Details

analyze1.3s (22.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
5.8%	94%	0.2%	9
7.6%	92.2%	0.2%	10
11.6%	88.2%	0.2%	11
18.5%	81.3%	0.2%	12
32.3%	66.9%	0.8%	13
37%	62.2%	0.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.3s (24.1%)

Symmetry

(sort x y)

Results

1.0s	8256×	body	128	valid
211.0ms	1528×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify170.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1483×	`associate-/l/_binary64`
1068×	`associate-/l*_binary64`
1015×	`associate-/r/_binary64`
675×	`*-commutative_binary64`
404×	`sqr-pow_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	17	10
2	41	7
3	91	7
4	366	7
5	1228	7
6	1212	7
7	1225	7
8	1238	7
9	1245	7
10	1252	7
11	1259	7
12	1266	7
13	1273	7
14	1280	7
15	1287	7
16	1294	7
17	1301	7
18	1308	7
19	1315	7
20	1322	7
21	3032	7
22	2753	7
23	2781	7
24	2833	7
25	2977	7
26	3074	7
27	3494	7
28	3743	7
29	4033	7
30	4473	7
31	5028	7

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

5.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.0b	(*.f64 x (/.f64 y z))

Compiler

Compiled 36 to 21 computations (41.7% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.7b	(*.f64 x (/.f64 y z))

series16.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

16.0ms

(*.f64 x (/.f64 y z))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
10×	`times-frac_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

1 → 34

Calls

1 calls:

5.0ms

(*.f64 x (/.f64 y z))

simplify118.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

736×	`fabs-mul_binary64`
732×	`sqr-pow_binary64`
503×	`pow-sqr_binary64`
384×	`associate-/l/_binary64`
307×	`unswap-sqr_binary64`

Counts

70 → 50

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	72	642
1	162	597
2	526	597
3	1312	597
4	2135	597
5	2239	597
6	2445	597
7	2751	597
8	3643	597
9	4500	597
10	4489	597
11	5931	597

prune39.0ms (0.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	40	10	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	11	51

Error

0.0b

Counts

51 → 11

Alt Table

Status	Error	Program
	5.7b	(.f64 (.f64 x (*.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z)))) (cbrt.f64 (/.f64 y z)))
	5.3b	(/.f64 (*.f64 y x) z)
	16.4b	(.f64 (.f64 x (sqrt.f64 y)) (/.f64 (sqrt.f64 y) z))
	5.7b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 y z)))
	5.5b	(.f64 (.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 y) z))
	29.1b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 y x) z) 3))
▶	5.2b	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)))
	5.3b	(.f64 (.f64 x y) (/.f64 1 z))
	54.8b	(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 y z))) (*.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 y z))))
	32.7b	(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 y (sqrt.f64 z)))
✓	5.0b	(*.f64 x (/.f64 y z))

Compiler

Compiled 839 to 332 computations (60.4% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 y (cbrt.f64 z))
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.5b	(cbrt.f64 z)
✓	4.4b	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)))

series433.0ms (7.9%)

Counts

4 → 84

Calls

4 calls:

307.0ms	(/.f64 y (cbrt.f64 z))
45.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
44.0ms	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)))
37.0ms	(cbrt.f64 z)

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-sqr-sqrt_binary64`
46×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-cube-cbrt_binary64`
42×	`cbrt-prod_binary64`

Counts

4 → 157

Calls

4 calls:

14.0ms	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)))
5.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
3.0ms	(/.f64 y (cbrt.f64 z))
1.0ms	(cbrt.f64 z)

simplify149.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

527×	`fma-neg_binary64`
473×	`associate-/r/_binary64`
442×	`*-commutative_binary64`
328×	`unswap-sqr_binary64`
168×	`associate-*r/_binary64`

Counts

241 → 233

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	193	3378
1	446	2551
2	1904	2483
3	2638	2429
4	4570	2429
5	4918	2429

prune155.0ms (2.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	267	2	269
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	269	11	280

Error

0.0b

Counts

280 → 11

Alt Table

Status	Error	Program
	5.7b	(.f64 (.f64 x (*.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z)))) (cbrt.f64 (/.f64 y z)))
	5.3b	(/.f64 (*.f64 y x) z)
	16.4b	(.f64 (.f64 x (sqrt.f64 y)) (/.f64 (sqrt.f64 y) z))
	5.7b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 y z)))
	5.5b	(.f64 (.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 y) z))
▶	5.2b	(/.f64 (.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) y) (cbrt.f64 z))
	5.5b	(/.f64 (.f64 x (/.f64 y (cbrt.f64 z))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))
	29.1b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 y x) z) 3))
	5.3b	(.f64 (.f64 x y) (/.f64 1 z))
	32.7b	(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 y (sqrt.f64 z)))
✓	5.0b	(*.f64 x (/.f64 y z))

Compiler

Compiled 5111 to 1353 computations (73.5% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
	0.5b	(cbrt.f64 z)
✓	1.7b	(/.f64 (.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) y) (cbrt.f64 z))
✓	4.1b	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) y)

series1.0s (18.6%)

