Details

analyze8.0ms (0.2%)

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)

sample1.8s (48.2%)

Results

581.0ms	1388×	body	1024	valid
508.0ms	1596×	body	512	valid
474.0ms	4524×	body	128	valid
162.0ms	748×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify16.0ms (0.4%)

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

9.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.9b	(+.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))
✓	2.5b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series13.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

6.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
3.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
2.0ms	(/.f64 1 (-.f64 x 1))
2.0ms	(/.f64 1 (+.f64 x 1))

rewrite101.0ms (2.7%)

Algorithm

1×	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:

97.0ms	(/.f64 1 (-.f64 x 1))
97.0ms	(/.f64 1 (+.f64 x 1))
97.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
97.0ms	(+.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

simplify80.0ms (2.2%)

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

prune293.0ms (7.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	222	1	223
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	222	2	224

Error

0.2b

Counts

224 → 2

Alt Table

Status	Error	Program
✓	9.9b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
▶	29.4b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))

Compiler

Compiled 5100 to 4041 computations (20.8% saved)

localize11.0ms (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 7))
✓	0.2b	(/.f64 2 (pow.f64 x 3))
✓	0.3b	(/.f64 2 (pow.f64 x 5))

series17.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

7.0ms	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7)))
3.0ms	(/.f64 2 (pow.f64 x 7))
3.0ms	(/.f64 2 (pow.f64 x 5))
3.0ms	(/.f64 2 (pow.f64 x 3))

rewrite78.0ms (2.1%)

Algorithm

1×	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 → 137

Calls

4 calls:

76.0ms	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7)))
76.0ms	(/.f64 2 (pow.f64 x 7))
76.0ms	(/.f64 2 (pow.f64 x 3))
76.0ms	(/.f64 2 (pow.f64 x 5))

Iterations

Useful iterations: 1 (0.0ms)

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

simplify109.0ms (2.9%)

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

149 → 139

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

prune296.0ms (8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	137	4	141

Error

Counts

141 → 4

Alt Table

Status	Error	Program
✓	9.9b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
	29.6b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (pow.f64 (/.f64 (cbrt.f64 2) x) 3) (/.f64 2 (pow.f64 x 7))))
✓	29.4b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
▶	29.2b	(+.f64 (/.f64 2 (pow.f64 x 5)) (*.f64 2 (+.f64 (pow.f64 x -3) (pow.f64 x -7))))

Compiler

Compiled 3131 to 2610 computations (16.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 2 (pow.f64 x 5)) (*.f64 2 (+.f64 (pow.f64 x -3) (pow.f64 x -7))))
✓	0.0b	(+.f64 (pow.f64 x -3) (pow.f64 x -7))
✓	0.0b	(*.f64 2 (+.f64 (pow.f64 x -3) (pow.f64 x -7)))
	0.3b	(/.f64 2 (pow.f64 x 5))

series16.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

6.0ms	(+.f64 (pow.f64 x -3) (pow.f64 x -7))
5.0ms	(*.f64 2 (+.f64 (pow.f64 x -3) (pow.f64 x -7)))
4.0ms	(+.f64 (/.f64 2 (pow.f64 x 5)) (*.f64 2 (+.f64 (pow.f64 x -3) (pow.f64 x -7))))

rewrite75.0ms (2%)

Algorithm

1×	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 → 145

Calls

3 calls:

72.0ms	(+.f64 (/.f64 2 (pow.f64 x 5)) (*.f64 2 (+.f64 (pow.f64 x -3) (pow.f64 x -7))))
72.0ms	(+.f64 (pow.f64 x -3) (pow.f64 x -7))
72.0ms	(*.f64 2 (+.f64 (pow.f64 x -3) (pow.f64 x -7)))

Iterations

Useful iterations: 1 (0.0ms)

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

simplify61.0ms (1.6%)

