Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample1.4s (36.4%)

Results

1.1s	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 47 to 38 computations (19.1% saved)

simplify233.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

2682×	`fma-neg_binary64`
690×	`times-frac_binary64`
636×	`fma-def_binary64`
533×	`sub-neg_binary64`
432×	`distribute-rgt-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	25	19
2	45	17
3	65	17
4	78	17
5	89	17
6	129	17
7	180	17
8	288	17
9	497	17
10	671	17
11	811	17
12	976	17
13	1611	17
14	3407	17
15	3743	17
16	3727	17
17	3787	17
18	3819	17
19	3887	17
20	3898	17
21	4186	17
22	4220	17
23	4236	17
24	4236	17
25	4236	17
26	6212	17

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
	0.1b	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))

Compiler

Compiled 83 to 64 computations (22.9% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
✓	0.1b	(fma.f64 6 x -6)
✓	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

series18.0ms (0.5%)

Counts

3 → 18

Calls

3 calls:

13.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
4.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
1.0ms	(fma.f64 6 x -6)

rewrite74.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

439×	`log-prod_binary64`
188×	`log1p-udef_binary64`
187×	`expm1-udef_binary64`
174×	`prod-diff_binary64`
171×	`pow3_binary64`

Counts

3 → 97

Calls

3 calls:

64.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
64.0ms	(fma.f64 6 x -6)
64.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	32
1	233	32
2	2592	32
3	4862	32
0	0	0
1	0	0

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-neg_binary64`
1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Counts

115 → 103

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	60
1	13	60
2	15	60
3	13	60

prune123.0ms (3.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	98	5	103
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	100	5	105

Error

Counts

105 → 5

Alt Table

Status	Error	Program
	0.2b	(*.f64 (fma.f64 6 x -6) (/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
	13.7b	(/.f64 (fma.f64 6 x -6) (/.f64 (-.f64 (.f64 (.f64 4 (sqrt.f64 x)) (.f64 4 (sqrt.f64 x))) (pow.f64 (+.f64 x 1) 2)) (-.f64 (.f64 4 (sqrt.f64 x)) (+.f64 x 1))))
	1.4b	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) 3)
▶	0.1b	(/.f64 (-.f64 (*.f64 6 x) 6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
	0.3b	(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (/.f64 (fma.f64 6 x -6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))

Compiler

Compiled 2007 to 1475 computations (26.5% saved)

localize13.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
✓	0.0b	(-.f64 (*.f64 6 x) 6)
✓	0.1b	(/.f64 (-.f64 (*.f64 6 x) 6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

series17.0ms (0.5%)

Counts

2 → 6

Calls

2 calls:

15.0ms	(/.f64 (-.f64 (*.f64 6 x) 6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
2.0ms	(-.f64 (*.f64 6 x) 6)

rewrite216.0ms (5.8%)

Algorithm

2×	batch-egg-rewrite

Rules

385×	`prod-diff_binary64`
267×	`fma-def_binary64`
209×	`log1p-udef_binary64`
208×	`expm1-udef_binary64`
204×	`fma-neg_binary64`

Counts

2 → 148

Calls

2 calls:

212.0ms	(-.f64 (*.f64 6 x) 6)
212.0ms	(/.f64 (-.f64 (*.f64 6 x) 6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	248	22
2	3061	22
3	4939	22
4	4987	22
0	0	0
1	0	0

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Counts

154 → 151

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	12
1	6	12
2	6	12

prune230.0ms (6.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	184	1	185
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	185	5	190

Error

Counts

190 → 5

Alt Table

Status	Error	Program
	0.2b	(*.f64 (fma.f64 6 x -6) (/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
	13.7b	(/.f64 (fma.f64 6 x -6) (/.f64 (-.f64 (.f64 (.f64 4 (sqrt.f64 x)) (.f64 4 (sqrt.f64 x))) (pow.f64 (+.f64 x 1) 2)) (-.f64 (.f64 4 (sqrt.f64 x)) (+.f64 x 1))))
▶	0.1b	(fma.f64 (/.f64 x 1) (/.f64 6 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (neg.f64 (/.f64 6 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	1.4b	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) 3)
✓	0.1b	(/.f64 (-.f64 (*.f64 6 x) 6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

Compiler

Compiled 7098 to 5123 computations (27.8% saved)

localize13.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
✓	0.0b	(/.f64 6 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
✓	0.1b	(fma.f64 (/.f64 x 1) (/.f64 6 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (neg.f64 (/.f64 6 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))

series29.0ms (0.8%)

Counts

2 → 6

Calls

2 calls:

