Details

analyze417.0ms (1.6%)

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
37.4%	62.4%	0.1%	8
40.6%	57.7%	1.7%	9
45.2%	51.1%	3.7%	10
57.7%	33.5%	8.7%	11
59.7%	29.4%	10.9%	12
62%	25%	13%	13
68.3%	17.4%	14.4%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.0s (3.9%)

Symmetry

(sort d2 d3)

Results

789.0ms	7733×	body	128	valid
75.0ms	700×	body	128	invalid
56.0ms	212×	body	512	valid
51.0ms	165×	body	1024	valid
32.0ms	146×	body	256	valid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

25×	`fma-def_binary64`
9×	`+-commutative_binary64`
9×	`*-commutative_binary64`
7×	`distribute-lft-out_binary64`
6×	`associate-+r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	20	10
2	44	10
3	64	10
4	66	10
5	67	10
6	67	10

prune3.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
▶	0.1b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))

Compiler

Compiled 69 to 45 computations (34.8% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))
✓	0.0b	(+.f64 (.f64 d1 3) (.f64 d1 d2))

series13.0ms (0%)

Counts

2 → 60

Calls

2 calls:

8.0ms	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))
4.0ms	(+.f64 (.f64 d1 3) (.f64 d1 d2))

rewrite71.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

758×	`fma-def_binary64`
346×	`fma-neg_binary64`
206×	`expm1-udef_binary64`
206×	`log1p-udef_binary64`
178×	`egg-rr`

Counts

2 → 178

Calls

2 calls:

65.0ms	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))
65.0ms	(+.f64 (.f64 d1 3) (.f64 d1 d2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	223	17
2	2988	17
3	5014	17
0	0	0
1	0	0

simplify19.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

31×	`fma-def_binary64`
9×	`+-commutative_binary64`
9×	`*-commutative_binary64`
6×	`distribute-rgt-in_binary64`
4×	`associate-+r+_binary64`

Counts

238 → 189

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	490
1	47	489
2	61	489
3	69	489
4	67	489

prune134.0ms (0.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	187	2	189
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	189	2	191

Error

0.0b

Counts

191 → 2

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 d1 3 (*.f64 d1 (+.f64 d2 d3)))
	1.3b	(pow.f64 (cbrt.f64 (*.f64 d1 (+.f64 (+.f64 3 d2) d3))) 3)

Compiler

Compiled 2887 to 1365 computations (52.7% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d2 d3))
✓	0.0b	(fma.f64 d1 3 (*.f64 d1 (+.f64 d2 d3)))

series32.0ms (0.1%)

Counts

2 → 60

Calls

2 calls:

23.0ms	(*.f64 d1 (+.f64 d2 d3))
8.0ms	(fma.f64 d1 3 (*.f64 d1 (+.f64 d2 d3)))

rewrite55.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

892×	`expm1-log1p-u_binary64`
813×	`prod-diff_binary64`
90×	`add-sqr-sqrt_binary64`
86×	`log1p-expm1-u_binary64`
84×	`add-log-exp_binary64`

Counts

2 → 51

Calls

2 calls:

53.0ms	(*.f64 d1 (+.f64 d2 d3))
53.0ms	(fma.f64 d1 3 (*.f64 d1 (+.f64 d2 d3)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	175	17
2	2205	17
3	5394	17
0	0	0
1	0	0

simplify20.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

28×	`fma-def_binary64`
10×	`+-commutative_binary64`
8×	`*-commutative_binary64`
5×	`associate-+r+_binary64`
5×	`distribute-rgt-in_binary64`

Counts

111 → 62

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	499
1	40	480
2	61	480
3	67	480
4	68	480
5	67	480

prune29.0ms (0.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	62	2	64

Error

0.0b

Counts

64 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 d1 3 (*.f64 d1 (+.f64 d2 d3)))
▶	1.3b	(pow.f64 (cbrt.f64 (*.f64 d1 (+.f64 (+.f64 3 d2) d3))) 3)

Compiler

Compiled 784 to 376 computations (52% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 (+.f64 3 d2) d3))
✓	0.6b	(cbrt.f64 (*.f64 d1 (+.f64 (+.f64 3 d2) d3)))
✓	0.7b	(pow.f64 (cbrt.f64 (*.f64 d1 (+.f64 (+.f64 3 d2) d3))) 3)

series23.8s (89%)

Counts

3 → 108

Calls

3 calls:

23.5s	(pow.f64 (cbrt.f64 (*.f64 d1 (+.f64 (+.f64 3 d2) d3))) 3)
305.0ms	(cbrt.f64 (*.f64 d1 (+.f64 (+.f64 3 d2) d3)))
7.0ms	(*.f64 d1 (+.f64 (+.f64 3 d2) d3))

rewrite66.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

836×	`prod-diff_binary64`
187×	`expm1-udef_binary64`
187×	`log1p-udef_binary64`
106×	`add-sqr-sqrt_binary64`
105×	`log1p-expm1-u_binary64`

Counts

3 → 101

Calls

3 calls:

