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
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample19.0ms (0.6%)

Algorithm

1×

intervals

Results

6.0ms	61×	body	1024	valid
4.0ms	140×	body	128	valid
3.0ms	37×	body	512	valid
1.0ms	14×	body	256	valid
1.0ms	4×	body	2048	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify176.0ms (5.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune2.0ms (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

Merged error: 28.9b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
2.6b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`sqrt-prod_binary64_12479`
14×	`*-un-lft-identity_binary64_12463` `add-sqr-sqrt_binary64_12485`
6×	`cancel-sign-sub-inv_binary64_12429`
5×	`add-cube-cbrt_binary64_12498`
4×	`difference-of-squares_binary64_12432` `add-log-exp_binary64_12502`
3×	`distribute-lft-out--_binary64_12415` `pow1_binary64_12524`
2×	`add-exp-log_binary64_12501` `sqrt-div_binary64_12480` `distribute-lft-out_binary64_12414` `add-cbrt-cube_binary64_12499`
1×	`pow1/2_binary64_12543` `sub-neg_binary64_12456` `rem-sqrt-square_binary64_12476` `flip--_binary64_12438` `diff-log_binary64_12555` `flip3-+_binary64_12466` `sqrt-pow1_binary64_12481` `flip3--_binary64_12467` `flip-+_binary64_12437`

Counts

2 → 40

Calls

2 calls:

10.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series100.0ms (2.9%)

Counts

2 → 6

Calls

2 calls:

70.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
30.0ms	(sqrt.f64 (+.f64 x 1))

simplify63.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5005	794

prune60.0ms (1.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	44	2	46
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	3	47

Merged error: 0.1b

Counts

47 → 3

Compiler

Compiled 860 to 591 computations (31.3% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

rewrite29.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_12463`
24×	`sqrt-prod_binary64_12479`
21×	`distribute-lft-out_binary64_12414`
18×	`times-frac_binary64_12469`
16×	`add-sqr-sqrt_binary64_12485`
15×	`add-cube-cbrt_binary64_12498`
7×	`add-exp-log_binary64_12501`
6×	`associate-/r*_binary64_12407`
5×	`pow1_binary64_12524` `add-log-exp_binary64_12502` `add-cbrt-cube_binary64_12499`
3×	`associate-/l*_binary64_12408` `flip3-+_binary64_12466` `flip-+_binary64_12437`
2×	`associate-/r/_binary64_12409` `sqrt-div_binary64_12480` `div-exp_binary64_12514`
1×	`clear-num_binary64_12462` `cbrt-undiv_binary64_12497` `pow1/2_binary64_12543` `rec-exp_binary64_12513` `rem-sqrt-square_binary64_12476` `+-commutative_binary64_12393` `1-exp_binary64_12507` `inv-pow_binary64_12548` `frac-2neg_binary64_12474` `pow-flip_binary64_12537` `sqrt-pow1_binary64_12481` `div-inv_binary64_12460` `sum-log_binary64_12554`

Counts

3 → 75

Calls

3 calls:

11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
9.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series135.0ms (3.9%)

Counts

3 → 9

Calls

3 calls:

62.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
46.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
27.0ms	(sqrt.f64 (+.f64 x 1))

simplify69.0ms (2%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4944	1516
1	4944	1516

prune199.0ms (5.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	79	5	84
Fresh	0	1	1
Picked	0	1	1
Done	1	0	1
Total	80	7	87

Merged error: 0.0b

Counts

87 → 7

Compiler

Compiled 3164 to 2408 computations (23.9% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.3b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

