Details

analyze391.0ms (6.5%)

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
12.5%	87.4%	0.1%	6
28.1%	71.8%	0.1%	7
42.1%	57.7%	0.1%	8
43.7%	56.2%	0.1%	9
64.4%	35.5%	0.1%	10
71.6%	28.3%	0.1%	11
72.2%	27.7%	0.1%	12
81.6%	18.2%	0.2%	13
84.9%	14.9%	0.2%	14

Compiler

Compiled 16 to 9 computations (43.8% saved)

sample1.2s (19.5%)

Results

1.0s	8256×	body	128	valid
34.0ms	270×	body	128	invalid

Compiler

Compiled 47 to 26 computations (44.7% saved)

simplify74.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-def_binary64`
505×	`times-frac_binary64`
497×	`div-sub_binary64`
469×	`neg-mul-1_binary64`
463×	`neg-sub0_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	30	18
2	83	18
3	193	18
4	334	18
5	435	18
6	600	18
7	871	18
8	1369	16
9	3594	16
10	4298	16
11	4856	16

prune4.0ms (0.1%)

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
▶	2.0b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	19.9b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))

Compiler

Compiled 84 to 47 computations (44% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 v (+.f64 t1 u))
✓	1.9b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

series93.0ms (1.6%)

Counts

2 → 60

Calls

2 calls:

72.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
21.0ms	(/.f64 v (+.f64 t1 u))

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

223×	`times-frac_binary64`
181×	`add-sqr-sqrt_binary64`
174×	`*-un-lft-identity_binary64`
86×	`add-cube-cbrt_binary64`
38×	`difference-of-squares_binary64`

Counts

2 → 186

Calls

2 calls:

12.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
4.0ms	(/.f64 v (+.f64 t1 u))

simplify193.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

795×	`times-frac_binary64`
383×	`fma-def_binary64`
336×	`fma-neg_binary64`
293×	`associate-/l/_binary64`
286×	`distribute-rgt-in_binary64`

Counts

246 → 219

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	326	7288
1	848	7129
2	2435	7053
3	4601	7053
4	5003	7053

prune157.0ms (2.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	215	4	219
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	215	6	221

Error

0.0b

Counts

221 → 6

Alt Table

Status	Error	Program
	2.8b	(/.f64 (.f64 (.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u)))) (cbrt.f64 (/.f64 v (+.f64 t1 u)))) (-.f64 -1 (/.f64 u t1)))
✓	2.0b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	21.9b	(/.f64 (/.f64 v (-.f64 (.f64 t1 t1) (.f64 u u))) (/.f64 (-.f64 -1 (/.f64 u t1)) (-.f64 t1 u)))
	19.9b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
▶	2.7b	(/.f64 v (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 1 (+.f64 t1 u))))
	13.0b	(.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 1 (.f64 (/.f64 u t1) (/.f64 u t1)))) (+.f64 -1 (/.f64 u t1)))

Compiler

Compiled 5557 to 2068 computations (62.8% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 t1 u))
✓	0.2b	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 1 (+.f64 t1 u)))
✓	2.6b	(/.f64 v (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 1 (+.f64 t1 u))))

series91.0ms (1.5%)

Counts

3 → 84

Calls

3 calls:

73.0ms	(/.f64 v (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 1 (+.f64 t1 u))))
9.0ms	(/.f64 1 (+.f64 t1 u))
9.0ms	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 1 (+.f64 t1 u)))

rewrite180.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

1354×	`times-frac_binary64`
924×	`add-sqr-sqrt_binary64`
845×	`*-un-lft-identity_binary64`
469×	`add-cube-cbrt_binary64`
182×	`difference-of-squares_binary64`

Counts

3 → 669

Calls

3 calls:

25.0ms	(/.f64 v (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 1 (+.f64 t1 u))))
18.0ms	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 1 (+.f64 t1 u)))
4.0ms	(/.f64 1 (+.f64 t1 u))

simplify898.0ms (15%)

