122
11	1081	1122
12	1081	1122
13	992	1122

prune405.0ms (3.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	337	2	339
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	340	5	345

Error

Counts

345 → 5

Alt Table

Status	Error	Program
▶	3.1b	(+.f64 (fma.f64 x 2 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 y (.f64 (.f64 z t) -9) (.f64 y (.f64 9 (.f64 z t)))))) (.f64 a (*.f64 27 b)))
	3.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 27 (.f64 a b)))
	3.1b	(+.f64 (-.f64 (.f64 x 2) (.f64 y (.f64 z (.f64 t 9)))) (.f64 a (.f64 27 b)))
	3.2b	(+.f64 (+.f64 (-.f64 (+.f64 x x) (.f64 (.f64 (.f64 y 9) z) t)) (+.f64 (fma.f64 (.f64 (.f64 y 9) z) (neg.f64 t) (.f64 (.f64 (.f64 y 9) z) t)) (fma.f64 (.f64 (.f64 y 9) z) (neg.f64 t) (.f64 (.f64 (.f64 y 9) z) t)))) (.f64 (*.f64 a 27) b))
	4.9b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 t (.f64 y 9)) z)) (.f64 a (.f64 27 b)))

Compiler

Compiled 10028 to 5521 computations (44.9% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 z t) -9)
	8.1b	(.f64 y (.f64 9 (*.f64 z t)))
✓	8.1b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 y (.f64 (.f64 z t) -9) (.f64 y (.f64 9 (*.f64 z t)))))
✓	48.9b	(fma.f64 y (.f64 (.f64 z t) -9) (.f64 y (.f64 9 (*.f64 z t))))

series52.0ms (0.4%)

Counts

3 → 96

Calls

3 calls:

25.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 y (.f64 (.f64 z t) -9) (.f64 y (.f64 9 (*.f64 z t)))))
22.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (.f64 y (.f64 9 (*.f64 z t))))
4.0ms	(.f64 (.f64 z t) -9)

rewrite202.0ms (1.8%)

Algorithm

3×	egg-rewrite

Rules

68×	`egg`
54×	`egg`
24×	`egg`

Counts

3 → 146

Calls

3 calls:

102.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 y (.f64 (.f64 z t) -9) (.f64 y (.f64 9 (*.f64 z t)))))
54.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (.f64 y (.f64 9 (*.f64 z t))))
43.0ms	(.f64 (.f64 z t) -9)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	226	19
2	2341	19
3	5326	19
0	12	30
1	246	29
2	2571	17
3	4978	17
4	5006	17
0	6	7
1	121	7
2	1358	7
3	5050	7

simplify44.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

25×	`associate-l_binary64`
18×	`*-commutative_binary64`
12×	`associate-r_binary64`

Counts

242 → 147

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	564
1	20	564
2	43	564
3	58	564
4	56	564
5	56	564

prune351.0ms (3.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	243	0	243
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	243	5	248

Error

Counts

248 → 5

Alt Table

Status	Error	Program
✓	3.1b	(+.f64 (fma.f64 x 2 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 y (.f64 (.f64 z t) -9) (.f64 y (.f64 9 (.f64 z t)))))) (.f64 a (*.f64 27 b)))
	3.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 27 (.f64 a b)))
	3.1b	(+.f64 (-.f64 (.f64 x 2) (.f64 y (.f64 z (.f64 t 9)))) (.f64 a (.f64 27 b)))
	3.2b	(+.f64 (+.f64 (-.f64 (+.f64 x x) (.f64 (.f64 (.f64 y 9) z) t)) (+.f64 (fma.f64 (.f64 (.f64 y 9) z) (neg.f64 t) (.f64 (.f64 (.f64 y 9) z) t)) (fma.f64 (.f64 (.f64 y 9) z) (neg.f64 t) (.f64 (.f64 (.f64 y 9) z) t)))) (.f64 (*.f64 a 27) b))
	4.9b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 t (.f64 y 9)) z)) (.f64 a (.f64 27 b)))

Compiler

Compiled 8483 to 4666 computations (45% saved)

regimes3.5s (30.7%)

Accuracy

Total 0.6b remaining (96%)

Threshold costs 0.6b (96%)

Counts

143 → 2

Compiler

Compiled 62571 to 45189 computations (27.8% saved)

bsearch5.0ms (0%)

Compiler: Compiled 11 to 9 computations (18.2% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

18×	`*-commutative_binary64`
13×	`+-commutative_binary64`
12×	`distribute-rgt-neg-in_binary64`
11×	`sub-neg_binary64`
10×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	62
1	48	62
2	72	62
3	99	62
4	117	62
5	123	62
6	124	62
7	123	62

end753.0ms (6.6%)

Compiler: Compiled 448 to 312 computations (30.4% saved)

Details

analyze2.0s (17.1%)

sample2.0s (17.1%)

simplify75.0ms (0.7%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series34.0ms (0.3%)

rewrite236.0ms (2.1%)

simplify114.0ms (1%)

prune542.0ms (4.7%)

localize12.0ms (0.1%)

series4.0ms (0%)

rewrite46.0ms (0.4%)

simplify11.0ms (0.1%)

prune750.0ms (6.5%)

localize11.0ms (0.1%)

series28.0ms (0.2%)

rewrite222.0ms (1.9%)

simplify104.0ms (0.9%)

prune405.0ms (3.5%)

localize18.0ms (0.2%)

series52.0ms (0.4%)

rewrite202.0ms (1.8%)

simplify44.0ms (0.4%)

prune351.0ms (3.1%)

regimes3.5s (30.7%)

bsearch5.0ms (0%)

simplify6.0ms (0%)

end753.0ms (6.6%)

Profiling