Details

analyze349.0ms (7.8%)

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
37.4%	62.4%	0.1%	9
46.8%	47.6%	5.6%	10
54.6%	39.4%	6%	11
62.8%	31%	6.2%	12
66.9%	23.9%	9.2%	13
71.7%	19%	9.4%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample833.0ms (18.5%)

Symmetry

(sort y z)

Results

753.0ms	8256×	body	128	valid
24.0ms	288×	body	128	invalid

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify16.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

100×	`fma-def_binary64`
56×	`fma-neg_binary64`
28×	`cancel-sign-sub-inv_binary64`
18×	`sub-neg_binary64`
13×	`distribute-rgt-neg-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	12	7
2	22	7
3	39	7
4	53	7
5	83	7
6	115	7
7	142	7
8	178	7
9	186	7
10	206	7
11	212	7
12	189	7

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 x (*.f64 y z))

Compiler

Compiled 24 to 15 computations (37.5% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 y z))

series5.0ms (0.1%)

Counts

1 → 9

Calls

1 calls:

5.0ms

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

rewrite72.0ms (1.6%)

Algorithm

1×	egg-rewrite

Rules

98× egg

Counts

1 → 98

Calls

1 calls:

70.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	132	7
2	1712	7
3	5386	7

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Counts

107 → 101

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	34
1	12	34
2	24	34
3	25	34
4	29	34
5	47	34
6	58	34
7	63	34
8	75	34
9	72	34
10	58	34

prune38.0ms (0.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	100	2	102

Error

0.0b

Counts

102 → 2

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 x (*.f64 y z))
▶	31.3b	(pow.f64 (sqrt.f64 (-.f64 x (*.f64 y z))) 2)

Compiler

Compiled 2216 to 393 computations (82.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 x (*.f64 y z))
✓	0.0b	(sqrt.f64 (-.f64 x (*.f64 y z)))
✓	0.3b	(pow.f64 (sqrt.f64 (-.f64 x (*.f64 y z))) 2)

series212.0ms (4.7%)

Counts

2 → 24

Calls

2 calls:

173.0ms	(pow.f64 (sqrt.f64 (-.f64 x (*.f64 y z))) 2)
38.0ms	(sqrt.f64 (-.f64 x (*.f64 y z)))

rewrite120.0ms (2.7%)

Algorithm

2×	egg-rewrite

Rules

104×	`egg`
25×	`egg`

Counts

2 → 129

Calls

2 calls:

65.0ms	(pow.f64 (sqrt.f64 (-.f64 x (*.f64 y z))) 2)
52.0ms	(sqrt.f64 (-.f64 x (*.f64 y z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	7
1	178	7
2	2084	7
3	6167	7
0	7	9
1	151	9
2	1905	9
3	5808	9

simplify70.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

501×	`distribute-rgt-neg-in_binary64`
499×	`distribute-lft-neg-in_binary64`
449×	`fma-neg_binary64`
420×	`neg-mul-1_binary64`
305×	`associate-r_binary64`

Counts

153 → 146

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	57	548
1	172	481
2	499	471
3	2264	447
4	4870	447
5	5247	447

prune112.0ms (2.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	246	1	247
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	246	3	249

Error

Counts

249 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 x (*.f64 y z))
✓	31.3b	(pow.f64 (sqrt.f64 (-.f64 x (*.f64 y z))) 2)
▶	0.5b	(+.f64 (fma.f64 x 1 (neg.f64 (.f64 (.f64 (cbrt.f64 y) z) (pow.f64 (cbrt.f64 y) 2)))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 y) z)) (pow.f64 (cbrt.f64 y) 2) (.f64 (*.f64 (cbrt.f64 y) z) (pow.f64 (cbrt.f64 y) 2))))

Compiler

Compiled 5557 to 1622 computations (70.8% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 y) z) (pow.f64 (cbrt.f64 y) 2))
✓	0.6b	(pow.f64 (cbrt.f64 y) 2)
✓	0.6b	(cbrt.f64 y)
✓	52.0b	(fma.f64 (neg.f64 (.f64 (cbrt.f64 y) z)) (pow.f64 (cbrt.f64 y) 2) (.f64 (*.f64 (cbrt.f64 y) z) (pow.f64 (cbrt.f64 y) 2)))

series1.6s (36.1%)

Counts

4 → 72

Calls

4 calls:

