Details

analyze4.0ms (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
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

Compiler

Compiled 9 to 5 computations (44.4% saved)

sample11.0ms (0.6%)

Algorithm

1×

intervals

Results

6.0ms

256×

body

128

valid

Compiler

Compiled 17 to 10 computations (41.2% saved)

simplify92.0ms (5.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

prune3.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 29.0b

Counts

2 → 1

Compiler

Compiled 12 to 8 computations (33.3% saved)

localize8.0ms (0.5%)

Local error

Found 1 expressions with local error:

28.1b

(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite6.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow1_binary64_139`
2×	`sqrt-pow1_binary64_96` `sqrt-div_binary64_95` `associate-*r/_binary64_20`
1×	`add-cbrt-cube_binary64_114` `sqrt-prod_binary64_94` `add-sqr-sqrt_binary64_100` `add-log-exp_binary64_117` `flip-+_binary64_52` `add-cube-cbrt_binary64_113` `add-exp-log_binary64_116` `pow-prod-down_binary64_149` `pow1/2_binary64_158` `*-un-lft-identity_binary64_78` `flip3-+_binary64_81`

Counts

1 → 13

Calls

1 calls:

5.0ms

(sqrt.f64 (*.f64 x (+.f64 x x)))

series24.0ms (1.5%)

Counts

1 → 3

Calls

1 calls:

24.0ms

(sqrt.f64 (*.f64 x (+.f64 x x)))

simplify69.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5009	140

prune19.0ms (1.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	11	5	16
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	11	6	17

Merged error: 0.2b

Counts

17 → 6

Compiler

Compiled 188 to 78 computations (58.5% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.4b	(*.f64 x (sqrt.f64 2))

rewrite6.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_100`
6×	`associate-r_binary64_18`
4×	`sqrt-prod_binary64_94` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
3×	`add-cbrt-cube_binary64_114` `associate-l_binary64_19` `add-exp-log_binary64_116` `pow1_binary64_139`
2×	`unswap-sqr_binary64_46`
1×	`*-commutative_binary64_9` `add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-prod-down_binary64_149`

Counts

1 → 22

Calls

1 calls:

5.0ms

(*.f64 x (sqrt.f64 2))

series26.0ms (1.6%)

Counts

1 → 3

Calls

1 calls:

26.0ms

(*.f64 x (sqrt.f64 2))

simplify44.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5010	211

prune21.0ms (1.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	23	2	25
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	24	7	31

Merged error: 0.1b

Counts

31 → 7

Compiler

Compiled 258 to 192 computations (25.6% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.3b	(*.f64 x (sqrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (.f64 x (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

rewrite20.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`sqrt-prod_binary64_94`
18×	`associate-r_binary64_18`
15×	`add-sqr-sqrt_binary64_100`
9×	`add-cbrt-cube_binary64_114` `add-cube-cbrt_binary64_113` `add-exp-log_binary64_116` `*-un-lft-identity_binary64_78` `pow1_binary64_139`
4×	`associate-l_binary64_19` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-prod-down_binary64_149`
3×	`unswap-sqr_binary64_46`
2×	`*-commutative_binary64_9` `add-log-exp_binary64_117`

Counts

2 → 50

Calls

2 calls:

10.0ms	(.f64 (.f64 x (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
6.0ms	(*.f64 x (sqrt.f64 (sqrt.f64 2)))

series67.0ms (4.1%)

Counts

2 → 6

Calls

2 calls:

40.0ms	(*.f64 x (sqrt.f64 (sqrt.f64 2)))
27.0ms	(.f64 (.f64 x (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

simplify76.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5269	559

prune47.0ms (2.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	56	7	63

Merged error: 0.1b

Counts

63 → 7

Compiler

Compiled 687 to 584 computations (15% saved)

localize6.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
0.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
28.1b	(sqrt.f64 (*.f64 x (+.f64 x x)))
28.1b	(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite46.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`sqrt-pow1_binary64_96`
71×	`pow1_binary64_139`
33×	`sqrt-prod_binary64_94`
32×	`sqrt-div_binary64_95`
28×	`add-sqr-sqrt_binary64_100`
25×	`pow-prod-down_binary64_149`
22×	`pow1/2_binary64_158`
20×	`associate-*r/_binary64_20`
14×	`pow-prod-up_binary64_148`
13×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
9×	`flip-+_binary64_52` `swap-sqr_binary64_45` `flip3-+_binary64_81`
8×	`pow-sqr_binary64_51`
7×	`associate-l_binary64_19` `associate-r_binary64_18`
6×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
4×	`add-log-exp_binary64_117` `frac-times_binary64_88` `unswap-sqr_binary64_46`
3×	`rem-sqrt-square_binary64_91`
2×	`associate-*l/_binary64_21`
1×	`pow2_binary64_159` `*-commutative_binary64_9` `sqr-abs_binary64_93` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `sqrt-unprod_binary64_98` `rem-square-sqrt_binary64_90` `pow-plus_binary64_141`

Counts

4 → 125

Calls

4 calls:

19.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
6.0ms	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

series97.0ms (6%)

Counts

4 → 12

Calls

4 calls:

28.0ms	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
27.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
22.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
21.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

simplify72.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5024	1447

prune83.0ms (5.1%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	137	7	144

Merged error: 0.1b

Counts

144 → 7

Compiler

Compiled 2000 to 518 computations (74.1% saved)

regimes180.0ms (11.1%)

Compiler: Compiled 917 to 640 computations (30.2% saved)

bsearch15.0ms (0.9%)

Steps

Iters	Range		Point
10	-3.043598496080998e-296	4.599112235904557e-306	4.6648851468538e-310

Compiler

Compiled 1 to 1 computations (0% saved)

simplify5.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	20
1	34	20

end0.0ms (0%)

sample570.0ms (35.1%)

Algorithm

1×

intervals

Results

183.0ms

8000×

body

128

valid

Compiler

Compiled 223 to 160 computations (28.3% saved)

Details

analyze4.0ms (0.2%)

sample11.0ms (0.6%)

simplify92.0ms (5.6%)

prune3.0ms (0.2%)

localize8.0ms (0.5%)

rewrite6.0ms (0.4%)

series24.0ms (1.5%)

simplify69.0ms (4.2%)

prune19.0ms (1.1%)

localize3.0ms (0.2%)

rewrite6.0ms (0.4%)

series26.0ms (1.6%)

simplify44.0ms (2.7%)

prune21.0ms (1.3%)

localize5.0ms (0.3%)

rewrite20.0ms (1.2%)

series67.0ms (4.1%)

simplify76.0ms (4.7%)

prune47.0ms (2.9%)

localize6.0ms (0.4%)

rewrite46.0ms (2.9%)

series97.0ms (6%)

simplify72.0ms (4.4%)

prune83.0ms (5.1%)

regimes180.0ms (11.1%)

bsearch15.0ms (0.9%)

simplify5.0ms (0.3%)

end0.0ms (0%)

sample570.0ms (35.1%)

Profiling