Details

analyze561.0ms (16.1%)

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
25%	74.9%	0.1%	7
31.2%	68.6%	0.1%	8
35.9%	64%	0.1%	9
47.6%	49.9%	2.5%	10
49.1%	46.8%	4%	11
51.1%	44.1%	4.8%	12
60.2%	29.9%	9.9%	13
60.6%	27.9%	11.6%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.1s (31.9%)

Symmetry

(sort x y)

Results

877.0ms	8256×	body	128	valid
162.0ms	1628×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify47.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

517×	`associate-/l*_binary64`
421×	`fma-def_binary64`
402×	`associate-/r/_binary64`
391×	`*-commutative_binary64`
352×	`associate-*r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	30	16
2	85	14
3	246	14
4	476	14
5	787	14
6	1035	14
7	1336	14
8	1933	14
9	3431	14
10	4252	14
11	4464	14
12	4589	14
13	4836	14

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (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

2.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	13.4b	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))
▶	3.9b	(*.f64 (/.f64 y z) (/.f64 x (fma.f64 z z z)))

Compiler

Compiled 78 to 45 computations (42.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	2.5b	(*.f64 (/.f64 y z) (/.f64 x (fma.f64 z z z)))
✓	5.5b	(/.f64 x (fma.f64 z z z))

series117.0ms (3.4%)

Counts

2 → 60

Calls

2 calls:

86.0ms	(*.f64 (/.f64 y z) (/.f64 x (fma.f64 z z z)))
30.0ms	(/.f64 x (fma.f64 z z z))

rewrite47.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

523×	`log-prod_binary64`
169×	`expm1-udef_binary64`
169×	`log1p-udef_binary64`
167×	`log-div_binary64`
152×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	176	22
2	2635	22

Stop Event

1×	node limit

Counts

2 → 99

Calls

2 calls:

45.0ms	(*.f64 (/.f64 y z) (/.f64 x (fma.f64 z z z)))
45.0ms	(/.f64 x (fma.f64 z z z))

simplify34.0ms (1%)

Algorithm

1×	egg-herbie

Rules

759×	`times-frac_binary64`
567×	`fma-def_binary64`
521×	`cancel-sign-sub-inv_binary64`
332×	`fma-neg_binary64`
257×	`associate-/l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	1016
1	157	942
2	447	897
3	1590	870

Stop Event

1×	node limit

Counts

159 → 134

prune125.0ms (3.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	127	7	134
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	129	7	136

Error

0.8b

Counts

136 → 7

Alt Table

Status	Error	Program
	32.5b	(/.f64 (/.f64 (*.f64 x (/.f64 y z)) (hypot.f64 z (sqrt.f64 z))) (hypot.f64 z (sqrt.f64 z)))
	6.5b	(/.f64 y (/.f64 z (/.f64 x (fma.f64 z z z))))
	3.7b	(/.f64 (/.f64 x (fma.f64 z z z)) (/.f64 z y))
	6.0b	(/.f64 x (*.f64 (fma.f64 z z z) (/.f64 z y)))
▶	3.1b	(/.f64 (*.f64 x (/.f64 y z)) (fma.f64 z z z))
	4.1b	(/.f64 (*.f64 (/.f64 x (fma.f64 z z z)) y) z)
	11.6b	(/.f64 y (/.f64 (*.f64 z (fma.f64 z z z)) x))

Compiler

Compiled 2099 to 655 computations (68.8% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	2.6b	(/.f64 (*.f64 x (/.f64 y z)) (fma.f64 z z z))
✓	3.1b	(*.f64 x (/.f64 y z))

series100.0ms (2.9%)

Counts

2 → 72

Calls

2 calls:

88.0ms	(/.f64 (*.f64 x (/.f64 y z)) (fma.f64 z z z))
11.0ms	(*.f64 x (/.f64 y z))

rewrite53.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

527×	`log-prod_binary64`
165×	`expm1-udef_binary64`
165×	`log1p-udef_binary64`
156×	`pow3_binary64`
150×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	173	21
2	2550	21

Stop Event

1×	node limit

Counts

2 → 75

Calls

2 calls:

51.0ms	(/.f64 (*.f64 x (/.f64 y z)) (fma.f64 z z z))
51.0ms	(*.f64 x (/.f64 y z))

simplify32.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

726×	`times-frac_binary64`
476×	`cancel-sign-sub-inv_binary64`
407×	`fma-def_binary64`
373×	`associate-/r*_binary64`
365×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	38	944
1	112	894
2	318	850
3	1207	825

Stop Event

1×	node limit

Counts

147 → 96

prune64.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	96	7	103

Error

0.8b

Counts

103 → 7

Alt Table

Status	Error	Program
	32.5b	(/.f64 (/.f64 (*.f64 x (/.f64 y z)) (hypot.f64 z (sqrt.f64 z))) (hypot.f64 z (sqrt.f64 z)))
	6.5b	(/.f64 y (/.f64 z (/.f64 x (fma.f64 z z z))))
▶	3.7b	(/.f64 (/.f64 x (fma.f64 z z z)) (/.f64 z y))
	6.0b	(/.f64 x (*.f64 (fma.f64 z z z) (/.f64 z y)))
✓	3.1b	(/.f64 (*.f64 x (/.f64 y z)) (fma.f64 z z z))
	4.1b	(/.f64 (*.f64 (/.f64 x (fma.f64 z z z)) y) z)
	11.6b	(/.f64 y (/.f64 (*.f64 z (fma.f64 z z z)) x))

Compiler

Compiled 1633 to 494 computations (69.7% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	2.3b	(/.f64 (/.f64 x (fma.f64 z z z)) (/.f64 z y))
	5.5b	(/.f64 x (fma.f64 z z z))

series86.0ms (2.5%)