16.0ms	(fma.f64 (/.f64 x 1) (/.f64 6 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (neg.f64 (/.f64 6 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
12.0ms	(/.f64 6 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

rewrite116.0ms (3.1%)

Algorithm

2×	batch-egg-rewrite

Rules

436×	`log-prod_binary64`
398×	`prod-diff_binary64`
202×	`fma-def_binary64`
182×	`log1p-udef_binary64`
181×	`expm1-udef_binary64`

Counts

2 → 161

Calls

2 calls:

110.0ms	(/.f64 6 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
110.0ms	(fma.f64 (/.f64 x 1) (/.f64 6 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (neg.f64 (/.f64 6 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	42
1	246	32
2	2623	32
3	5062	32
0	0	0
1	0	0

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

167 → 164

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	12
1	5	12

prune398.0ms (10.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	272	0	272
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	272	5	277

Error

Counts

277 → 5

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 (fma.f64 6 x -6) (/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
	13.7b	(/.f64 (fma.f64 6 x -6) (/.f64 (-.f64 (.f64 (.f64 4 (sqrt.f64 x)) (.f64 4 (sqrt.f64 x))) (pow.f64 (+.f64 x 1) 2)) (-.f64 (.f64 4 (sqrt.f64 x)) (+.f64 x 1))))
✓	0.1b	(fma.f64 (/.f64 x 1) (/.f64 6 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (neg.f64 (/.f64 6 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	1.4b	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) 3)
✓	0.1b	(/.f64 (-.f64 (*.f64 6 x) 6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

Compiler

Compiled 11697 to 8540 computations (27% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
✓	0.1b	(/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
	0.1b	(fma.f64 6 x -6)
✓	0.2b	(*.f64 (fma.f64 6 x -6) (/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

series20.0ms (0.5%)

Counts

2 → 6

Calls

2 calls:

10.0ms	(*.f64 (fma.f64 6 x -6) (/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
10.0ms	(/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

rewrite74.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

480×	`log-prod_binary64`
201×	`log1p-udef_binary64`
200×	`expm1-udef_binary64`
172×	`log-pow_binary64`
167×	`fma-def_binary64`

Counts

2 → 60

Calls

2 calls:

73.0ms	(/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
73.0ms	(*.f64 (fma.f64 6 x -6) (/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	30
1	256	30
2	2754	30
3	4908	30
0	0	0
1	0	0

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Counts

66 → 64

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	12
1	8	12
2	7	12

prune142.0ms (3.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	127	5	132

Error

Counts

132 → 5

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 (fma.f64 6 x -6) (/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
	13.7b	(/.f64 (fma.f64 6 x -6) (/.f64 (-.f64 (.f64 (.f64 4 (sqrt.f64 x)) (.f64 4 (sqrt.f64 x))) (pow.f64 (+.f64 x 1) 2)) (-.f64 (.f64 4 (sqrt.f64 x)) (+.f64 x 1))))
✓	0.1b	(fma.f64 (/.f64 x 1) (/.f64 6 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (neg.f64 (/.f64 6 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	1.4b	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) 3)
✓	0.1b	(/.f64 (-.f64 (*.f64 6 x) 6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

Compiler

Compiled 2433 to 1823 computations (25.1% saved)

regimes468.0ms (12.6%)

Accuracy

Total 0.0b remaining (63.5%)

Threshold costs 0.0b (63.5%)

Counts

155 → 1

Compiler

Compiled 5969 to 4724 computations (20.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`distribute-neg-frac_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	21	29
2	23	29
3	24	29
4	22	29

end114.0ms (3.1%)

Compiler: Compiled 141 to 106 computations (24.8% saved)

Details

analyze4.0ms (0.1%)

sample1.4s (36.4%)

simplify233.0ms (6.3%)

prune5.0ms (0.1%)

localize7.0ms (0.2%)

series18.0ms (0.5%)

rewrite74.0ms (2%)

simplify8.0ms (0.2%)

prune123.0ms (3.3%)

localize13.0ms (0.3%)

series17.0ms (0.5%)

rewrite216.0ms (5.8%)

simplify10.0ms (0.3%)

prune230.0ms (6.2%)

localize13.0ms (0.3%)

series29.0ms (0.8%)

rewrite116.0ms (3.1%)

simplify10.0ms (0.3%)

prune398.0ms (10.7%)

localize13.0ms (0.3%)

series20.0ms (0.5%)

rewrite74.0ms (2%)

simplify7.0ms (0.2%)

prune142.0ms (3.8%)

regimes468.0ms (12.6%)

simplify3.0ms (0.1%)

end114.0ms (3.1%)

Profiling