Details

analyze16.0ms (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)

sample2.9s (54.8%)

Results

916.0ms	1390×	body	1024	valid
852.0ms	4526×	body	128	valid
716.0ms	1538×	body	512	valid
309.0ms	802×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify29.0ms (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

prune4.0ms (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)

localize17.0ms (0.3%)

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)))

series19.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

6.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
4.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
4.0ms	(/.f64 1 (-.f64 x 1))
4.0ms	(/.f64 1 (+.f64 x 1))

rewrite138.0ms (2.6%)

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:

132.0ms	(/.f64 1 (-.f64 x 1))
132.0ms	(/.f64 1 (+.f64 x 1))
132.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
132.0ms	(+.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

simplify117.0ms (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

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

prune312.0ms (6%)

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

0.4b

Counts

220 → 3

Alt Table

Status	Error	Program
▶	25.5b	(+.f64 (/.f64 (-.f64 x (.f64 (+.f64 1 x) 2)) (.f64 x (+.f64 1 x))) (/.f64 1 (-.f64 x 1)))
	31.6b	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 5)))
✓	9.9b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 5068 to 4013 computations (20.8% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (+.f64 1 x))
✓	0.0b	(-.f64 x (*.f64 (+.f64 1 x) 2))
✓	1.7b	(+.f64 (/.f64 (-.f64 x (.f64 (+.f64 1 x) 2)) (.f64 x (+.f64 1 x))) (/.f64 1 (-.f64 x 1)))
✓	15.0b	(/.f64 (-.f64 x (.f64 (+.f64 1 x) 2)) (.f64 x (+.f64 1 x)))

series21.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

7.0ms	(+.f64 (/.f64 (-.f64 x (.f64 (+.f64 1 x) 2)) (.f64 x (+.f64 1 x))) (/.f64 1 (-.f64 x 1)))
6.0ms	(*.f64 x (+.f64 1 x))
5.0ms	(/.f64 (-.f64 x (.f64 (+.f64 1 x) 2)) (.f64 x (+.f64 1 x)))
2.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))

rewrite147.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

263×	`expm1-udef_binary64`
263×	`log1p-udef_binary64`
167×	`egg-rr`
151×	`add-sqr-sqrt_binary64`
147×	`log1p-expm1-u_binary64`

Counts

4 → 167

Calls

4 calls:

139.0ms	(*.f64 x (+.f64 1 x))
139.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
139.0ms	(+.f64 (/.f64 (-.f64 x (.f64 (+.f64 1 x) 2)) (.f64 x (+.f64 1 x))) (/.f64 1 (-.f64 x 1)))
139.0ms	(/.f64 (-.f64 x (.f64 (+.f64 1 x) 2)) (.f64 x (+.f64 1 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	64
1	297	64
2	4504	64
3	5203	64
0	0	0
1	0	0

simplify136.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

513×	`fma-neg_binary64`
507×	`div-sub_binary64`
506×	`sub-neg_binary64`
348×	`cancel-sign-sub-inv_binary64`
312×	`times-frac_binary64`

Counts

215 → 204

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	62	537
1	190	489
2	512	483
3	1409	483
4	3480	483
5	4294	483
6	4872	483
7	5199	483

prune258.0ms (4.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	204	3	207

Error

0.4b

Counts

207 → 3

Alt Table

Status	Error	Program
✓	25.5b	(+.f64 (/.f64 (-.f64 x (.f64 (+.f64 1 x) 2)) (.f64 x (+.f64 1 x))) (/.f64 1 (-.f64 x 1)))
▶	31.6b	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 5)))
✓	9.9b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 5352 to 3977 computations (25.7% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 5)))
✓	0.2b	(/.f64 2 (pow.f64 x 5))
✓	0.4b	(/.f64 2 (pow.f64 x 3))

series20.0ms (0.4%)

Counts

3 → 12

Calls

3 calls:

8.0ms	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 5)))
6.0ms	(/.f64 2 (pow.f64 x 5))
5.0ms	(/.f64 2 (pow.f64 x 3))

rewrite90.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

931×	`prod-diff_binary64`
199×	`log1p-udef_binary64`
114×	`add-sqr-sqrt_binary64`
113×	`log1p-expm1-u_binary64`
113×	`expm1-log1p-u_binary64`

