Details

analyze38.0ms (1.7%)

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
25%	74.9%	0.1%	4
37.5%	62.4%	0.1%	5
62.4%	37.5%	0.1%	6
87.4%	12.5%	0.1%	7
87.4%	12.5%	0.1%	8
93.7%	6.2%	0.1%	9
93.7%	6.2%	0.1%	10
96.8%	3.1%	0.1%	11
96.8%	3.1%	0.1%	12
98.3%	1.6%	0.1%	13
98.3%	1.6%	0.1%	14

Compiler

Compiled 10 to 6 computations (40% saved)

sample801.0ms (34.8%)

Results

706.0ms

8256×

body

128

valid

Compiler

Compiled 29 to 17 computations (41.4% saved)

simplify69.0ms (3%)

Algorithm

1×	egg-herbie

Rules

516×	`fma-neg_binary64`
439×	`fma-def_binary64`
382×	`times-frac_binary64`
357×	`div-sub_binary64`
168×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	9	10
2	14	10
3	21	10
4	28	10
5	51	10
6	74	10
7	104	10
8	154	10
9	319	10
10	479	10
11	806	10
12	1050	10
13	1216	10
14	1316	10
15	1330	10
16	1350	10
17	1350	10
18	1250	10

prune2.0ms (0.1%)

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 (+.f64 x y) (-.f64 x y))

Compiler

Compiled 27 to 15 computations (44.4% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))

series8.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(/.f64 (+.f64 x y) (-.f64 x y))

rewrite51.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

828×	`log1p-expm1-u_binary64`
828×	`expm1-log1p-u_binary64`
552×	`prod-diff_binary64`
74×	`add-sqr-sqrt_binary64`
69×	`add-log-exp_binary64`

Counts

1 → 36

Calls

1 calls:

50.0ms

(/.f64 (+.f64 x y) (-.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	140	10
2	2045	10
3	6174	10
0	0	0
1	0	0

simplify51.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

825×	`associate-/l*_binary64`
574×	`fma-neg_binary64`
505×	`associate-/r*_binary64`
368×	`associate-/r/_binary64`
338×	`cancel-sign-sub-inv_binary64`

Counts

60 → 50

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	38	417
1	119	399
2	366	339
3	1394	327
4	4483	318
5	4972	318

prune40.0ms (1.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	47	3	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	3	51

Error

Counts

51 → 3

Alt Table

Status	Error	Program
▶	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3))
	29.9b	(fma.f64 2 (*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x)) 1)
	34.1b	(fma.f64 -2 (+.f64 (/.f64 x y) (fma.f64 (/.f64 x y) (/.f64 x y) (pow.f64 (/.f64 x y) 3))) -1)

Compiler

Compiled 740 to 305 computations (58.8% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))
✓	0.0b	(pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3)
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3))

series27.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

16.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3))
11.0ms	(pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3)

rewrite86.0ms (3.7%)

Algorithm

2×	batch-egg-rewrite

Rules

653×	`prod-diff_binary64`
239×	`fma-def_binary64`
165×	`expm1-udef_binary64`
165×	`log1p-udef_binary64`
144×	`log-pow_binary64`

Counts

2 → 91

Calls

2 calls:

84.0ms	(pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3)
84.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	189	23
2	2522	23
3	4861	23
4	5035	23
0	0	0
1	0	0

simplify67.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

500×	`fma-neg_binary64`
364×	`distribute-rgt-neg-in_binary64`
330×	`times-frac_binary64`
291×	`fma-def_binary64`
279×	`distribute-neg-frac_binary64`

Counts

139 → 125

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	883
1	269	853
2	862	753
3	3457	741
4	4967	741
5	5063	741

prune115.0ms (5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	175	3	178

Error

Counts

178 → 3

Alt Table

Status	Error	Program
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3))
▶	29.9b	(fma.f64 2 (*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x)) 1)
	34.1b	(fma.f64 -2 (+.f64 (/.f64 x y) (fma.f64 (/.f64 x y) (/.f64 x y) (pow.f64 (/.f64 x y) 3))) -1)

Compiler

Compiled 2770 to 1181 computations (57.4% saved)

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x))

series12.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

12.0ms

(*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x))

rewrite59.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

785×	`log1p-expm1-u_binary64`
785×	`expm1-log1p-u_binary64`
250×	`prod-diff_binary64`
75×	`add-sqr-sqrt_binary64`
70×	`add-log-exp_binary64`

Counts

1 → 43

Calls

1 calls:

