Details

analyze658.0ms (14.7%)

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
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample1.0s (22.8%)

Results

940.0ms	8256×	body	128	valid
56.0ms	449×	body	128	invalid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	18	18
2	22	18
3	22	18

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

22.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	22.9b	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))

Compiler

Compiled 66 to 32 computations (51.5% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(fma.f64 a c (*.f64 b d))
✓	22.5b	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))

series85.0ms (1.9%)

Counts

2 → 96

Calls

2 calls:

76.0ms	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))
8.0ms	(fma.f64 a c (*.f64 b d))

rewrite82.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

512×	`log-prod_binary64`
348×	`prod-diff_binary64`
186×	`expm1-udef_binary64`
186×	`log1p-udef_binary64`
175×	`pow3_binary64`

Counts

2 → 66

Calls

2 calls:

80.0ms	(fma.f64 a c (*.f64 b d))
80.0ms	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	203	25
2	2457	25
3	4976	25
4	5153	25
0	0	0
1	0	0

simplify51.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

598×	`associate-*l/_binary64`
518×	`fma-def_binary64`
410×	`associate-/r/_binary64`
354×	`fma-neg_binary64`
282×	`associate-/l/_binary64`

Counts

162 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	1626
1	112	1542
2	350	1458
3	1545	1410
4	5146	1410

prune52.0ms (1.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	84	6	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	6	91

Error

1.1b

Counts

91 → 6

Alt Table

Status	Error	Program
	22.9b	(/.f64 (fma.f64 d b (.f64 c a)) (fma.f64 c c (.f64 d d)))
	36.3b	(fma.f64 b (/.f64 d (*.f64 c c)) (/.f64 a c))
	38.5b	(/.f64 a c)
	33.5b	(fma.f64 a (/.f64 c (*.f64 d d)) (/.f64 b d))
	39.2b	(pow.f64 (/.f64 (sqrt.f64 (fma.f64 a c (*.f64 b d))) (hypot.f64 c d)) 2)
▶	12.4b	(.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d)))

Compiler

Compiled 1822 to 631 computations (65.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (hypot.f64 c d))
✓	0.2b	(.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d)))
	0.5b	(fma.f64 a c (*.f64 b d))
✓	11.5b	(/.f64 (fma.f64 a c (*.f64 b d)) (hypot.f64 c d))

series203.0ms (4.5%)

Counts

3 → 120

Calls

3 calls:

97.0ms	(.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d)))
89.0ms	(/.f64 (fma.f64 a c (*.f64 b d)) (hypot.f64 c d))
17.0ms	(/.f64 1 (hypot.f64 c d))

rewrite76.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

614×	`log-prod_binary64`
254×	`prod-diff_binary64`
213×	`expm1-udef_binary64`
213×	`log1p-udef_binary64`
200×	`log-pow_binary64`

Counts

3 → 124

Calls

3 calls:

73.0ms	(/.f64 1 (hypot.f64 c d))
73.0ms	(.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d)))
73.0ms	(/.f64 (fma.f64 a c (*.f64 b d)) (hypot.f64 c d))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	41
1	245	38
2	2944	38
3	5627	38
0	0	0
1	0	0

simplify91.0ms (2%)

Algorithm

1×	egg-herbie

Rules

600×	`fma-neg_binary64`
573×	`times-frac_binary64`
429×	`associate-/l*_binary64`
359×	`fma-def_binary64`
322×	`cancel-sign-sub-inv_binary64`

Counts

244 → 208

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	117	3002
1	376	2830
2	1268	2666
3	4825	2658
4	5248	2658

prune145.0ms (3.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	237	4	241
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	240	7	247

Error

0.1b

Counts

247 → 7

Alt Table

Status	Error	Program
	22.9b	(/.f64 (fma.f64 d b (.f64 c a)) (fma.f64 c c (.f64 d d)))
	44.4b	(*.f64 (/.f64 1 (hypot.f64 c d)) (fma.f64 (/.f64 d c) b a))
	33.5b	(fma.f64 a (/.f64 c (*.f64 d d)) (/.f64 b d))
	33.5b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))
	30.7b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
▶	13.0b	(/.f64 1 (.f64 (/.f64 (hypot.f64 c d) (fma.f64 a c (.f64 b d))) (hypot.f64 c d)))
✓	12.4b	(.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d)))

Compiler

Compiled 5441 to 1996 computations (63.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 (hypot.f64 c d) (fma.f64 a c (.f64 b d))) (hypot.f64 c d))
	0.5b	(fma.f64 a c (*.f64 b d))
✓	0.7b	(/.f64 1 (.f64 (/.f64 (hypot.f64 c d) (fma.f64 a c (.f64 b d))) (hypot.f64 c d)))
✓	11.6b	(/.f64 (hypot.f64 c d) (fma.f64 a c (*.f64 b d)))

series226.0ms (5.1%)

Counts

3 → 144

Calls

3 calls:

98.0ms

(/.f64 1 (*.f64 (/.f64 (hypot.f64 c d) (fma.f64 a c (*.f64 b d))) (hypot.f64 c d)))

67.0ms

(*.f64 (/.f64 (hypot.f64 c d) (fma.f64 a c (*.f64 b d))) (hypot.f64 c d))

61.0ms

(/.f64 (hypot.f64 c d) (fma.f64 a c (*.f64 b d)))

rewrite79.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

617×	`log-prod_binary64`
245×	`prod-diff_binary64`
217×	`expm1-udef_binary64`
217×	`log1p-udef_binary64`
203×	`log-pow_binary64`