Counts

3 → 104

Calls

3 calls:

87.0ms	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 5)))
87.0ms	(/.f64 2 (pow.f64 x 5))
87.0ms	(/.f64 2 (pow.f64 x 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	237	27
2	2976	27
3	5022	27
0	0	0
1	0	0

simplify160.0ms (3.1%)

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

116 → 108

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	3733	165
8	3737	165
9	4307	165
10	4626	165
11	4835	165
12	4902	165

prune123.0ms (2.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	108	3	111

Error

Counts

111 → 3

Alt Table

Status	Error	Program
✓	25.5b	(+.f64 (/.f64 (-.f64 x (.f64 (+.f64 1 x) 2)) (.f64 x (+.f64 1 x))) (/.f64 1 (-.f64 x 1)))
▶	31.2b	(*.f64 2 (+.f64 (pow.f64 x -3) (pow.f64 x -5)))
✓	9.9b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 1840 to 1531 computations (16.8% saved)

localize9.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 x -3) (pow.f64 x -5))

series8.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

8.0ms

(+.f64 (pow.f64 x -3) (pow.f64 x -5))

rewrite74.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

754×	`log1p-expm1-u_binary64`
754×	`expm1-log1p-u_binary64`
556×	`prod-diff_binary64`
80×	`add-sqr-sqrt_binary64`
76×	`add-log-exp_binary64`

Counts

1 → 35

Calls

1 calls:

72.0ms

(+.f64 (pow.f64 x -3) (pow.f64 x -5))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	163	10
2	1887	10
3	5441	10
0	0	0
1	0	0

simplify158.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1024×	`sqr-pow_binary64`
724×	`unswap-sqr_binary64`
630×	`associate-/l/_binary64`
502×	`cube-prod_binary64`
470×	`pow-sqr_binary64`

Counts

47 → 38

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	165
1	25	165
2	43	165
3	70	165
4	132	165
5	302	165
6	867	165
7	1452	165
8	1591	165
9	1853	165
10	2158	165
11	2448	165
12	3302	165
13	3656	165
14	3839	165
15	4096	165
16	4235	165
17	4314	165
18	4394	165
19	4920	165

prune44.0ms (0.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	38	3	41

Error

Counts

41 → 3

Alt Table

Status	Error	Program
✓	25.5b	(+.f64 (/.f64 (-.f64 x (.f64 (+.f64 1 x) 2)) (.f64 x (+.f64 1 x))) (/.f64 1 (-.f64 x 1)))
✓	31.2b	(*.f64 2 (+.f64 (pow.f64 x -3) (pow.f64 x -5)))
✓	9.9b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 608 to 485 computations (20.2% saved)

regimes236.0ms (4.5%)

Accuracy

Total 0.1b remaining (62.1%)

Threshold costs 0.1b (62.1%)

Counts

37 → 3

Compiler

Compiled 1406 to 1124 computations (20.1% saved)

bsearch3.0ms (0%)

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

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

14×	`+-commutative_binary64`
9×	`sub-neg_binary64`
8×	`*-commutative_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	117
1	57	117
2	77	117
3	87	117
4	92	117
5	93	117
6	90	117

end175.0ms (3.4%)

Compiler: Compiled 204 to 162 computations (20.6% 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

analyze16.0ms (0.3%)

sample2.9s (54.8%)

simplify29.0ms (0.6%)

prune4.0ms (0.1%)

localize17.0ms (0.3%)

series19.0ms (0.4%)

rewrite138.0ms (2.6%)

simplify117.0ms (2.2%)

prune312.0ms (6%)

localize18.0ms (0.3%)

series21.0ms (0.4%)

rewrite147.0ms (2.8%)

simplify136.0ms (2.6%)

prune258.0ms (4.9%)

localize12.0ms (0.2%)

series20.0ms (0.4%)

rewrite90.0ms (1.7%)

simplify160.0ms (3.1%)

prune123.0ms (2.4%)

localize9.0ms (0.2%)

series8.0ms (0.2%)

rewrite74.0ms (1.4%)

simplify158.0ms (3%)

prune44.0ms (0.8%)

regimes236.0ms (4.5%)

bsearch3.0ms (0%)

simplify10.0ms (0.2%)

end175.0ms (3.4%)

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