Details

analyze35.0ms (1.6%)

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)

sample31.0ms (1.4%)

Algorithm

1×

intervals

Results

18.0ms

256×

body

128

valid

Compiler

Compiled 20 to 16 computations (20% saved)

simplify16.0ms (0.7%)

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

0.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize10.0ms (0.4%)

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)))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series117.0ms (5.3%)

Counts

3 → 12

Calls

3 calls:

86.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
16.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
14.0ms	(sqrt.f64 (+.f64 x 1))

rewrite35.0ms (1.6%)

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:

13.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
9.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms	(sqrt.f64 (+.f64 x 1))

simplify166.0ms (7.5%)

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

prune150.0ms (6.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	106	3	109

Error

Counts

109 → 3

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 x (+.f64 1 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (sqrt.f64 (+.f64 x 1))))))
	37.4b	(*.f64 -1 (-.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 1601 to 1232 computations (23% saved)

localize15.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

series127.0ms (5.7%)

Counts

4 → 24

Calls

4 calls:

88.0ms	(/.f64 x (+.f64 1 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (sqrt.f64 (+.f64 x 1))))))
17.0ms	(+.f64 1 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (sqrt.f64 (+.f64 x 1)))))
14.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (sqrt.f64 (+.f64 x 1))))
8.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x 1)))

rewrite71.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`sqrt-prod_binary64`
75×	`add-sqr-sqrt_binary64`
43×	`*-un-lft-identity_binary64`
36×	`sqrt-pow1_binary64`
29×	`pow1_binary64`

Counts

4 → 169

Calls

4 calls:

26.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (sqrt.f64 (+.f64 x 1))))
6.0ms	(/.f64 x (+.f64 1 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (sqrt.f64 (+.f64 x 1))))))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x 1)))
4.0ms	(+.f64 1 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (sqrt.f64 (+.f64 x 1)))))

simplify141.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

763×	`fma-neg_binary64`
585×	`fma-def_binary64`
409×	`associate-r_binary64`
267×	`times-frac_binary64`
203×	`sub-neg_binary64`

Counts

193 → 252

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	229	2742
1	488	2527
2	1298	2386
3	3921	2323
4	4753	2323
5	4871	2323

prune260.0ms (11.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	305	0	305
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	305	3	308

Error

Counts

308 → 3

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 x (+.f64 1 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (sqrt.f64 (+.f64 x 1))))))
▶	37.4b	(*.f64 -1 (-.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 6735 to 5449 computations (19.1% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 x 1))
✓	4.9b	(-.f64 1 (sqrt.f64 (+.f64 x 1)))

series9.0ms (0.4%)

Counts

1 → 4

Calls

1 calls:

9.0ms

(-.f64 1 (sqrt.f64 (+.f64 x 1)))

rewrite9.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
21×	`prod-diff_binary64`
20×	`sqrt-prod_binary64`
17×	`add-cube-cbrt_binary64`

Counts

1 → 51

Calls

1 calls:

6.0ms

(-.f64 1 (sqrt.f64 (+.f64 x 1)))

simplify93.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

1016×	`fma-neg_binary64`
557×	`unsub-neg_binary64`
351×	`cancel-sign-sub-inv_binary64`
329×	`unswap-sqr_binary64`
299×	`distribute-rgt-in_binary64`

Counts

55 → 52

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	88	978
1	173	803
2	467	629
3	1485	621
4	3213	617
5	4137	617
6	4903	617

prune50.0ms (2.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	81	3	84

Error

Counts

84 → 3

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 x (+.f64 1 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (sqrt.f64 (+.f64 x 1))))))
✓	37.4b	(*.f64 -1 (-.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 1611 to 1390 computations (13.7% saved)

regimes84.0ms (3.8%)

Accuracy

Total 0.2b remaining (93.2%)

Threshold costs 0.2b (93.2%)

Counts

40 → 1

Compiler

Compiled 1298 to 1016 computations (21.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

sample793.0ms (35.7%)

Algorithm

1×

intervals

Results

445.0ms	7997×	body	128	valid
1.0ms	3×	body	2048	valid

Compiler

Compiled 54 to 44 computations (18.5% saved)

Details

analyze35.0ms (1.6%)

sample31.0ms (1.4%)

simplify16.0ms (0.7%)

prune3.0ms (0.1%)

localize10.0ms (0.4%)

series117.0ms (5.3%)

rewrite35.0ms (1.6%)

simplify166.0ms (7.5%)

prune150.0ms (6.8%)

localize15.0ms (0.7%)

series127.0ms (5.7%)

rewrite71.0ms (3.2%)

simplify141.0ms (6.3%)

prune260.0ms (11.7%)

localize5.0ms (0.2%)

series9.0ms (0.4%)

rewrite9.0ms (0.4%)

simplify93.0ms (4.2%)

prune50.0ms (2.2%)

regimes84.0ms (3.8%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample793.0ms (35.7%)

Profiling