Details

analyze8.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample1.7s (53%)

Results

533.0ms	4544×	body	128	valid
472.0ms	1381×	body	1024	valid
444.0ms	1545×	body	512	valid
203.0ms	786×	body	256	valid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify19.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

127×	`fma-neg_binary64`
82×	`fma-def_binary64`
41×	`cancel-sign-sub-inv_binary64`
41×	`sub-neg_binary64`
28×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

8.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	8.4b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 63 to 51 computations (19% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	0.0b	(/.f64 1 (-.f64 x 1))
✓	0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
✓	2.2b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series12.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

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

rewrite82.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

425×	`fma-neg_binary64`
236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`
170×	`egg-rr`
136×	`add-sqr-sqrt_binary64`

Counts

4 → 170

Calls

4 calls:

77.0ms	(/.f64 1 (+.f64 x 1))
77.0ms	(/.f64 1 (-.f64 x 1))
77.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
77.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	49
1	272	49
2	3856	49
3	4912	49
0	0	0
1	0	0

simplify80.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

653×	`fma-neg_binary64`
489×	`cancel-sign-sub-inv_binary64`
328×	`sub-neg_binary64`
312×	`times-frac_binary64`
273×	`unsub-neg_binary64`

Counts

218 → 223

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	752
1	246	726
2	697	720
3	1844	717
4	4130	717
5	4617	717
6	4921	717

prune169.0ms (5.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	220	3	223
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	221	3	224

Error

0.1b

Counts

224 → 3

Alt Table

Status	Error	Program
▶	8.4b	(-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (+.f64 1 x))) (/.f64 2 x))
	31.9b	(/.f64 2 (pow.f64 x 3))
	26.6b	(/.f64 (+.f64 (.f64 x (+.f64 1 x)) (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))) (.f64 (-.f64 x 1) (*.f64 x (+.f64 1 x))))

Compiler

Compiled 5148 to 4074 computations (20.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 1 x))
	0.0b	(/.f64 1 (-.f64 x 1))
✓	1.5b	(-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (+.f64 1 x))) (/.f64 2 x))
✓	2.3b	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (+.f64 1 x)))

series11.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

5.0ms	(/.f64 1 (+.f64 1 x))
3.0ms	(-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (+.f64 1 x))) (/.f64 2 x))
3.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (+.f64 1 x)))

rewrite81.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

399×	`fma-neg_binary64`
236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`
138×	`add-sqr-sqrt_binary64`
136×	`egg-rr`

Counts

3 → 136

Calls

3 calls:

78.0ms	(/.f64 1 (+.f64 1 x))
78.0ms	(-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (+.f64 1 x))) (/.f64 2 x))
78.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (+.f64 1 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	45
1	274	45
2	3882	45
3	4928	45
0	0	0
1	0	0

simplify59.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

574×	`sub-neg_binary64`
367×	`fma-def_binary64`
314×	`associate-l_binary64`
291×	`times-frac_binary64`
264×	`distribute-lft-out_binary64`

Counts

172 → 177

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	595
1	222	581
2	670	569
3	1937	568
4	4176	568
5	5086	568

prune158.0ms (5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	217	3	220

Error

0.1b

Counts

220 → 3

Alt Table

Status	Error	Program
✓	8.4b	(-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (+.f64 1 x))) (/.f64 2 x))
	31.9b	(/.f64 2 (pow.f64 x 3))
▶	26.6b	(/.f64 (+.f64 (.f64 x (+.f64 1 x)) (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))) (.f64 (-.f64 x 1) (*.f64 x (+.f64 1 x))))

Compiler

Compiled 4933 to 3945 computations (20% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
✓	0.0b	(/.f64 (+.f64 (.f64 x (+.f64 1 x)) (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))) (.f64 (-.f64 x 1) (*.f64 x (+.f64 1 x))))
✓	0.0b	(.f64 (-.f64 x 1) (.f64 x (+.f64 1 x)))
✓	18.7b	(+.f64 (.f64 x (+.f64 1 x)) (.f64 (-.f64 x 1) (-.f64 x (*.f64 (+.f64 1 x) 2))))

series11.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

4.0ms	(.f64 (-.f64 x 1) (.f64 x (+.f64 1 x)))
3.0ms	(/.f64 (+.f64 (.f64 x (+.f64 1 x)) (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))) (.f64 (-.f64 x 1) (*.f64 x (+.f64 1 x))))
2.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
1.0ms	(+.f64 (.f64 x (+.f64 1 x)) (.f64 (-.f64 x 1) (-.f64 x (*.f64 (+.f64 1 x) 2))))

rewrite89.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

269×	`expm1-udef_binary64`
269×	`log1p-udef_binary64`
154×	`add-sqr-sqrt_binary64`
149×	`log1p-expm1-u_binary64`
149×	`expm1-log1p-u_binary64`

Counts

4 → 147

Calls

4 calls:

84.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
84.0ms	(/.f64 (+.f64 (.f64 x (+.f64 1 x)) (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))) (.f64 (-.f64 x 1) (*.f64 x (+.f64 1 x))))
84.0ms	(.f64 (-.f64 x 1) (.f64 x (+.f64 1 x)))
84.0ms	(+.f64 (.f64 x (+.f64 1 x)) (.f64 (-.f64 x 1) (-.f64 x (*.f64 (+.f64 1 x) 2))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	90
1	308	80
2	4387	80
3	5122	80
0	0	0
1	0	0

simplify85.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

497×	`fma-neg_binary64`
353×	`cancel-sign-sub-inv_binary64`
350×	`sub-neg_binary64`
349×	`distribute-rgt-neg-in_binary64`
303×	`distribute-lft-neg-in_binary64`

Counts

195 → 173

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	50	404
1	151	382
2	415	376
3	1167	376
4	2923	376
5	4039	376
6	4745	376
7	4937	376

prune126.0ms (3.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	174	2	176

Error

0.1b

Counts

176 → 2

Alt Table

Status	Error	Program
✓	8.4b	(-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (+.f64 1 x))) (/.f64 2 x))
▶	0.1b	(/.f64 2 (.f64 (-.f64 x 1) (.f64 x (+.f64 1 x))))

Compiler

Compiled 5711 to 4015 computations (29.7% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (+.f64 1 x))
	0.0b	(.f64 (-.f64 x 1) (.f64 x (+.f64 1 x)))
✓	0.1b	(/.f64 2 (.f64 (-.f64 x 1) (.f64 x (+.f64 1 x))))

series11.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

8.0ms	(*.f64 x (+.f64 1 x))
3.0ms	(/.f64 2 (.f64 (-.f64 x 1) (.f64 x (+.f64 1 x))))

rewrite59.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

462×	`log-prod_binary64`
313×	`fma-def_binary64`
245×	`prod-diff_binary64`
168×	`expm1-udef_binary64`
168×	`log1p-udef_binary64`

Counts

2 → 78

Calls

2 calls:

58.0ms	(*.f64 x (+.f64 1 x))
58.0ms	(/.f64 2 (.f64 (-.f64 x 1) (.f64 x (+.f64 1 x))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	205	18
2	2559	16
3	5147	16
0	0	0
1	0	0

simplify64.0ms (2%)

Algorithm

1×	egg-herbie

Rules

680×	`fma-def_binary64`
508×	`unswap-sqr_binary64`
464×	`fma-neg_binary64`
351×	`distribute-rgt-neg-in_binary64`
321×	`cancel-sign-sub-inv_binary64`

Counts

102 → 96

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	43	295
1	133	271
2	375	265
3	1068	265
4	2950	265
5	4040	265
6	5043	265

prune109.0ms (3.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	127	3	130
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	127	5	132

Error

0.0b

Counts

132 → 5

Alt Table

Status	Error	Program
	0.1b	(*.f64 (/.f64 2 (-.f64 x 1)) (/.f64 1 (fma.f64 x x x)))
✓	8.4b	(-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (+.f64 1 x))) (/.f64 2 x))
✓	0.1b	(/.f64 2 (.f64 (-.f64 x 1) (.f64 x (+.f64 1 x))))
	21.2b	(pow.f64 (sqrt.f64 (/.f64 2 (*.f64 x (fma.f64 x x -1)))) 2)
	27.4b	(/.f64 2 (*.f64 (-.f64 x 1) (cbrt.f64 (pow.f64 (fma.f64 x x x) 3))))

Compiler

Compiled 1896 to 1225 computations (35.4% saved)

regimes162.0ms (5.1%)

Accuracy

Total 0.1b remaining (67.9%)

Threshold costs 0.1b (67.9%)

Counts

95 → 1

Compiler

Compiled 2972 to 2240 computations (24.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	15	17
2	16	17
3	14	17

end71.0ms (2.2%)

Compiler: Compiled 93 to 68 computations (26.9% saved)

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

Details

analyze8.0ms (0.3%)

sample1.7s (53%)

simplify19.0ms (0.6%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series12.0ms (0.4%)

rewrite82.0ms (2.6%)

simplify80.0ms (2.5%)

prune169.0ms (5.3%)

localize8.0ms (0.2%)

series11.0ms (0.4%)

rewrite81.0ms (2.5%)

simplify59.0ms (1.9%)

prune158.0ms (5%)

localize10.0ms (0.3%)

series11.0ms (0.4%)

rewrite89.0ms (2.8%)

simplify85.0ms (2.7%)

prune126.0ms (3.9%)

localize6.0ms (0.2%)

series11.0ms (0.3%)

rewrite59.0ms (1.9%)

simplify64.0ms (2%)

prune109.0ms (3.4%)

regimes162.0ms (5.1%)

simplify2.0ms (0.1%)

end71.0ms (2.2%)

Profiling

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22