Algorithm

1×	egg-herbie

Rules

498×	`associate-/r/_binary64`
468×	`fma-def_binary64`
387×	`associate-*l/_binary64`
376×	`associate-/l/_binary64`
342×	`*-commutative_binary64`

Counts

753 → 739

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	541	23987
1	1314	23137
2	4556	23097
3	5004	23097

prune623.0ms (10.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	738	1	739
Fresh	0	4	4
Picked	0	1	1
Done	1	0	1
Total	739	6	745

Error

0.0b

Counts

745 → 6

Alt Table

Status	Error	Program
	21.9b	(/.f64 (/.f64 v (-.f64 (.f64 t1 t1) (.f64 u u))) (/.f64 (-.f64 -1 (/.f64 u t1)) (-.f64 t1 u)))
	19.9b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	13.0b	(.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 1 (.f64 (/.f64 u t1) (/.f64 u t1)))) (+.f64 -1 (/.f64 u t1)))
▶	1.7b	(/.f64 (/.f64 v (-.f64 -1 (/.f64 u t1))) (+.f64 t1 u))
	2.8b	(/.f64 (.f64 (.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u)))) (cbrt.f64 (/.f64 v (+.f64 t1 u)))) (-.f64 -1 (/.f64 u t1)))
✓	2.7b	(/.f64 v (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 1 (+.f64 t1 u))))

Compiler

Compiled 22337 to 10491 computations (53% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 (/.f64 v (-.f64 -1 (/.f64 u t1))) (+.f64 t1 u))
✓	3.7b	(/.f64 v (-.f64 -1 (/.f64 u t1)))

series109.0ms (1.8%)

Counts

2 → 72

Calls

2 calls:

78.0ms	(/.f64 (/.f64 v (-.f64 -1 (/.f64 u t1))) (+.f64 t1 u))
31.0ms	(/.f64 v (-.f64 -1 (/.f64 u t1)))

rewrite46.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

223×	`times-frac_binary64`
183×	`add-sqr-sqrt_binary64`
176×	`*-un-lft-identity_binary64`
88×	`add-cube-cbrt_binary64`
38×	`difference-of-squares_binary64`

Counts

2 → 186

Calls

2 calls:

13.0ms	(/.f64 (/.f64 v (-.f64 -1 (/.f64 u t1))) (+.f64 t1 u))
7.0ms	(/.f64 v (-.f64 -1 (/.f64 u t1)))

simplify250.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

779×	`associate-/l*_binary64`
346×	`fma-def_binary64`
316×	`associate-/r/_binary64`
291×	`fma-neg_binary64`
283×	`associate-/l/_binary64`

Counts

258 → 282

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	334	7376
1	823	7177
2	2373	7080
3	4873	7080
4	5034	7080

prune209.0ms (3.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	280	2	282
Fresh	1	3	4
Picked	0	1	1
Done	1	0	1
Total	282	6	288

Error

0.0b

Counts

288 → 6

Alt Table

Status	Error	Program
	21.9b	(/.f64 (/.f64 v (-.f64 (.f64 t1 t1) (.f64 u u))) (/.f64 (-.f64 -1 (/.f64 u t1)) (-.f64 t1 u)))
	19.9b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	36.8b	(/.f64 (.f64 -1 (/.f64 (.f64 t1 v) u)) (+.f64 t1 u))
	2.8b	(/.f64 (.f64 (.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u)))) (cbrt.f64 (/.f64 v (+.f64 t1 u)))) (-.f64 -1 (/.f64 u t1)))
✓	1.7b	(/.f64 (/.f64 v (-.f64 -1 (/.f64 u t1))) (+.f64 t1 u))
▶	2.6b	(*.f64 v (/.f64 (/.f64 1 (-.f64 -1 (/.f64 u t1))) (+.f64 u t1)))

Compiler

Compiled 7193 to 2969 computations (58.7% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 1 (-.f64 -1 (/.f64 u t1))) (+.f64 u t1))
✓	0.3b	(/.f64 1 (-.f64 -1 (/.f64 u t1)))
✓	2.5b	(*.f64 v (/.f64 (/.f64 1 (-.f64 -1 (/.f64 u t1))) (+.f64 u t1)))

series107.0ms (1.8%)

