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)

sample753.0ms (35.4%)

Results

724.0ms	8254×	body	128	valid
1.0ms	2×	body	2048	valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify6.0ms (0.3%)

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)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series57.0ms (2.7%)

Counts

3 → 12

Calls

3 calls:

42.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
8.0ms	(sqrt.f64 (+.f64 x 1))
8.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))

rewrite54.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

93× egg-rr

Counts

3 → 93

Calls

2 calls:

52.0ms	((/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 (+.f64 x 1)) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.0ms	()

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

simplify74.0ms (3.5%)

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

105 → 114

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 (3.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	111	4	115

Error

Counts

115 → 4

Alt Table

Status	Error	Program
	18.7b	(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
▶	7.7b	(/.f64 x (+.f64 1 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))))
	35.8b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))

Compiler

Compiled 1549 to 1207 computations (22.1% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 x 1) 3/2)
✓	0.0b	(+.f64 1 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)))
✓	0.2b	(/.f64 x (+.f64 1 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))))
✓	7.6b	(cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))

series62.0ms (2.9%)

Counts

4 → 24

Calls

4 calls:

42.0ms	(/.f64 x (+.f64 1 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))))
9.0ms	(+.f64 1 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)))
7.0ms	(cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))
4.0ms	(pow.f64 (+.f64 x 1) 3/2)

rewrite87.0ms (4.1%)

Algorithm

2×	batch-egg-rewrite

Rules

139× egg-rr

Counts

4 → 139

Calls

2 calls:

85.0ms	((cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (/.f64 x (+.f64 1 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)))) (+.f64 1 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))) (pow.f64 (+.f64 x 1) 3/2))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	43
1	201	34
2	2376	34
3	4973	34
4	5133	34
0	0	0
1	0	0

simplify61.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

373×	`cancel-sign-sub-inv_binary64`
347×	`unswap-sqr_binary64`
329×	`associate-l_binary64`
325×	`associate-r_binary64`
311×	`times-frac_binary64`

Counts

163 → 181

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	69	486
1	182	464
2	459	355
3	1450	291
4	4341	288
5	5105	288

prune126.0ms (5.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	181	4	185

Error

Counts

185 → 4

Alt Table

Status	Error	Program
▶	18.7b	(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	7.7b	(/.f64 x (+.f64 1 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))))
	20.9b	(.f64 x (+.f64 1/2 (.f64 x -1/8)))

Compiler

Compiled 2756 to 2199 computations (20.2% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series109.0ms (5.1%)

Counts

2 → 4

Calls

2 calls:

66.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
43.0ms	(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

rewrite94.0ms (4.4%)

Algorithm

2×	batch-egg-rewrite

Rules

81× egg-rr

Counts

2 → 81

Calls

2 calls:

92.0ms	((*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	206	26
2	2627	26
3	4910	26
4	5567	26
0	0	0
1	0	0

simplify91.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

446×	`distribute-rgt-out--_binary64`
394×	`distribute-rgt-out_binary64`
363×	`distribute-rgt-neg-in_binary64`
348×	`*-commutative_binary64`
305×	`distribute-lft-neg-in_binary64`

Counts

85 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	64
1	58	60
2	147	56
3	438	47
4	1554	47
5	3222	47
6	4633	47
7	4985	47
8	4884	47

prune96.0ms (4.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	160	4	164

Error

Counts

164 → 4

Alt Table

Status	Error	Program
✓	18.7b	(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	7.7b	(/.f64 x (+.f64 1 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))))
▶	20.9b	(.f64 x (+.f64 1/2 (.f64 x -1/8)))

Compiler

Compiled 2791 to 1978 computations (29.1% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (+.f64 1/2 (.f64 x -1/8)))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(*.f64 x (+.f64 1/2 (*.f64 x -1/8)))

rewrite41.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

26× egg-rr

Counts

1 → 26

Calls

2 calls:

40.0ms	((.f64 x (+.f64 1/2 (.f64 x -1/8))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	158	8
2	1895	8
3	5032	8
0	0	0
1	0	0

simplify128.0ms (6%)

Algorithm

1×	egg-herbie

Rules

1661×	`fma-def_binary64`
724×	`fma-neg_binary64`
531×	`unsub-neg_binary64`
521×	`distribute-rgt-neg-in_binary64`
420×	`distribute-lft-neg-in_binary64`

Counts

38 → 31

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	135
1	24	117
2	44	108
3	109	90
4	282	90
5	807	90
6	1429	90
7	2364	90
8	3739	90
9	3984	90
10	3335	90
11	3606	90
12	3787	90
13	4893	90
14	4770	90

prune19.0ms (0.9%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	31	4	35

Error

Counts

35 → 4

Alt Table

Status	Error	Program
✓	18.7b	(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	7.7b	(/.f64 x (+.f64 1 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))))
✓	20.9b	(.f64 x (+.f64 1/2 (.f64 x -1/8)))

Compiler

Compiled 401 to 295 computations (26.4% saved)

regimes99.0ms (4.7%)

Accuracy

Total 0.2b remaining (95.4%)

Threshold costs 0.2b (95.4%)

Counts

51 → 1

Compiler

Compiled 1228 to 974 computations (20.7% 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

end57.0ms (2.7%)

Compiler: Compiled 61 to 47 computations (23% saved)

Details

analyze3.0ms (0.1%)

sample753.0ms (35.4%)

simplify6.0ms (0.3%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series57.0ms (2.7%)

rewrite54.0ms (2.5%)

simplify74.0ms (3.5%)

prune81.0ms (3.8%)

localize9.0ms (0.4%)

series62.0ms (2.9%)

rewrite87.0ms (4.1%)

simplify61.0ms (2.9%)

prune126.0ms (5.9%)

localize8.0ms (0.4%)

series109.0ms (5.1%)

rewrite94.0ms (4.4%)

simplify91.0ms (4.3%)

prune96.0ms (4.5%)

localize4.0ms (0.2%)

series3.0ms (0.1%)

rewrite41.0ms (1.9%)

simplify128.0ms (6%)

prune19.0ms (0.9%)

regimes99.0ms (4.7%)

simplify2.0ms (0.1%)

end57.0ms (2.7%)

Profiling