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)

sample1.5s (46.8%)

Results

468.0ms	4586×	body	128	valid
452.0ms	1328×	body	1024	valid
397.0ms	1571×	body	512	valid
140.0ms	771×	body	256	valid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify15.0ms (0.5%)

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

prune2.0ms (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

9.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.4b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 63 to 51 computations (19% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	0.0b	(/.f64 1 (-.f64 x 1))
✓	3.3b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series11.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

4.0ms	(+.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))

rewrite88.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

4 → 166

Calls

4 calls:

79.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
79.0ms	(/.f64 1 (+.f64 x 1))
78.0ms	(/.f64 1 (-.f64 x 1))
78.0ms	(+.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

simplify83.0ms (2.6%)

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

214 → 219

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

prune150.0ms (4.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	217	2	219
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	217	3	220

Error

0.1b

Counts

220 → 3

Alt Table

Status	Error	Program
	33.3b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
▶	30.6b	(fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x))
✓	9.4b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 5062 to 4009 computations (20.8% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x))

rewrite44.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

851×	`log1p-expm1-u_binary64`
851×	`expm1-log1p-u_binary64`
672×	`prod-diff_binary64`
88×	`add-sqr-sqrt_binary64`
83×	`add-cbrt-cube_binary64`

Counts

1 → 24

Calls

1 calls:

44.0ms

(fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	181	14
2	2170	14
3	6342	14
0	0	0
1	0	0

simplify115.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

1220×	`fma-neg_binary64`
747×	`fma-def_binary64`
602×	`associate-/l*_binary64`
520×	`distribute-rgt-neg-in_binary64`
376×	`cancel-sign-sub-inv_binary64`

Counts

36 → 32

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	162
1	58	144
2	167	130
3	457	130
4	1041	130
5	1673	130
6	2454	130
7	3304	130
8	3452	130
9	3806	130
10	4999	130
11	4780	130

prune17.0ms (0.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	32	0	32
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	32	3	35

Error

0.1b

Counts

35 → 3

Alt Table

Status	Error	Program
▶	33.3b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
✓	30.6b	(fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x))
✓	9.4b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 524 to 399 computations (23.9% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7)))
✓	0.1b	(/.f64 2 (pow.f64 x 3))
✓	0.2b	(/.f64 2 (pow.f64 x 5))
✓	0.2b	(/.f64 2 (pow.f64 x 7))

series19.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

8.0ms	(/.f64 2 (pow.f64 x 7))
5.0ms	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7)))
3.0ms	(/.f64 2 (pow.f64 x 5))
3.0ms	(/.f64 2 (pow.f64 x 3))

rewrite90.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

325×	`fma-def_binary64`
253×	`expm1-udef_binary64`
253×	`log1p-udef_binary64`
176×	`fma-neg_binary64`
147×	`add-sqr-sqrt_binary64`

Counts

4 → 134

Calls

4 calls:

88.0ms	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7)))
88.0ms	(/.f64 2 (pow.f64 x 3))
88.0ms	(/.f64 2 (pow.f64 x 5))
88.0ms	(/.f64 2 (pow.f64 x 7))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	37
1	308	34
2	3735	34
3	4776	34
0	0	0
1	0	0

simplify111.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

724×	`unswap-sqr_binary64`
503×	`associate-/l/_binary64`
501×	`associate-/r*_binary64`
402×	`fma-def_binary64`
356×	`times-frac_binary64`

Counts

146 → 138

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	165
1	35	165
2	67	165
3	119	165
4	233	165
5	649	165
6	2447	165
7	3734	165
8	3739	165
9	4310	165
10	4629	165
11	4838	165
12	4977	165
13	4903	165

prune134.0ms (4.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	137	4	141

Error

Counts

141 → 4

Alt Table

Status	Error	Program
▶	33.2b	(+.f64 (/.f64 2 (pow.f64 x 5)) (*.f64 2 (+.f64 (pow.f64 x -7) (pow.f64 x -3))))
✓	9.4b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
	33.5b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (pow.f64 (/.f64 (cbrt.f64 2) x) 3) (/.f64 2 (pow.f64 x 7))))
✓	30.6b	(fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x))