Counts

3 → 99

Calls

3 calls:

77.0ms

(*.f64 (/.f64 (hypot.f64 c d) (fma.f64 a c (*.f64 b d))) (hypot.f64 c d))

77.0ms

(/.f64 1 (*.f64 (/.f64 (hypot.f64 c d) (fma.f64 a c (*.f64 b d))) (hypot.f64 c d)))

77.0ms

(/.f64 (hypot.f64 c d) (fma.f64 a c (*.f64 b d)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	57
1	246	51
2	2960	51
3	5643	51
0	0	0
1	0	0

simplify188.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

887×	`cancel-sign-sub-inv_binary64`
326×	`times-frac_binary64`
321×	`sub-neg_binary64`
309×	`fma-neg_binary64`
256×	`associate-/l*_binary64`

Counts

243 → 195

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	194	6642
1	713	5852
2	3325	5816
3	5442	5816

prune175.0ms (3.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	228	0	228
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	228	7	235

Error

0.1b

Counts

235 → 7

Alt Table

Status	Error	Program
▶	22.9b	(/.f64 (fma.f64 d b (.f64 c a)) (fma.f64 c c (.f64 d d)))
	44.4b	(*.f64 (/.f64 1 (hypot.f64 c d)) (fma.f64 (/.f64 d c) b a))
	33.5b	(fma.f64 a (/.f64 c (*.f64 d d)) (/.f64 b d))
	33.5b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))
	30.7b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
✓	13.0b	(/.f64 1 (.f64 (/.f64 (hypot.f64 c d) (fma.f64 a c (.f64 b d))) (hypot.f64 c d)))
✓	12.4b	(.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d)))

Compiler

Compiled 6578 to 2797 computations (57.5% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 d b (*.f64 c a))
✓	22.5b	(/.f64 (fma.f64 d b (.f64 c a)) (fma.f64 c c (.f64 d d)))

series92.0ms (2.1%)

Counts

2 → 96

Calls

2 calls:

82.0ms	(/.f64 (fma.f64 d b (.f64 c a)) (fma.f64 c c (.f64 d d)))
10.0ms	(fma.f64 d b (*.f64 c a))

rewrite82.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

512×	`log-prod_binary64`
348×	`prod-diff_binary64`
186×	`expm1-udef_binary64`
186×	`log1p-udef_binary64`
175×	`pow3_binary64`

Counts

2 → 66

Calls

2 calls:

80.0ms	(fma.f64 d b (*.f64 c a))
80.0ms	(/.f64 (fma.f64 d b (.f64 c a)) (fma.f64 c c (.f64 d d)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	203	25
2	2457	25
3	4979	25
4	5156	25
0	0	0
1	0	0

simplify53.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

598×	`associate-*l/_binary64`
518×	`fma-def_binary64`
410×	`associate-/r/_binary64`
354×	`fma-neg_binary64`
282×	`associate-/l/_binary64`

Counts

162 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	1626
1	112	1542
2	350	1458
3	1545	1410
4	5146	1410

prune44.0ms (1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	90	7	97

Error

0.1b

Counts

97 → 7

Alt Table

Status	Error	Program
✓	22.9b	(/.f64 (fma.f64 d b (.f64 c a)) (fma.f64 c c (.f64 d d)))
	44.4b	(*.f64 (/.f64 1 (hypot.f64 c d)) (fma.f64 (/.f64 d c) b a))
	33.5b	(fma.f64 a (/.f64 c (*.f64 d d)) (/.f64 b d))
	33.5b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))
	30.7b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
✓	13.0b	(/.f64 1 (.f64 (/.f64 (hypot.f64 c d) (fma.f64 a c (.f64 b d))) (hypot.f64 c d)))
✓	12.4b	(.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d)))

Compiler

Compiled 1755 to 587 computations (66.6% saved)

regimes830.0ms (18.6%)

Accuracy

Total 10.1b remaining (97.8%)

Threshold costs 0b (0%)

Counts

76 → 5

Compiler

Compiled 6408 to 3994 computations (37.7% saved)

bsearch90.0ms (2%)

Steps

Iters	Range		Point
9	3.366100743382238e+180	6.148811803831594e+186	3.408225542871235e+180
6	7.633393291458624e-213	8.584019608971907e-212	4.5110647824345223e-212
11	-7.076260634261073e-232	-9.681289010105418e-256	-4.084260136662665e-238
10	-1.2042930726255398e+162	-4.505010813841915e+149	-9.705756685731516e+151

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	111
1	45	111
2	52	109
3	60	109
4	63	109
5	64	109
6	62	109

end96.0ms (2.1%)

Compiler: Compiled 275 to 131 computations (52.4% saved)

Details

analyze658.0ms (14.7%)

sample1.0s (22.8%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series85.0ms (1.9%)

rewrite82.0ms (1.8%)

simplify51.0ms (1.1%)

prune52.0ms (1.2%)

localize10.0ms (0.2%)

series203.0ms (4.5%)

rewrite76.0ms (1.7%)

simplify91.0ms (2%)

prune145.0ms (3.2%)

localize9.0ms (0.2%)

series226.0ms (5.1%)

rewrite79.0ms (1.8%)

simplify188.0ms (4.2%)

prune175.0ms (3.9%)

localize8.0ms (0.2%)

series92.0ms (2.1%)

rewrite82.0ms (1.8%)

simplify53.0ms (1.2%)

prune44.0ms (1%)

regimes830.0ms (18.6%)

bsearch90.0ms (2%)

simplify5.0ms (0.1%)

end96.0ms (2.1%)

Profiling