1.5s	(fma.f64 (neg.f64 (.f64 (cbrt.f64 y) z)) (pow.f64 (cbrt.f64 y) 2) (.f64 (*.f64 (cbrt.f64 y) z) (pow.f64 (cbrt.f64 y) 2)))
43.0ms	(pow.f64 (cbrt.f64 y) 2)
40.0ms	(cbrt.f64 y)
19.0ms	(.f64 (.f64 (cbrt.f64 y) z) (pow.f64 (cbrt.f64 y) 2))

rewrite341.0ms (7.6%)

Algorithm

4×	egg-rewrite

Rules

43×	`egg`
39×	`egg`
33×	`egg`
24×	`egg`

Counts

4 → 139

Calls

4 calls:

150.0ms	(pow.f64 (cbrt.f64 y) 2)
78.0ms	(cbrt.f64 y)
64.0ms	(fma.f64 (neg.f64 (.f64 (cbrt.f64 y) z)) (pow.f64 (cbrt.f64 y) 2) (.f64 (*.f64 (cbrt.f64 y) z) (pow.f64 (cbrt.f64 y) 2)))
46.0ms	(.f64 (.f64 (cbrt.f64 y) z) (pow.f64 (cbrt.f64 y) 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	208	10
2	2102	10
3	6120	10
0	3	3
1	56	3
2	621	3
3	4737	3
4	5240	3
0	5	6
1	99	4
2	936	4
3	4427	4
4	5288	4
0	8	14
1	160	4
2	1693	4
3	4966	4

simplify144.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

776×	`fma-def_binary64`
735×	`sqr-pow_binary64`
412×	`unswap-sqr_binary64`
336×	`*-commutative_binary64`
328×	`cube-prod_binary64`

Counts

211 → 145

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	299
1	45	299
2	87	299
3	198	299
4	583	299
5	983	299
6	1046	299
7	1259	299
8	1532	299
9	1823	299
10	2170	299
11	2526	299
12	2988	299
13	3707	299
14	4621	299
15	4909	299
16	4818	299

prune394.0ms (8.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	452	0	452
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	452	3	455

Error

Counts

455 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 x (*.f64 y z))
✓	31.3b	(pow.f64 (sqrt.f64 (-.f64 x (*.f64 y z))) 2)
✓	0.5b	(+.f64 (fma.f64 x 1 (neg.f64 (.f64 (.f64 (cbrt.f64 y) z) (pow.f64 (cbrt.f64 y) 2)))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 y) z)) (pow.f64 (cbrt.f64 y) 2) (.f64 (*.f64 (cbrt.f64 y) z) (pow.f64 (cbrt.f64 y) 2))))

Compiler

Compiled 16203 to 7218 computations (55.5% saved)

regimes47.0ms (1%)

Accuracy

Total 0.0b remaining (25%)

Threshold costs 0.0b (25%)

Counts

8 → 1

Compiler

Compiled 587 to 366 computations (37.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	12	7
2	22	7
3	28	7
4	32	7
5	33	7
6	33	7

end79.0ms (1.8%)

Remove: (sort y z)
Compiler: Compiled 87 to 52 computations (40.2% saved)

Iter	Nodes	Cost
0	6	7
1	12	7
2	22	7
3	39	7
4	53	7
5	83	7
6	115	7
7	142	7
8	178	7
9	186	7
10	206	7
11	212	7
12	189	7

Iter	Nodes	Cost
0	6	7
1	12	7
2	22	7
3	39	7
4	53	7
5	83	7
6	115	7
7	142	7
8	178	7
9	186	7
10	206	7
11	212	7
12	189	7

Details

analyze349.0ms (7.8%)

sample833.0ms (18.5%)

simplify16.0ms (0.4%)

prune2.0ms (0%)

localize4.0ms (0.1%)

series5.0ms (0.1%)

rewrite72.0ms (1.6%)

simplify11.0ms (0.2%)

prune38.0ms (0.8%)

localize6.0ms (0.1%)

series212.0ms (4.7%)

rewrite120.0ms (2.7%)

simplify70.0ms (1.6%)

prune112.0ms (2.5%)

localize13.0ms (0.3%)

series1.6s (36.1%)

rewrite341.0ms (7.6%)

simplify144.0ms (3.2%)

prune394.0ms (8.8%)

regimes47.0ms (1%)

simplify2.0ms (0.1%)

end79.0ms (1.8%)

Profiling

Iter	Nodes	Cost
0	6	7
1	12	7
2	22	7
3	39	7
4	53	7
5	83	7
6	115	7
7	142	7
8	178	7
9	186	7
10	206	7
11	212	7
12	189	7