58.0ms

(*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	150	13
2	1970	13
3	5305	13
0	0	0
1	0	0

simplify97.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

1254×	`fma-def_binary64`
1250×	`associate-/r/_binary64`
570×	`unswap-sqr_binary64`
560×	`times-frac_binary64`
356×	`sqr-pow_binary64`

Counts

67 → 49

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	10	330
1	18	330
2	30	276
3	76	276
4	286	276
5	1826	276
6	3059	240
7	3437	240
8	3687	240
9	3960	240
10	4232	240
11	5216	240

prune28.0ms (1.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	49	3	52

Error

Counts

52 → 3

Alt Table

Status	Error	Program
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3))
✓	29.9b	(fma.f64 2 (*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x)) 1)
▶	34.1b	(fma.f64 -2 (+.f64 (/.f64 x y) (fma.f64 (/.f64 x y) (/.f64 x y) (pow.f64 (/.f64 x y) 3))) -1)

Compiler

Compiled 905 to 517 computations (42.9% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x y) (fma.f64 (/.f64 x y) (/.f64 x y) (pow.f64 (/.f64 x y) 3)))
✓	0.2b	(pow.f64 (/.f64 x y) 3)
✓	5.9b	(fma.f64 (/.f64 x y) (/.f64 x y) (pow.f64 (/.f64 x y) 3))

series48.0ms (2.1%)

Counts

3 → 72

Calls

3 calls:

20.0ms	(fma.f64 (/.f64 x y) (/.f64 x y) (pow.f64 (/.f64 x y) 3))
15.0ms	(+.f64 (/.f64 x y) (fma.f64 (/.f64 x y) (/.f64 x y) (pow.f64 (/.f64 x y) 3)))
13.0ms	(pow.f64 (/.f64 x y) 3)

rewrite69.0ms (3%)

Algorithm

2×	batch-egg-rewrite

Rules

923×	`log1p-expm1-u_binary64`
923×	`expm1-log1p-u_binary64`
99×	`egg-rr`
89×	`add-sqr-sqrt_binary64`
83×	`add-cbrt-cube_binary64`

Counts

3 → 99

Calls

3 calls:

67.0ms	(+.f64 (/.f64 x y) (fma.f64 (/.f64 x y) (/.f64 x y) (pow.f64 (/.f64 x y) 3)))
67.0ms	(pow.f64 (/.f64 x y) 3)
67.0ms	(fma.f64 (/.f64 x y) (/.f64 x y) (pow.f64 (/.f64 x y) 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	47
1	181	45
2	2314	45
3	5544	45
0	0	0
1	0	0

simplify123.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

536×	`fma-def_binary64`
497×	`unswap-sqr_binary64`
490×	`sqr-pow_binary64`
349×	`times-frac_binary64`
268×	`*-commutative_binary64`

Counts

171 → 109

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	16	1188
1	37	1188
2	90	912
3	335	888
4	1708	882
5	3301	882
6	3725	882
7	3959	882
8	4269	882
9	4821	882
10	4991	882

prune108.0ms (4.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	109	3	112

Error

Counts

112 → 3

Alt Table

Status	Error	Program
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3))
✓	29.9b	(fma.f64 2 (*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x)) 1)
✓	34.1b	(fma.f64 -2 (+.f64 (/.f64 x y) (fma.f64 (/.f64 x y) (/.f64 x y) (pow.f64 (/.f64 x y) 3))) -1)

Compiler

Compiled 2792 to 1396 computations (50% saved)

regimes298.0ms (12.9%)

Accuracy

Total 0.0b remaining (61.2%)

Threshold costs 0.0b (61.2%)

Counts

85 → 1

Compiler

Compiled 3474 to 2235 computations (35.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	11	14
2	16	14
3	18	14
4	19	14
5	19	14

end78.0ms (3.4%)

Compiler: Compiled 69 to 41 computations (40.6% saved)

Details

analyze38.0ms (1.7%)

sample801.0ms (34.8%)

simplify69.0ms (3%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series8.0ms (0.3%)

rewrite51.0ms (2.2%)

simplify51.0ms (2.2%)

prune40.0ms (1.7%)

localize7.0ms (0.3%)

series27.0ms (1.2%)

rewrite86.0ms (3.7%)

simplify67.0ms (2.9%)

prune115.0ms (5%)

localize6.0ms (0.3%)

series12.0ms (0.5%)

rewrite59.0ms (2.6%)

simplify97.0ms (4.2%)

prune28.0ms (1.2%)

localize8.0ms (0.3%)

series48.0ms (2.1%)

rewrite69.0ms (3%)

simplify123.0ms (5.3%)

prune108.0ms (4.7%)

regimes298.0ms (12.9%)

simplify3.0ms (0.1%)

end78.0ms (3.4%)

Profiling