Counts

2 → 72

Calls

2 calls:

984.0ms	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) y)
42.0ms	(/.f64 (.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) y) (cbrt.f64 z))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-exp-log_binary64`
17×	`add-cbrt-cube_binary64`
13×	`add-sqr-sqrt_binary64`
10×	`times-frac_binary64`
9×	`*-un-lft-identity_binary64`

Counts

2 → 64

Calls

2 calls:

12.0ms	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) y)
8.0ms	(/.f64 (.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) y) (cbrt.f64 z))

simplify100.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

521×	`associate-l_binary64`
504×	`associate-/r*_binary64`
422×	`associate-r_binary64`
274×	`associate-/r/_binary64`
242×	`unswap-sqr_binary64`

Counts

136 → 108

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	124	2328
1	277	1782
2	1088	1770
3	3429	1696
4	4078	1696
5	4934	1696

prune127.0ms (2.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	220	1	221
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	222	10	232

Error

0.0b

Counts

232 → 10

Alt Table

Status	Error	Program
	16.4b	(.f64 (.f64 x (sqrt.f64 y)) (/.f64 (sqrt.f64 y) z))
	5.7b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 y z)))
	5.6b	(/.f64 1 (/.f64 z (*.f64 y x)))
✓	5.0b	(*.f64 x (/.f64 y z))
	5.5b	(.f64 (.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 y) z))
✓	5.2b	(/.f64 (.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) y) (cbrt.f64 z))
	29.1b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 y x) z) 3))
	5.3b	(.f64 (.f64 x y) (/.f64 1 z))
▶	5.3b	(/.f64 (*.f64 y x) z)
	32.7b	(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 y (sqrt.f64 z)))

Compiler

Compiled 3945 to 1234 computations (68.7% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	5.1b	(/.f64 (*.f64 y x) z)

series13.0ms (0.2%)

Counts

1 → 0

Calls

1 calls:

13.0ms

(/.f64 (*.f64 y x) z)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
3×	`associate-/r*_binary64`
3×	`*-un-lft-identity_binary64`
3×	`times-frac_binary64`

Counts

1 → 23

Calls

1 calls:

4.0ms

(/.f64 (*.f64 y x) z)

simplify96.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1114×	`div-sub_binary64`
994×	`associate-/r/_binary64`
985×	`fma-neg_binary64`
841×	`fma-def_binary64`
355×	`associate-/l*_binary64`

Counts

23 → 28

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	51	261
1	117	216
2	399	216
3	1584	216
4	1842	216
5	1965	216
6	2373	216
7	3409	216
8	4190	216
9	4557	216
10	4731	216

prune20.0ms (0.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	26	2	28
Fresh	2	5	7
Picked	0	1	1
Done	0	2	2
Total	28	10	38

Error

0.0b

Counts

38 → 10

Alt Table

Status	Error	Program
	6.2b	(/.f64 y (/.f64 z x))
	16.4b	(.f64 (.f64 x (sqrt.f64 y)) (/.f64 (sqrt.f64 y) z))
	5.7b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 y z)))
	6.4b	(*.f64 y (/.f64 x z))
	32.7b	(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 y (sqrt.f64 z)))
	5.6b	(/.f64 1 (/.f64 z (*.f64 y x)))
✓	5.0b	(*.f64 x (/.f64 y z))
✓	5.2b	(/.f64 (.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) y) (cbrt.f64 z))
	29.1b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 y x) z) 3))
✓	5.3b	(/.f64 (*.f64 y x) z)

Compiler

Compiled 388 to 162 computations (58.2% saved)

regimes260.0ms (4.7%)

Accuracy

Total 1.9b remaining (99.7%)

Threshold costs 0b (0%)

Counts

38 → 1

Compiler

Compiled 4395 to 2527 computations (42.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	31
1	14	31
2	14	31

end101.0ms (1.8%)

Remove: (sort x y)
Compiler: Compiled 209 to 123 computations (41.1% saved)

Details

analyze1.3s (22.8%)

sample1.3s (24.1%)

simplify170.0ms (3.1%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series16.0ms (0.3%)

rewrite7.0ms (0.1%)

simplify118.0ms (2.1%)

prune39.0ms (0.7%)

localize7.0ms (0.1%)

series433.0ms (7.9%)

rewrite32.0ms (0.6%)

simplify149.0ms (2.7%)

prune155.0ms (2.8%)

localize7.0ms (0.1%)

series1.0s (18.6%)

rewrite24.0ms (0.4%)

simplify100.0ms (1.8%)

prune127.0ms (2.3%)

localize5.0ms (0.1%)

series13.0ms (0.2%)

rewrite4.0ms (0.1%)

simplify96.0ms (1.8%)

prune20.0ms (0.4%)

regimes260.0ms (4.7%)

simplify3.0ms (0%)

end101.0ms (1.8%)

Profiling