64.0ms	(*.f64 d1 (+.f64 (+.f64 3 d2) d3))
64.0ms	(cbrt.f64 (*.f64 d1 (+.f64 (+.f64 3 d2) d3)))
64.0ms	(pow.f64 (cbrt.f64 (*.f64 d1 (+.f64 (+.f64 3 d2) d3))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	32
1	214	32
2	2800	32
3	4923	32
0	0	0
1	0	0

simplify143.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

282×	`fma-def_binary64`
281×	`sub-neg_binary64`
234×	`associate-r_binary64`
202×	`fma-neg_binary64`
197×	`*-commutative_binary64`

Counts

209 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	364	4968
1	1091	4389
2	3899	4165
3	4947	4165
4	4937	4165

prune128.0ms (0.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	168	3	171

Error

Counts

171 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 d1 3 (*.f64 d1 (+.f64 d2 d3)))
▶	25.7b	(/.f64 (.f64 (-.f64 (pow.f64 (+.f64 3 d2) 2) (.f64 d3 d3)) d1) (-.f64 (+.f64 3 d2) d3))
✓	1.3b	(pow.f64 (cbrt.f64 (*.f64 d1 (+.f64 (+.f64 3 d2) d3))) 3)

Compiler

Compiled 5564 to 3719 computations (33.2% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 3 d2) d3)
✓	2.8b	(-.f64 (pow.f64 (+.f64 3 d2) 2) (*.f64 d3 d3))
✓	8.1b	(.f64 (-.f64 (pow.f64 (+.f64 3 d2) 2) (.f64 d3 d3)) d1)
✓	16.0b	(/.f64 (.f64 (-.f64 (pow.f64 (+.f64 3 d2) 2) (.f64 d3 d3)) d1) (-.f64 (+.f64 3 d2) d3))

series96.0ms (0.4%)

Counts

4 → 114

Calls

4 calls:

56.0ms	(/.f64 (.f64 (-.f64 (pow.f64 (+.f64 3 d2) 2) (.f64 d3 d3)) d1) (-.f64 (+.f64 3 d2) d3))
27.0ms	(.f64 (-.f64 (pow.f64 (+.f64 3 d2) 2) (.f64 d3 d3)) d1)
9.0ms	(-.f64 (pow.f64 (+.f64 3 d2) 2) (*.f64 d3 d3))
3.0ms	(-.f64 (+.f64 3 d2) d3)

rewrite89.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

265×	`expm1-udef_binary64`
265×	`log1p-udef_binary64`
249×	`fma-neg_binary64`
163×	`egg-rr`
149×	`add-sqr-sqrt_binary64`

Counts

4 → 163

Calls

4 calls:

86.0ms	(-.f64 (+.f64 3 d2) d3)
86.0ms	(-.f64 (pow.f64 (+.f64 3 d2) 2) (*.f64 d3 d3))
86.0ms	(.f64 (-.f64 (pow.f64 (+.f64 3 d2) 2) (.f64 d3 d3)) d1)
86.0ms	(/.f64 (.f64 (-.f64 (pow.f64 (+.f64 3 d2) 2) (.f64 d3 d3)) d1) (-.f64 (+.f64 3 d2) d3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	61
1	303	46
2	3980	46
3	4976	46
0	0	0
1	0	0

simplify95.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

496×	`associate-/r*_binary64`
379×	`associate-*l/_binary64`
274×	`associate-/r/_binary64`
182×	`associate-+r+_binary64`
169×	`fma-def_binary64`

Counts

277 → 225

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	168	2815
1	578	2445
2	2266	2336
3	4864	2336
4	5053	2336

prune153.0ms (0.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	225	0	225
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	225	3	228

Error

Counts

228 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 d1 3 (*.f64 d1 (+.f64 d2 d3)))
✓	25.7b	(/.f64 (.f64 (-.f64 (pow.f64 (+.f64 3 d2) 2) (.f64 d3 d3)) d1) (-.f64 (+.f64 3 d2) d3))
✓	1.3b	(pow.f64 (cbrt.f64 (*.f64 d1 (+.f64 (+.f64 3 d2) d3))) 3)

Compiler

Compiled 5917 to 3806 computations (35.7% saved)

regimes246.0ms (0.9%)

Accuracy

Total 0.0b remaining (50.7%)

Threshold costs 0.0b (50.7%)

Counts

63 → 1

Compiler

Compiled 3628 to 2544 computations (29.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	9	12
2	9	12

end61.0ms (0.2%)

Remove: (sort d2 d3)
Compiler: Compiled 92 to 59 computations (35.9% saved)

Details

analyze417.0ms (1.6%)

sample1.0s (3.9%)

simplify7.0ms (0%)

prune3.0ms (0%)

localize7.0ms (0%)

series13.0ms (0%)

rewrite71.0ms (0.3%)

simplify19.0ms (0.1%)

prune134.0ms (0.5%)

localize5.0ms (0%)

series32.0ms (0.1%)

rewrite55.0ms (0.2%)

simplify20.0ms (0.1%)

prune29.0ms (0.1%)

localize7.0ms (0%)

series23.8s (89%)

rewrite66.0ms (0.2%)

simplify143.0ms (0.5%)

prune128.0ms (0.5%)

localize11.0ms (0%)

series96.0ms (0.4%)

rewrite89.0ms (0.3%)

simplify95.0ms (0.4%)

prune153.0ms (0.6%)

regimes246.0ms (0.9%)

simplify2.0ms (0%)

end61.0ms (0.2%)

Profiling