Details

analyze1.1s (22.2%)

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)

sample1.4s (30%)

Symmetry

(sort x y)

Results

1.1s	8256×	body	128	valid
273.0ms	1561×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify169.0ms (3.5%)

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

7.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.0b	(*.f64 x (/.f64 y z))

Compiler

Compiled 36 to 21 computations (41.7% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	6.7b	(*.f64 x (/.f64 y z))

series13.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

13.0ms

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

rewrite6.0ms (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))

simplify109.0ms (2.3%)

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

prune37.0ms (0.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	42	8	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	42	9	51

Error

0.0b

Counts

51 → 9

Alt Table

Status	Error	Program
	6.7b	(.f64 (.f64 x y) (/.f64 1 z))
	7.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 y z)))
✓	7.0b	(*.f64 x (/.f64 y z))
	34.2b	(.f64 (.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (sqrt.f64 z))) (/.f64 (cbrt.f64 y) (sqrt.f64 z)))
	7.7b	(.f64 (.f64 x (*.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z)))) (cbrt.f64 (/.f64 y z)))
	6.7b	(/.f64 (*.f64 y x) z)
	29.2b	(.f64 (sqrt.f64 (.f64 x (/.f64 y z))) (sqrt.f64 (*.f64 x (/.f64 y z))))
▶	5.1b	(.f64 (.f64 x (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 y (cbrt.f64 z)))
	20.4b	(.f64 (.f64 x (sqrt.f64 y)) (/.f64 (sqrt.f64 y) z))

Compiler

Compiled 797 to 304 computations (61.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)
✓	4.2b	(.f64 (.f64 x (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 y (cbrt.f64 z)))

series191.0ms (4%)

Counts

4 → 72

Calls

4 calls:

74.0ms	(/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
42.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
40.0ms	(.f64 (.f64 x (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 y (cbrt.f64 z)))
35.0ms	(cbrt.f64 z)

rewrite36.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`add-exp-log_binary64`
40×	`prod-exp_binary64`
36×	`add-sqr-sqrt_binary64`
31×	`add-cbrt-cube_binary64`
28×	`cbrt-prod_binary64`

Counts

4 → 156

Calls

4 calls:

13.0ms	(.f64 (.f64 x (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 y (cbrt.f64 z)))
4.0ms	(/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
4.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms	(cbrt.f64 z)

simplify136.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

540×	`associate-/r/_binary64`
464×	`associate-/l/_binary64`
419×	`unswap-sqr_binary64`
320×	`fma-neg_binary64`
281×	`associate-l_binary64`

Counts

228 → 220

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	194	3159
1	422	2008
2	1800	1909
3	3462	1837
4	4761	1837
5	4990	1837
6	4970	1837

prune132.0ms (2.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	256	9	265

Error

0.0b

Counts

265 → 9

Alt Table

Status	Error	Program
	6.7b	(.f64 (.f64 x y) (/.f64 1 z))
	7.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 y z)))
✓	7.0b	(*.f64 x (/.f64 y z))
	34.2b	(.f64 (.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (sqrt.f64 z))) (/.f64 (cbrt.f64 y) (sqrt.f64 z)))
	7.7b	(.f64 (.f64 x (*.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z)))) (cbrt.f64 (/.f64 y z)))
▶	6.7b	(/.f64 (*.f64 y x) z)
	29.2b	(.f64 (sqrt.f64 (.f64 x (/.f64 y z))) (sqrt.f64 (*.f64 x (/.f64 y z))))
✓	5.1b	(.f64 (.f64 x (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 y (cbrt.f64 z)))
	20.4b	(.f64 (.f64 x (sqrt.f64 y)) (/.f64 (sqrt.f64 y) z))

Compiler

Compiled 5000 to 1884 computations (62.3% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	6.4b	(/.f64 (*.f64 y x) z)

series14.0ms (0.3%)

Counts

1 → 0

Calls

1 calls:

14.0ms

(/.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:

3.0ms

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

simplify91.0ms (1.9%)

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

prune23.0ms (0.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	3	3	6
Picked	0	1	1
Done	0	2	2
Total	30	7	37

Error

Counts

37 → 7

Alt Table

Status	Error	Program
	34.2b	(.f64 (.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (sqrt.f64 z))) (/.f64 (cbrt.f64 y) (sqrt.f64 z)))
✓	6.7b	(/.f64 (*.f64 y x) z)
✓	7.0b	(*.f64 x (/.f64 y z))
▶	5.2b	(/.f64 y (/.f64 z x))
	29.2b	(.f64 (sqrt.f64 (.f64 x (/.f64 y z))) (sqrt.f64 (*.f64 x (/.f64 y z))))
✓	5.1b	(.f64 (.f64 x (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 y (cbrt.f64 z)))
	20.4b	(.f64 (.f64 x (sqrt.f64 y)) (/.f64 (sqrt.f64 y) z))

Compiler

Compiled 425 to 176 computations (58.6% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series12.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

12.0ms

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

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
43×	`add-cube-cbrt_binary64`
13×	`associate-/r*_binary64`

Counts

1 → 72

Calls

1 calls:

4.0ms

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

simplify135.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1089×	`associate-/r/_binary64`
835×	`fma-def_binary64`
611×	`fma-neg_binary64`
460×	`distribute-rgt-in_binary64`
452×	`div-sub_binary64`

Counts

108 → 114

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	1514
1	310	1454
2	924	1451
3	2212	1451
4	2356	1451
5	2544	1451
6	2955	1451
7	3895	1451
8	4379	1451
9	5031	1451

prune62.0ms (1.3%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	114	7	121

Error

Counts

121 → 7

Alt Table

Status	Error	Program
	34.2b	(.f64 (.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (sqrt.f64 z))) (/.f64 (cbrt.f64 y) (sqrt.f64 z)))
✓	6.7b	(/.f64 (*.f64 y x) z)
✓	7.0b	(*.f64 x (/.f64 y z))
✓	5.2b	(/.f64 y (/.f64 z x))
	29.2b	(.f64 (sqrt.f64 (.f64 x (/.f64 y z))) (sqrt.f64 (*.f64 x (/.f64 y z))))
✓	5.1b	(.f64 (.f64 x (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 y (cbrt.f64 z)))
	20.4b	(.f64 (.f64 x (sqrt.f64 y)) (/.f64 (sqrt.f64 y) z))

Compiler

Compiled 1629 to 432 computations (73.5% saved)

regimes849.0ms (17.8%)

Accuracy

Total 1.0b remaining (97.9%)

Threshold costs 0b (0%)

Counts

69 → 5

Compiler

Compiled 7750 to 4609 computations (40.5% saved)

bsearch2.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	71
1	25	71
2	25	71

end223.0ms (4.7%)

Compiler: Compiled 307 to 144 computations (53.1% saved)

Details

analyze1.1s (22.2%)

sample1.4s (30%)

simplify169.0ms (3.5%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series13.0ms (0.3%)

rewrite6.0ms (0.1%)

simplify109.0ms (2.3%)

prune37.0ms (0.8%)

localize8.0ms (0.2%)

series191.0ms (4%)

rewrite36.0ms (0.7%)

simplify136.0ms (2.9%)

prune132.0ms (2.8%)

localize4.0ms (0.1%)

series14.0ms (0.3%)

rewrite4.0ms (0.1%)

simplify91.0ms (1.9%)

prune23.0ms (0.5%)

localize4.0ms (0.1%)

series12.0ms (0.2%)

rewrite11.0ms (0.2%)

simplify135.0ms (2.8%)

prune62.0ms (1.3%)

regimes849.0ms (17.8%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end223.0ms (4.7%)

Profiling