Details

analyze186.0ms (4.9%)

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
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 34 to 22 computations (35.3% saved)

sample1.2s (32.5%)

Results

1.2s	8256×	body	128	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 101 to 65 computations (35.6% saved)

simplify51.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

725×	`fma-def_binary64`
669×	`unsub-neg_binary64`
596×	`cancel-sign-sub-inv_binary64`
340×	`+-commutative_binary64`
277×	`fma-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	20	42
1	63	40
2	170	36
3	542	36
4	1867	32
5	3281	32
6	4881	32
7	4958	32

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
▶	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Status

Error

Program

0.2b

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)

▶

0.0b

(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 172 to 108 computations (37.2% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.0b	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
✓	0.1b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
✓	0.4b	(.f64 (.f64 b b) (fma.f64 a -3 1))

series71.0ms (1.9%)

Counts

4 → 96

Calls

4 calls:

28.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
24.0ms	(pow.f64 (hypot.f64 a b) 4)
11.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
8.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))

rewrite98.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

440×	`prod-diff_binary64`
320×	`fma-udef_binary64`
233×	`expm1-udef_binary64`
233×	`log1p-udef_binary64`
209×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	66
1	283	66
2	2972	66
3	4897	66
4	4993	66
5	4944	66

Stop Event

1×	node limit

Counts

4 → 87

Calls

4 calls:

96.0ms	(pow.f64 (hypot.f64 a b) 4)
96.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
96.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
96.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))

simplify91.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

668×	`fma-def_binary64`
562×	`sub-neg_binary64`
420×	`fma-neg_binary64`
418×	`associate--l+_binary64`
402×	`associate-+l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	1987
1	200	1861
2	602	1583
3	2348	1560
4	4292	1560
5	4919	1560
6	5026	1560

Stop Event

1×	node limit

Counts

183 → 133

prune158.0ms (4.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	130	3	133
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	131	4	135

Error

Counts

135 → 4

Alt Table

Status	Error	Program
	6.0b	(+.f64 (fma.f64 4 (exp.f64 (log.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))))) (pow.f64 (hypot.f64 a b) 4)) -1)
▶	0.1b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (*.f64 a a))) (pow.f64 a 4))) -1)
	10.9b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))) -1)
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 3813 to 2144 computations (43.8% saved)

localize20.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (*.f64 a a))) (pow.f64 a 4)))
	0.1b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
✓	0.2b	(fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (*.f64 a a))) (pow.f64 a 4))
	0.4b	(.f64 (.f64 b b) (fma.f64 a -3 1))

series34.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

21.0ms

(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 2 (*.f64 a a))) (pow.f64 a 4)))

12.0ms

(fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 2 (*.f64 a a))) (pow.f64 a 4))

rewrite53.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

879×	`prod-diff_binary64`
166×	`add-sqr-sqrt_binary64`
159×	`log1p-expm1-u_binary64`
159×	`expm1-log1p-u_binary64`
158×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	64
1	360	64
2	3756	64
3	5310	64

Stop Event

1×	node limit

Counts

2 → 47

Calls

2 calls:

51.0ms

(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 2 (*.f64 a a))) (pow.f64 a 4)))

51.0ms

(fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 2 (*.f64 a a))) (pow.f64 a 4))

simplify69.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

616×	`associate-l_binary64`
564×	`fma-def_binary64`
550×	`unswap-sqr_binary64`
489×	`cancel-sign-sub-inv_binary64`
417×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	1207
1	154	1169
2	482	982
3	2006	959
4	4335	959
5	5434	959

Stop Event

1×	node limit

Counts

95 → 77

prune246.0ms (6.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	138	4	142

Error

Counts

142 → 4

Alt Table

Status	Error	Program
▶	6.0b	(+.f64 (fma.f64 4 (exp.f64 (log.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))))) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	0.1b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (*.f64 a a))) (pow.f64 a 4))) -1)
	10.9b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))) -1)
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 5176 to 2706 computations (47.7% saved)

localize36.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
	0.4b	(.f64 (.f64 b b) (fma.f64 a -3 1))
✓	3.8b	(exp.f64 (log.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))))
✓	8.6b	(log.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))))

series63.0ms (1.6%)

Counts

2 → 48

Calls

2 calls:

35.0ms	(log.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))))
27.0ms	(exp.f64 (log.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))))

rewrite48.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

879×	`log1p-expm1-u_binary64`
879×	`expm1-log1p-u_binary64`
300×	`prod-diff_binary64`
103×	`add-sqr-sqrt_binary64`
95×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	40
1	212	40
2	2296	40
3	5950	40