Compiler

Compiled 3107 to 2589 computations (16.7% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (+.f64 (pow.f64 x -7) (pow.f64 x -3)))
✓	0.0b	(+.f64 (/.f64 2 (pow.f64 x 5)) (*.f64 2 (+.f64 (pow.f64 x -7) (pow.f64 x -3))))
✓	0.0b	(+.f64 (pow.f64 x -7) (pow.f64 x -3))
	0.2b	(/.f64 2 (pow.f64 x 5))

series14.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

5.0ms	(*.f64 2 (+.f64 (pow.f64 x -7) (pow.f64 x -3)))
5.0ms	(+.f64 (pow.f64 x -7) (pow.f64 x -3))
4.0ms	(+.f64 (/.f64 2 (pow.f64 x 5)) (*.f64 2 (+.f64 (pow.f64 x -7) (pow.f64 x -3))))

rewrite180.0ms (5.6%)

Algorithm

2×	batch-egg-rewrite

Rules

488×	`fma-def_binary64`
262×	`expm1-udef_binary64`
262×	`log1p-udef_binary64`
247×	`fma-neg_binary64`
153×	`add-sqr-sqrt_binary64`

Counts

3 → 143

Calls

3 calls:

177.0ms	(*.f64 2 (+.f64 (pow.f64 x -7) (pow.f64 x -3)))
177.0ms	(+.f64 (/.f64 2 (pow.f64 x 5)) (*.f64 2 (+.f64 (pow.f64 x -7) (pow.f64 x -3))))
177.0ms	(+.f64 (pow.f64 x -7) (pow.f64 x -3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	45
1	312	42
2	3771	42
3	5049	42
0	0	0
1	0	0

simplify63.0ms (2%)

Algorithm

1×	egg-herbie

Rules

817×	`fma-def_binary64`
533×	`times-frac_binary64`
500×	`distribute-lft-out_binary64`
493×	`associate-l_binary64`
354×	`associate-/l*_binary64`

Counts

179 → 156

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	549
1	60	549
2	122	549
3	205	549
4	373	549
5	997	549
6	3228	549
7	3983	549
8	5062	549

prune272.0ms (8.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	178	4	182

Error

Counts

182 → 4

Alt Table

Status	Error	Program
✓	33.2b	(+.f64 (/.f64 2 (pow.f64 x 5)) (*.f64 2 (+.f64 (pow.f64 x -7) (pow.f64 x -3))))
✓	9.4b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
	33.5b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (pow.f64 (/.f64 (cbrt.f64 2) x) 3) (/.f64 2 (pow.f64 x 7))))
✓	30.6b	(fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x))

Compiler

Compiled 3806 to 3098 computations (18.6% saved)

regimes115.0ms (3.6%)

Accuracy

Total 0.4b remaining (94%)

Threshold costs 0.4b (94%)

Counts

34 → 3

Compiler

Compiled 976 to 794 computations (18.6% saved)

bsearch1.0ms (0%)

Compiler: Compiled 16 to 13 computations (18.8% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
5×	`sub-neg_binary64`
3×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	110
1	54	110
2	62	110
3	65	110
4	66	110
5	63	110

end129.0ms (4%)

Compiler: Compiled 212 to 170 computations (19.8% 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%)

sample1.5s (46.8%)

simplify15.0ms (0.5%)

prune2.0ms (0.1%)

localize12.0ms (0.4%)

series11.0ms (0.3%)

rewrite88.0ms (2.8%)

simplify83.0ms (2.6%)

prune150.0ms (4.7%)

localize5.0ms (0.2%)

series3.0ms (0.1%)

rewrite44.0ms (1.4%)

simplify115.0ms (3.6%)

prune17.0ms (0.5%)

localize10.0ms (0.3%)

series19.0ms (0.6%)

rewrite90.0ms (2.8%)

simplify111.0ms (3.5%)

prune134.0ms (4.2%)

localize8.0ms (0.3%)

series14.0ms (0.5%)

rewrite180.0ms (5.6%)

simplify63.0ms (2%)

prune272.0ms (8.5%)

regimes115.0ms (3.6%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end129.0ms (4%)

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