Counts

1 → 36

Calls

1 calls:

85.0ms

(/.f64 (/.f64 x (fma.f64 z z z)) (/.f64 z y))

rewrite50.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

564×	`log-prod_binary64`
196×	`log-div_binary64`
171×	`expm1-udef_binary64`
171×	`log1p-udef_binary64`
161×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	179	14
2	2795	14

Stop Event

1×	node limit

Counts

1 → 54

Calls

1 calls:

49.0ms

(/.f64 (/.f64 x (fma.f64 z z z)) (/.f64 z y))

simplify35.0ms (1%)

Algorithm

1×	egg-herbie

Rules

726×	`times-frac_binary64`
476×	`cancel-sign-sub-inv_binary64`
407×	`fma-def_binary64`
374×	`associate-/r*_binary64`
367×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	38	692
1	112	642
2	318	598
3	1208	573

Stop Event

1×	node limit

Counts

90 → 73

prune97.0ms (2.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	126	7	133

Error

0.8b

Counts

133 → 7

Alt Table

Status	Error	Program
	32.5b	(/.f64 (/.f64 (*.f64 x (/.f64 y z)) (hypot.f64 z (sqrt.f64 z))) (hypot.f64 z (sqrt.f64 z)))
	6.5b	(/.f64 y (/.f64 z (/.f64 x (fma.f64 z z z))))
✓	3.7b	(/.f64 (/.f64 x (fma.f64 z z z)) (/.f64 z y))
	6.0b	(/.f64 x (*.f64 (fma.f64 z z z) (/.f64 z y)))
✓	3.1b	(/.f64 (*.f64 x (/.f64 y z)) (fma.f64 z z z))
▶	4.1b	(/.f64 (*.f64 (/.f64 x (fma.f64 z z z)) y) z)
	11.6b	(/.f64 y (/.f64 (*.f64 z (fma.f64 z z z)) x))

Compiler

Compiled 2151 to 674 computations (68.7% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.8b	(/.f64 (*.f64 (/.f64 x (fma.f64 z z z)) y) z)
	5.5b	(/.f64 x (fma.f64 z z z))
✓	6.2b	(*.f64 (/.f64 x (fma.f64 z z z)) y)

series154.0ms (4.4%)

Counts

2 → 72

Calls

2 calls:

86.0ms	(/.f64 (*.f64 (/.f64 x (fma.f64 z z z)) y) z)
68.0ms	(*.f64 (/.f64 x (fma.f64 z z z)) y)

rewrite48.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

521×	`log-prod_binary64`
165×	`expm1-udef_binary64`
165×	`log1p-udef_binary64`
156×	`pow3_binary64`
150×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	25
1	173	25
2	2548	25

Stop Event

1×	node limit

Counts

2 → 77

Calls

2 calls:

47.0ms	(/.f64 (*.f64 (/.f64 x (fma.f64 z z z)) y) z)
47.0ms	(*.f64 (/.f64 x (fma.f64 z z z)) y)

simplify40.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

613×	`fma-neg_binary64`
505×	`associate-/l*_binary64`
284×	`associate-/l/_binary64`
185×	`sub-neg_binary64`
177×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	1301
1	158	1197
2	476	1096
3	1956	1064

Stop Event

1×	node limit

Counts

149 → 112

prune107.0ms (3.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	165	7	172

Error

0.8b

Counts

172 → 7

Alt Table

Status	Error	Program
	32.5b	(/.f64 (/.f64 (*.f64 x (/.f64 y z)) (hypot.f64 z (sqrt.f64 z))) (hypot.f64 z (sqrt.f64 z)))
	6.5b	(/.f64 y (/.f64 z (/.f64 x (fma.f64 z z z))))
✓	3.7b	(/.f64 (/.f64 x (fma.f64 z z z)) (/.f64 z y))
	6.0b	(/.f64 x (*.f64 (fma.f64 z z z) (/.f64 z y)))
✓	3.1b	(/.f64 (*.f64 x (/.f64 y z)) (fma.f64 z z z))
✓	4.1b	(/.f64 (*.f64 (/.f64 x (fma.f64 z z z)) y) z)
	11.6b	(/.f64 y (/.f64 (*.f64 z (fma.f64 z z z)) x))

Compiler

Compiled 2656 to 849 computations (68% saved)

regimes321.0ms (9.2%)

Accuracy

Total 3.8b remaining (79.5%)

Threshold costs 0b (0%)

Counts

64 → 1

Compiler

Compiled 5637 to 3334 computations (40.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	9	14

Stop Event

1×

saturated

end219.0ms (6.3%)

Compiler: Compiled 148 to 79 computations (46.6% saved)

Details

analyze561.0ms (16.1%)

sample1.1s (31.9%)

simplify47.0ms (1.4%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series117.0ms (3.4%)

rewrite47.0ms (1.4%)

simplify34.0ms (1%)

prune125.0ms (3.6%)

localize7.0ms (0.2%)

series100.0ms (2.9%)

rewrite53.0ms (1.5%)

simplify32.0ms (0.9%)

prune64.0ms (1.8%)

localize6.0ms (0.2%)

series86.0ms (2.5%)

rewrite50.0ms (1.4%)

simplify35.0ms (1%)

prune97.0ms (2.8%)

localize6.0ms (0.2%)

series154.0ms (4.4%)

rewrite48.0ms (1.4%)

simplify40.0ms (1.2%)

prune107.0ms (3.1%)

regimes321.0ms (9.2%)

simplify2.0ms (0.1%)

end219.0ms (6.3%)

Profiling