Counts

3 → 84

Calls

3 calls:

80.0ms	(*.f64 v (/.f64 (/.f64 1 (-.f64 -1 (/.f64 u t1))) (+.f64 u t1)))
17.0ms	(/.f64 (/.f64 1 (-.f64 -1 (/.f64 u t1))) (+.f64 u t1))
10.0ms	(/.f64 1 (-.f64 -1 (/.f64 u t1)))

rewrite103.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

408×	`times-frac_binary64`
322×	`add-sqr-sqrt_binary64`
316×	`*-un-lft-identity_binary64`
155×	`add-cube-cbrt_binary64`
102×	`associate-r_binary64`

Counts

3 → 321

Calls

3 calls:

30.0ms	(*.f64 v (/.f64 (/.f64 1 (-.f64 -1 (/.f64 u t1))) (+.f64 u t1)))
13.0ms	(/.f64 (/.f64 1 (-.f64 -1 (/.f64 u t1))) (+.f64 u t1))
8.0ms	(/.f64 1 (-.f64 -1 (/.f64 u t1)))

simplify312.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

389×	`associate-/l/_binary64`
384×	`fma-def_binary64`
366×	`fma-neg_binary64`
311×	`associate-/r/_binary64`
213×	`distribute-rgt-in_binary64`

Counts

405 → 429

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	314	10036
1	815	9460
2	2698	9366
3	4738	9342
4	4993	9342
5	4961	9342

prune313.0ms (5.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	429	0	429
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	429	6	435

Error

0.0b

Counts

435 → 6

Alt Table

Status	Error	Program
	21.9b	(/.f64 (/.f64 v (-.f64 (.f64 t1 t1) (.f64 u u))) (/.f64 (-.f64 -1 (/.f64 u t1)) (-.f64 t1 u)))
	19.9b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	36.8b	(/.f64 (.f64 -1 (/.f64 (.f64 t1 v) u)) (+.f64 t1 u))
	2.8b	(/.f64 (.f64 (.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u)))) (cbrt.f64 (/.f64 v (+.f64 t1 u)))) (-.f64 -1 (/.f64 u t1)))
✓	1.7b	(/.f64 (/.f64 v (-.f64 -1 (/.f64 u t1))) (+.f64 t1 u))
✓	2.6b	(*.f64 v (/.f64 (/.f64 1 (-.f64 -1 (/.f64 u t1))) (+.f64 u t1)))

Compiler

Compiled 11519 to 5720 computations (50.3% saved)

regimes503.0ms (8.4%)

Accuracy

Total 1.3b remaining (97.9%)

Threshold costs 0b (0%)

Counts

129 → 1

Compiler

Compiled 9814 to 6178 computations (37% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	13	16
2	19	16
3	23	16
4	26	16
5	27	16
6	27	16

end77.0ms (1.3%)

Compiler: Compiled 138 to 80 computations (42% saved)

Details

analyze391.0ms (6.5%)

sample1.2s (19.5%)

simplify74.0ms (1.2%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series93.0ms (1.6%)

rewrite41.0ms (0.7%)

simplify193.0ms (3.2%)

prune157.0ms (2.6%)

localize8.0ms (0.1%)

series91.0ms (1.5%)

rewrite180.0ms (3%)

simplify898.0ms (15%)

prune623.0ms (10.4%)

localize7.0ms (0.1%)

series109.0ms (1.8%)

rewrite46.0ms (0.8%)

simplify250.0ms (4.2%)

prune209.0ms (3.5%)

localize8.0ms (0.1%)

series107.0ms (1.8%)

rewrite103.0ms (1.7%)

simplify312.0ms (5.2%)

prune313.0ms (5.2%)

regimes503.0ms (8.4%)

simplify3.0ms (0%)

end77.0ms (1.3%)

Profiling