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

181 → 158

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

prune149.0ms (4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Error

Counts

185 → 4

Alt Table

Status	Error	Program
✓	9.9b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
▶	29.6b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (pow.f64 (/.f64 (cbrt.f64 2) x) 3) (/.f64 2 (pow.f64 x 7))))
✓	29.4b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
✓	29.2b	(+.f64 (/.f64 2 (pow.f64 x 5)) (*.f64 2 (+.f64 (pow.f64 x -3) (pow.f64 x -7))))

Compiler

Compiled 3889 to 3167 computations (18.6% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (cbrt.f64 2) x)
	0.3b	(/.f64 2 (pow.f64 x 5))
✓	0.3b	(pow.f64 (/.f64 (cbrt.f64 2) x) 3)
✓	1.0b	(cbrt.f64 2)

series18.0ms (0.5%)

Counts

3 → 12

Calls

3 calls:

13.0ms	(pow.f64 (/.f64 (cbrt.f64 2) x) 3)
5.0ms	(/.f64 (cbrt.f64 2) x)
0.0ms	(cbrt.f64 2)

rewrite48.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

636×	`log1p-expm1-u_binary64`
636×	`expm1-log1p-u_binary64`
298×	`log-prod_binary64`
117×	`expm1-udef_binary64`
117×	`log1p-udef_binary64`

Counts

3 → 97

Calls

3 calls:

47.0ms	(/.f64 (cbrt.f64 2) x)
47.0ms	(pow.f64 (/.f64 (cbrt.f64 2) x) 3)
47.0ms	(cbrt.f64 2)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	150	16
2	1654	16
3	4915	16

simplify132.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

1032×	`sqr-pow_binary64`
522×	`pow-sqr_binary64`
471×	`cube-prod_binary64`
456×	`associate-/r*_binary64`
430×	`fabs-mul_binary64`

Counts

109 → 97

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	13	84
2	24	84
3	38	84
4	69	84
5	156	84
6	442	84
7	1227	84
8	1217	84
9	1325	84
10	1470	84
11	1603	84
12	1798	84
13	2099	84
14	2447	84
15	2922	84
16	3540	84
17	3736	84
18	3910	84
19	4024	84
20	4071	84
21	4123	84
22	4683	84

prune101.0ms (2.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	120	4	124

Error

Counts

124 → 4

Alt Table

Status	Error	Program
✓	9.9b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
✓	29.6b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (pow.f64 (/.f64 (cbrt.f64 2) x) 3) (/.f64 2 (pow.f64 x 7))))
✓	29.4b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
✓	29.2b	(+.f64 (/.f64 2 (pow.f64 x 5)) (*.f64 2 (+.f64 (pow.f64 x -3) (pow.f64 x -7))))

Compiler

Compiled 2756 to 2334 computations (15.3% saved)

regimes158.0ms (4.3%)

Accuracy

Total 0.2b remaining (89.1%)

Threshold costs 0.2b (89.1%)

Counts

38 → 3

Compiler

Compiled 1104 to 902 computations (18.3% saved)

bsearch1.0ms (0%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-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	32	118
1	47	118
2	57	118
3	60	118
4	61	118
5	58	118

end106.0ms (2.9%)

Compiler: Compiled 227 to 179 computations (21.1% 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 (0.2%)

sample1.8s (48.2%)

simplify16.0ms (0.4%)

prune2.0ms (0.1%)

localize8.0ms (0.2%)

series13.0ms (0.4%)

rewrite101.0ms (2.7%)

simplify80.0ms (2.2%)

prune293.0ms (7.9%)

localize11.0ms (0.3%)

series17.0ms (0.5%)

rewrite78.0ms (2.1%)

simplify109.0ms (2.9%)

prune296.0ms (8%)

localize8.0ms (0.2%)

series16.0ms (0.4%)

rewrite75.0ms (2%)

simplify61.0ms (1.6%)

prune149.0ms (4%)

localize12.0ms (0.3%)

series18.0ms (0.5%)

rewrite48.0ms (1.3%)

simplify132.0ms (3.6%)

prune101.0ms (2.7%)

regimes158.0ms (4.3%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end106.0ms (2.9%)

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