Stop Event

1×	node limit

Counts

2 → 44

Calls

2 calls:

47.0ms	(exp.f64 (log.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))))
47.0ms	(log.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))))

simplify59.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

825×	`associate-/l*_binary64`
784×	`fma-def_binary64`
341×	`cancel-sign-sub-inv_binary64`
262×	`sub-neg_binary64`
134×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	2176
1	570	2024
2	2202	1780
3	5583	1780

Stop Event

1×	node limit

Counts

92 → 105

prune206.0ms (5.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	166	4	170

Error

Counts

170 → 4

Alt Table

Status	Error	Program
✓	6.0b	(+.f64 (fma.f64 4 (exp.f64 (log.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))))) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	0.1b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (*.f64 a a))) (pow.f64 a 4))) -1)
▶	10.9b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))) -1)
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 6141 to 3854 computations (37.2% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 4 (.f64 2 (.f64 b b)))
✓	0.0b	(.f64 2 (.f64 b b))
✓	0.0b	(*.f64 a (+.f64 4 a))
✓	1.9b	(.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b)))))

series22.0ms (0.6%)

Counts

4 → 60

Calls

4 calls:

16.0ms	(.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b)))))
2.0ms	(.f64 2 (.f64 b b))
2.0ms	(+.f64 4 (.f64 2 (.f64 b b)))
2.0ms	(*.f64 a (+.f64 4 a))

rewrite66.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

359×	`fma-neg_binary64`
259×	`expm1-udef_binary64`
259×	`log1p-udef_binary64`
147×	`add-sqr-sqrt_binary64`
145×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	47
1	302	43
2	3917	43
3	4984	43

Stop Event

1×	node limit

Counts

4 → 100

Calls

4 calls:

64.0ms	(+.f64 4 (.f64 2 (.f64 b b)))
64.0ms	(.f64 2 (.f64 b b))
64.0ms	(*.f64 a (+.f64 4 a))
64.0ms	(.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b)))))

simplify110.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

676×	`fma-def_binary64`
466×	`distribute-rgt-out_binary64`
452×	`unswap-sqr_binary64`
449×	`associate-l_binary64`
369×	`associate-+l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	28	904
1	79	759
2	205	738
3	590	676
4	1947	676
5	3498	676
6	3881	676
7	4300	676
8	4512	676
9	4747	676
10	4864	676

Stop Event

1×	node limit

Counts

160 → 123

prune165.0ms (4.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	123	4	127

Error

Counts

127 → 4

Alt Table

Status	Error	Program
✓	6.0b	(+.f64 (fma.f64 4 (exp.f64 (log.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))))) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	0.1b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (*.f64 a a))) (pow.f64 a 4))) -1)
✓	10.9b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))) -1)
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 2961 to 1857 computations (37.3% saved)

regimes575.0ms (15%)

Accuracy

Total 0.0b remaining (63.4%)

Threshold costs 0.0b (63.4%)

Counts

104 → 1

Compiler

Compiled 11941 to 8489 computations (28.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
6×	`*-commutative_binary64`
5×	`sub-neg_binary64`
4×	`distribute-lft-neg-in_binary64`
4×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	41
1	30	41
2	37	41
3	47	41
4	54	41
5	59	41
6	61	41
7	60	41

Stop Event

1×

saturated

end122.0ms (3.2%)

Compiler: Compiled 168 to 115 computations (31.5% saved)

Details

analyze186.0ms (4.9%)

sample1.2s (32.5%)

simplify51.0ms (1.3%)

prune5.0ms (0.1%)

localize13.0ms (0.4%)

series71.0ms (1.9%)

rewrite98.0ms (2.6%)

simplify91.0ms (2.4%)

prune158.0ms (4.1%)

localize20.0ms (0.5%)

series34.0ms (0.9%)

rewrite53.0ms (1.4%)

simplify69.0ms (1.8%)

prune246.0ms (6.4%)

localize36.0ms (1%)

series63.0ms (1.6%)

rewrite48.0ms (1.3%)

simplify59.0ms (1.6%)

prune206.0ms (5.4%)

localize11.0ms (0.3%)

series22.0ms (0.6%)

rewrite66.0ms (1.7%)

simplify110.0ms (2.9%)

prune165.0ms (4.3%)

regimes575.0ms (15%)

simplify3.0ms (0.1%)

end122.0ms (3.2%)

Profiling