Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample816.0ms (35.6%)

Results

788.0ms	8254×	body	128	valid
1.0ms	2×	body	2048	valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	11	12
2	10	12

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series37.0ms (1.6%)

Counts

3 → 12

Calls

3 calls:

26.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
5.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms	(sqrt.f64 (+.f64 x 1))

rewrite64.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

804×	`log1p-expm1-u_binary64`
804×	`expm1-log1p-u_binary64`
424×	`prod-diff_binary64`
96×	`egg-rr`
76×	`add-sqr-sqrt_binary64`

Counts

3 → 96

Calls

3 calls:

62.0ms	(sqrt.f64 (+.f64 x 1))
62.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
62.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	27
1	156	27
2	2015	27
3	5666	27
0	0	0
1	0	0

simplify76.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

594×	`fma-def_binary64`
446×	`distribute-rgt-out--_binary64`
382×	`sub-neg_binary64`
363×	`distribute-rgt-neg-in_binary64`
348×	`*-commutative_binary64`

Counts

108 → 117

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	31	158
1	87	142
2	211	130
3	622	109
4	2023	109
5	3826	109
6	4801	109
7	4921	109

prune81.0ms (3.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	113	4	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	4	118

Error

Counts

118 → 4

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 x (fma.f64 1 (sqrt.f64 (+.f64 x 1)) 1))
	1.0b	(/.f64 x (pow.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) 2))
	39.7b	(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
	21.2b	(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

Compiler

Compiled 1584 to 1232 computations (22.2% saved)

localize50.0ms (2.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.0b	(fma.f64 1 (sqrt.f64 (+.f64 x 1)) 1)
✓	0.2b	(/.f64 x (fma.f64 1 (sqrt.f64 (+.f64 x 1)) 1))

series34.0ms (1.5%)

Counts

2 → 8

Calls

2 calls:

28.0ms	(/.f64 x (fma.f64 1 (sqrt.f64 (+.f64 x 1)) 1))
6.0ms	(fma.f64 1 (sqrt.f64 (+.f64 x 1)) 1)

rewrite52.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

703×	`log1p-expm1-u_binary64`
703×	`expm1-log1p-u_binary64`
145×	`fma-def_binary64`
123×	`log1p-udef_binary64`
122×	`expm1-udef_binary64`

Counts

2 → 56

Calls

2 calls:

51.0ms	(fma.f64 1 (sqrt.f64 (+.f64 x 1)) 1)
50.0ms	(/.f64 x (fma.f64 1 (sqrt.f64 (+.f64 x 1)) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	21
1	148	21
2	1793	21
3	4980	21
0	0	0
1	0	0

simplify74.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

446×	`distribute-rgt-out--_binary64`
433×	`fma-def_binary64`
394×	`distribute-rgt-out_binary64`
363×	`distribute-rgt-neg-in_binary64`
348×	`*-commutative_binary64`

Counts

64 → 70

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	26	111
1	72	101
2	179	93
3	530	78
4	1789	78
5	3528	78
6	4650	78
7	4901	78

prune61.0ms (2.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	104	4	108

Error

Counts

108 → 4

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 x (fma.f64 1 (sqrt.f64 (+.f64 x 1)) 1))
▶	1.0b	(/.f64 x (pow.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) 2))
	39.7b	(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
	21.2b	(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

Compiler

Compiled 1391 to 1090 computations (21.6% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 x 1) 1/4)
✓	0.0b	(hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))
✓	0.2b	(/.f64 x (pow.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) 2))
✓	0.9b	(pow.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) 2)

series116.0ms (5%)

Counts

4 → 48

Calls

4 calls:

61.0ms	(/.f64 x (pow.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) 2))
30.0ms	(hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))
20.0ms	(pow.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) 2)
4.0ms	(pow.f64 (+.f64 x 1) 1/4)

rewrite63.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

910×	`log1p-expm1-u_binary64`
910×	`expm1-log1p-u_binary64`
158×	`prod-diff_binary64`
100×	`add-sqr-sqrt_binary64`
97×	`add-log-exp_binary64`

Counts

4 → 96

Calls

4 calls:

61.0ms	(pow.f64 (+.f64 x 1) 1/4)
61.0ms	(hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))
61.0ms	(/.f64 x (pow.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) 2))
61.0ms	(pow.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	46
1	220	38
2	2335	38
3	5755	38
0	0	0
1	0	0

simplify81.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

961×	`times-frac_binary64`
531×	`cancel-sign-sub-inv_binary64`
210×	`fma-def_binary64`
200×	`sub-neg_binary64`
161×	`fma-neg_binary64`

Counts

144 → 186

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	275	2905
1	819	2732
2	2834	2248
3	5214	2248

prune163.0ms (7.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	185	1	186
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	186	4	190

Error

Counts

190 → 4

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 x (fma.f64 1 (sqrt.f64 (+.f64 x 1)) 1))
✓	1.0b	(/.f64 x (pow.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) 2))
	39.7b	(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
▶	20.8b	(-.f64 (/.f64 x 2) (.f64 1/2 (/.f64 (.f64 x x) 4)))

Compiler

Compiled 5075 to 4116 computations (18.9% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (*.f64 x x) 4)
✓	0.0b	(-.f64 (/.f64 x 2) (.f64 1/2 (/.f64 (.f64 x x) 4)))
✓	0.0b	(.f64 1/2 (/.f64 (.f64 x x) 4))

series7.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(-.f64 (/.f64 x 2) (.f64 1/2 (/.f64 (.f64 x x) 4)))
2.0ms	(.f64 1/2 (/.f64 (.f64 x x) 4))
2.0ms	(/.f64 (*.f64 x x) 4)

rewrite74.0ms (3.2%)

Algorithm

2×	batch-egg-rewrite

Rules

476×	`log-prod_binary64`
327×	`fma-def_binary64`
196×	`fma-neg_binary64`
185×	`expm1-udef_binary64`
185×	`log1p-udef_binary64`

Counts

3 → 177

Calls

3 calls:

70.0ms	(/.f64 (*.f64 x x) 4)
70.0ms	(-.f64 (/.f64 x 2) (.f64 1/2 (/.f64 (.f64 x x) 4)))
70.0ms	(.f64 1/2 (/.f64 (.f64 x x) 4))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	33
1	233	27
2	2717	27
3	4972	27
0	0	0
1	0	0

simplify71.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

687×	`unsub-neg_binary64`
626×	`fma-neg_binary64`
596×	`fma-def_binary64`
521×	`distribute-rgt-neg-in_binary64`
420×	`distribute-lft-neg-in_binary64`

Counts

213 → 186

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	303
1	27	285
2	51	276
3	123	258
4	318	258
5	913	258
6	1533	258
7	2468	258
8	3993	258
9	5110	258

prune123.0ms (5.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	186	4	190

Error

Counts

190 → 4

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 x (fma.f64 1 (sqrt.f64 (+.f64 x 1)) 1))
✓	1.0b	(/.f64 x (pow.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) 2))
	39.7b	(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
✓	20.8b	(-.f64 (/.f64 x 2) (.f64 1/2 (/.f64 (.f64 x x) 4)))

Compiler

Compiled 3397 to 2240 computations (34.1% saved)

regimes139.0ms (6.1%)

Accuracy

Total 0.2b remaining (97.4%)

Threshold costs 0.2b (97.4%)

Counts

57 → 1

Compiler

Compiled 1406 to 1094 computations (22.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	11	12
2	10	12

end69.0ms (3%)

Compiler: Compiled 63 to 49 computations (22.2% saved)

Details

analyze3.0ms (0.1%)

sample816.0ms (35.6%)

simplify6.0ms (0.2%)

prune2.0ms (0.1%)

localize10.0ms (0.4%)

series37.0ms (1.6%)

rewrite64.0ms (2.8%)

simplify76.0ms (3.3%)

prune81.0ms (3.5%)

localize50.0ms (2.2%)

series34.0ms (1.5%)

rewrite52.0ms (2.3%)

simplify74.0ms (3.2%)

prune61.0ms (2.6%)

localize9.0ms (0.4%)

series116.0ms (5%)

rewrite63.0ms (2.7%)

simplify81.0ms (3.5%)

prune163.0ms (7.1%)

localize8.0ms (0.4%)

series7.0ms (0.3%)

rewrite74.0ms (3.2%)

simplify71.0ms (3.1%)

prune123.0ms (5.4%)

regimes139.0ms (6.1%)

simplify2.0ms (0.1%)

end69.0ms (3%)

Profiling