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
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 9 to 7 computations (22.2% saved)

sample1.6s (48.4%)

Results

671.0ms	2103×	body	1024	valid
424.0ms	4339×	body	128	valid
263.0ms	1075×	body	512	valid
93.0ms	251×	body	2048	valid
85.0ms	488×	body	256	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify12.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

prune2.0ms (0%)

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

27.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	27.4b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	3.1b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series15.0ms (0.5%)

Counts

2 → 5

Calls

2 calls:

10.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
5.0ms	(sqrt.f64 (+.f64 x 1))

rewrite61.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

832×	`prod-diff_binary64`
742×	`log1p-expm1-u_binary64`
742×	`expm1-log1p-u_binary64`
116×	`egg-rr`
72×	`add-sqr-sqrt_binary64`

Counts

2 → 116

Calls

2 calls:

56.0ms	(sqrt.f64 (+.f64 x 1))
56.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	151	17
2	1841	17
3	6015	17

simplify75.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-def_binary64`
635×	`associate-l_binary64`
538×	`unswap-sqr_binary64`
518×	`distribute-rgt-neg-in_binary64`
478×	`distribute-lft-neg-in_binary64`

Counts

121 → 123

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	18	48
1	50	44
2	113	38
3	305	34
4	801	29
5	2479	29
6	4718	29
7	4924	29
8	5130	29

prune150.0ms (4.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	115	8	123
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	8	124

Error

26.1b

Counts

124 → 8

Alt Table

Status	Error	Program
▶	27.0b	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
	27.3b	(+.f64 (fma.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))
	28.6b	1
	28.0b	(+.f64 (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (.f64 x x)))))) (fma.f64 (neg.f64 (sqrt.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 (.f64 x x))) (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (*.f64 x x))))))
	27.9b	(+.f64 (fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (.f64 x x)))))) (fma.f64 (neg.f64 (sqrt.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 (.f64 x x))) (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (*.f64 x x))))))
	27.9b	(+.f64 (fma.f64 1 (sqrt.f64 (+.f64 x 1)) (neg.f64 (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (.f64 x x)))))) (fma.f64 (neg.f64 (sqrt.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 (.f64 x x))) (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (*.f64 x x))))))
	27.5b	(+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x))) (fma.f64 -1 (sqrt.f64 x) (sqrt.f64 x)))
	27.4b	(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))

Compiler

Compiled 2830 to 1599 computations (43.5% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓	0.0b	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
✓	2.7b	(+.f64 x (-.f64 1 x))

series17.0ms (0.5%)

Counts

3 → 14

Calls

3 calls:

9.0ms	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
6.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
1.0ms	(+.f64 x (-.f64 1 x))

rewrite91.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

689×	`fma-def_binary64`
347×	`fma-neg_binary64`
277×	`egg-rr`
199×	`expm1-udef_binary64`
199×	`log1p-udef_binary64`

Counts

3 → 277

Calls

3 calls:

86.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
86.0ms	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
85.0ms	(+.f64 x (-.f64 1 x))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	38
1	232	29
2	3194	29
3	4955	29

simplify15.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Counts

291 → 278

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	14
1	4	14
2	3	14

prune245.0ms (7.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	308	3	311
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	316	3	319

Error

0.1b

Counts

319 → 3

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
	27.6b	(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (*.f64 -1 (sqrt.f64 x)))
	26.9b	(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (+.f64 (+.f64 x 1) (-.f64 x (hypot.f64 x (sqrt.f64 x)))))

Compiler

Compiled 6673 to 4191 computations (37.2% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series9.0ms (0.3%)

Counts

1 → 1

Calls

1 calls:

9.0ms

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

rewrite42.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

845×	`log1p-expm1-u_binary64`
845×	`expm1-log1p-u_binary64`
84×	`add-sqr-sqrt_binary64`
79×	`add-cbrt-cube_binary64`
79×	`add-log-exp_binary64`

Counts

1 → 26

Calls

1 calls:

41.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	176	14
2	2142	14
3	5096	14

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Counts

27 → 27

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
1	4	1
2	3	1

prune115.0ms (3.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	104	6	110
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	106	7	113

Error

0.0b

Counts

113 → 7

Alt Table

Status	Error	Program
	0.4b	(*.f64 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1) (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1))
	0.3b	(/.f64 1 (fma.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
✓	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
	7.5b	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))
▶	0.2b	(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
	0.7b	(pow.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3)
	14.8b	(.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 (+.f64 1 x) (-.f64 x (sqrt.f64 (.f64 (+.f64 1 x) x)))))

Compiler

Compiled 1775 to 1281 computations (27.8% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1 x))
✓	0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓	0.1b	(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
✓	0.3b	(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)

series36.0ms (1.1%)

Counts

4 → 7

Calls

4 calls:

13.0ms	(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)
11.0ms	(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
7.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
5.0ms	(sqrt.f64 (+.f64 1 x))

rewrite63.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

439×	`fma-def_binary64`
414×	`log-prod_binary64`
218×	`fma-neg_binary64`
171×	`expm1-udef_binary64`
171×	`log1p-udef_binary64`

Counts

4 → 139

Calls

4 calls:

61.0ms	(sqrt.f64 (+.f64 1 x))
61.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
61.0ms	(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
61.0ms	(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	45
1	213	45
2	2442	45
3	4940	45

simplify71.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-def_binary64`
635×	`associate-l_binary64`
538×	`unswap-sqr_binary64`
518×	`distribute-rgt-neg-in_binary64`
478×	`distribute-lft-neg-in_binary64`

Counts

146 → 146

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	18	50
1	50	46
2	113	40
3	305	36
4	801	31
5	2479	31
6	4718	31
7	4924	31
8	5130	31

prune176.0ms (5.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	145	8	153

Error

0.0b

Counts

153 → 8

Alt Table

Status	Error	Program
	0.4b	(*.f64 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1) (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1))
	0.3b	(/.f64 1 (fma.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
	0.5b	(*.f64 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
✓	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
	0.3b	(sqrt.f64 (*.f64 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -2) (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -2)))
✓	0.2b	(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
	0.7b	(pow.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3)
	14.8b	(.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 (+.f64 1 x) (-.f64 x (sqrt.f64 (.f64 (+.f64 1 x) x)))))

Compiler

Compiled 2446 to 1822 computations (25.5% saved)

regimes314.0ms (9.7%)

Accuracy

Total 0.2b remaining (85%)

Threshold costs 0.2b (85%)

Counts

186 → 1

Compiler

Compiled 6530 to 4895 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	16	20
2	15	20

end124.0ms (3.8%)

Compiler: Compiled 167 to 133 computations (20.4% saved)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

Details

analyze3.0ms (0.1%)

sample1.6s (48.4%)

simplify12.0ms (0.4%)

prune2.0ms (0%)

localize5.0ms (0.2%)

series15.0ms (0.5%)

rewrite61.0ms (1.9%)

simplify75.0ms (2.3%)

prune150.0ms (4.6%)

localize8.0ms (0.3%)

series17.0ms (0.5%)

rewrite91.0ms (2.8%)

simplify15.0ms (0.5%)

prune245.0ms (7.6%)

localize6.0ms (0.2%)

series9.0ms (0.3%)

rewrite42.0ms (1.3%)

simplify6.0ms (0.2%)

prune115.0ms (3.6%)

localize7.0ms (0.2%)

series36.0ms (1.1%)

rewrite63.0ms (1.9%)

simplify71.0ms (2.2%)

prune176.0ms (5.4%)

regimes314.0ms (9.7%)

simplify3.0ms (0.1%)

end124.0ms (3.8%)

Profiling

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11