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
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample935.0ms (39.4%)

Results

906.0ms	8255×	body	128	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	11	12
2	10	12

prune3.0ms (0.1%)

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

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	0.1b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series55.0ms (2.3%)

Counts

3 → 12

Calls

3 calls:

42.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
7.0ms	(sqrt.f64 (+.f64 x 1))
5.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))

rewrite17.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
21×	`distribute-lft-out_binary64`
18×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`

Counts

3 → 82

Calls

3 calls:

6.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
4.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
2.0ms	(sqrt.f64 (+.f64 x 1))

simplify129.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

733×	`fma-neg_binary64`
333×	`associate-/r*_binary64`
321×	`associate-/l/_binary64`
303×	`associate-*l/_binary64`
284×	`cancel-sign-sub-inv_binary64`

Counts

94 → 108

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	123	1335
1	263	1239
2	634	1227
3	1878	1212
4	4323	1211
5	4987	1211
6	4875	1211

prune95.0ms (4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	3	109

Error

Counts

109 → 3

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
	24.7b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
	16.6b	(-.f64 (+.f64 (.f64 1/16 (pow.f64 x 3)) (.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))

Compiler

Compiled 1622 to 1245 computations (23.2% 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 1 (sqrt.f64 (+.f64 x 1)))
✓	0.1b	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	0.1b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

series50.0ms (2.1%)

Counts

2 → 8

Calls

2 calls:

27.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
23.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite26.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`*-un-lft-identity_binary64`
45×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
28×	`distribute-lft-out_binary64`
24×	`associate-r_binary64`

Counts

2 → 96

Calls

2 calls:

12.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
8.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify122.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

663×	`fma-def_binary64`
514×	`div-sub_binary64`
377×	`associate-/l*_binary64`
327×	`cancel-sign-sub-inv_binary64`
296×	`fma-neg_binary64`

Counts

104 → 126

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	103	1541
1	244	1376
2	627	1359
3	1566	1326
4	4268	1326
5	4530	1326
6	5302	1326

prune131.0ms (5.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	184	3	187

Error

Counts

187 → 3

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
	24.7b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
▶	16.6b	(-.f64 (+.f64 (.f64 1/16 (pow.f64 x 3)) (.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))

Compiler

Compiled 3128 to 2568 computations (17.9% saved)

localize12.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	7.6b	(-.f64 (+.f64 (.f64 1/16 (pow.f64 x 3)) (.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))

series3.0ms (0.1%)

Counts

1 → 10

Calls

1 calls:

3.0ms

(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))

rewrite9.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-log-exp_binary64`
3×	`fma-neg_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`prod-diff_binary64`

Counts

1 → 22

Calls

1 calls:

8.0ms

(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))

simplify50.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

453×	`distribute-rgt-out_binary64`
393×	`associate-l_binary64`
367×	`associate-r_binary64`
350×	`fma-neg_binary64`
297×	`cancel-sign-sub-inv_binary64`

Counts

32 → 45

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	59	737
1	151	619
2	516	558
3	2869	508
4	4890	508

prune87.0ms (3.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	45	0	45
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	45	3	48

Error

Counts

48 → 3

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
▶	24.7b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	16.6b	(-.f64 (+.f64 (.f64 1/16 (pow.f64 x 3)) (.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))

Compiler

Compiled 1074 to 843 computations (21.5% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series74.0ms (3.1%)

Counts

2 → 4

Calls

2 calls:

46.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
27.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

rewrite40.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

109×	`*-un-lft-identity_binary64`
86×	`add-sqr-sqrt_binary64`
76×	`times-frac_binary64`
73×	`sqrt-prod_binary64`
52×	`distribute-lft-out_binary64`

Counts

2 → 134

Calls

2 calls:

17.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
12.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify123.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

861×	`fma-neg_binary64`
610×	`fma-def_binary64`
361×	`associate-/l*_binary64`
342×	`cancel-sign-sub-inv_binary64`
342×	`times-frac_binary64`

Counts

138 → 143

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	129	2881
1	294	2630
2	880	2596
3	2525	2587
4	4564	2587
5	5069	2587

prune124.0ms (5.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	201	3	204

Error

Counts

204 → 3

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	24.7b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	16.6b	(-.f64 (+.f64 (.f64 1/16 (pow.f64 x 3)) (.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))

Compiler

Compiled 4048 to 2595 computations (35.9% saved)

regimes200.0ms (8.4%)

Accuracy

Total 0.2b remaining (94.7%)

Threshold costs 0.2b (94.7%)

Counts

89 → 1

Compiler

Compiled 2174 to 1694 computations (22.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	14	12
2	12	12

end57.0ms (2.4%)

Compiler: Compiled 58 to 45 computations (22.4% saved)

Details

analyze3.0ms (0.1%)

sample935.0ms (39.4%)

simplify6.0ms (0.3%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series55.0ms (2.3%)

rewrite17.0ms (0.7%)

simplify129.0ms (5.4%)

prune95.0ms (4%)

localize8.0ms (0.3%)

series50.0ms (2.1%)

rewrite26.0ms (1.1%)

simplify122.0ms (5.1%)

prune131.0ms (5.5%)

localize12.0ms (0.5%)

series3.0ms (0.1%)

rewrite9.0ms (0.4%)

simplify50.0ms (2.1%)

prune87.0ms (3.7%)

localize7.0ms (0.3%)

series74.0ms (3.1%)

rewrite40.0ms (1.7%)

simplify123.0ms (5.2%)

prune124.0ms (5.2%)

regimes200.0ms (8.4%)

simplify2.0ms (0.1%)

end57.0ms (2.4%)

Profiling