rewrite128.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Rules

310×	`*-un-lft-identity_binary64_12463`
290×	`sqrt-prod_binary64_12479`
172×	`times-frac_binary64_12469`
144×	`add-sqr-sqrt_binary64_12485`
116×	`distribute-lft-out_binary64_12414`
88×	`add-cube-cbrt_binary64_12498`
43×	`swap-sqr_binary64_12430`
31×	`pow1_binary64_12524`
27×	`associate-l_binary64_12404` `associate-r_binary64_12403` `sqrt-pow1_binary64_12481`
16×	`unswap-sqr_binary64_12431`
14×	`add-exp-log_binary64_12501` `associate-/r/_binary64_12409`
12×	`associate-/r*_binary64_12407`
11×	`inv-pow_binary64_12548` `pow-flip_binary64_12537`
10×	`add-cbrt-cube_binary64_12499`
9×	`pow1/2_binary64_12543` `rem-sqrt-square_binary64_12476` `pow-prod-up_binary64_12533` `div-inv_binary64_12460`
7×	`flip3-+_binary64_12466` `flip-+_binary64_12437`
6×	`associate-/l*_binary64_12408`
5×	`pow-sqr_binary64_12436` `sqrt-div_binary64_12480` `pow-prod-down_binary64_12534`
4×	`add-log-exp_binary64_12502` `div-exp_binary64_12514`
3×	`sqr-abs_binary64_12478`
2×	`clear-num_binary64_12462` `cbrt-undiv_binary64_12497` `rec-exp_binary64_12513` `1-exp_binary64_12507` `frac-2neg_binary64_12474`
1×	`prod-exp_binary64_12512` `rem-square-sqrt_binary64_12475` `cbrt-unprod_binary64_12496` `-commutative_binary64_12394` `sqrt-unprod_binary64_12483` `associate-l/_binary64_12406` `frac-times_binary64_12473` `pow-plus_binary64_12526` `associate-*r/_binary64_12405` `pow2_binary64_12544`

Counts

4 → 281

Calls

4 calls:

46.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
16.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
12.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series270.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

97.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
69.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
52.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
51.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify132.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4932	6672
1	4932	6672

prune630.0ms (18.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	289	4	293
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	292	8	300

Merged error: 0b

Counts

300 → 8

Compiler

Compiled 9105 to 6793 computations (25.4% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.5b	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4)

rewrite43.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64_12463`
28×	`sqrt-prod_binary64_12479`
13×	`distribute-lft-out_binary64_12414`
11×	`add-sqr-sqrt_binary64_12485`
9×	`add-cube-cbrt_binary64_12498` `unpow-prod-down_binary64_12542`
8×	`pow1_binary64_12524`
6×	`add-log-exp_binary64_12502`
5×	`add-exp-log_binary64_12501`
4×	`sqrt-div_binary64_12480` `add-cbrt-cube_binary64_12499`
3×	`pow-pow_binary64_12535` `pow1/2_binary64_12543` `pow-unpow_binary64_12540` `flip3-+_binary64_12466` `sqrt-pow1_binary64_12481` `flip-+_binary64_12437`
2×	`rem-sqrt-square_binary64_12476`
1×	`+-commutative_binary64_12393` `pow-to-exp_binary64_12532` `pow-exp_binary64_12531` `sqr-pow_binary64_12435` `sqrt-pow2_binary64_12482` `sum-log_binary64_12554`

Counts

4 → 74

Calls

4 calls:

12.0ms	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4)
9.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
9.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
7.0ms	(sqrt.f64 (+.f64 1 x))

series264.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

129.0ms	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4)
72.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
39.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
24.0ms	(sqrt.f64 (+.f64 1 x))

simplify80.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4899	1663
1	4899	1663

prune137.0ms (4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	86	8	94

Merged error: 0b

Counts

94 → 8

Compiler

Compiled 2430 to 1885 computations (22.4% saved)

regimes24.0ms (0.7%)

Compiler: Compiled 194 to 155 computations (20.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample805.0ms (23.6%)

Algorithm

1×

intervals

Results

215.0ms	2125×	body	1024	valid
124.0ms	4200×	body	128	valid
72.0ms	952×	body	512	valid
28.0ms	222×	body	2048	valid
25.0ms	501×	body	256	valid
0.0ms	3×	body	128	nan

Compiler

Compiled 218 to 177 computations (18.8% saved)

Details

analyze3.0ms (0.1%)

sample19.0ms (0.6%)

simplify176.0ms (5.1%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

rewrite16.0ms (0.5%)

series100.0ms (2.9%)

simplify63.0ms (1.8%)

prune60.0ms (1.7%)

localize6.0ms (0.2%)

rewrite29.0ms (0.8%)

series135.0ms (3.9%)

simplify69.0ms (2%)

prune199.0ms (5.8%)

localize9.0ms (0.3%)

rewrite128.0ms (3.7%)

series270.0ms (7.9%)

simplify132.0ms (3.9%)

prune630.0ms (18.4%)

localize14.0ms (0.4%)

rewrite43.0ms (1.3%)

series264.0ms (7.7%)

simplify80.0ms (2.3%)

prune137.0ms (4%)

regimes24.0ms (0.7%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample805.0ms (23.6%)

Profiling