Details

analyze468.0ms (10%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
28.1%	71.8%	0.1%	9
42.1%	57.7%	0.1%	10
49.1%	50.7%	0.1%	11
57.3%	42.5%	0.1%	12
66.9%	33%	0.1%	13
71.7%	28.2%	0.1%	14

Compiler

Compiled 13 to 10 computations (23.1% saved)

sample20.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 25 to 22 computations (12% saved)

simplify102.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	18
1	20	18

prune2.0ms (0%)

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

34.9b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

32.4b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
32.4b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`sqrt-prod_binary64_20400` `add-sqr-sqrt_binary64_20406`
2×	`sqrt-div_binary64_20401` `*-un-lft-identity_binary64_20384` `pow1_binary64_20445` `add-cube-cbrt_binary64_20419`
1×	`flip3-+_binary64_20387` `add-cbrt-cube_binary64_20420` `add-log-exp_binary64_20423` `add-exp-log_binary64_20422` `flip-+_binary64_20358` `rem-sqrt-square_binary64_20397` `pow1/2_binary64_20464` `sqrt-pow1_binary64_20402`

Counts

1 → 15

Calls

2 calls:

6.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
0.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

series297.0ms (6.4%)

Counts

1 → 26

Calls

1 calls:

297.0ms

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

Compiler

Compiled 1161 to 995 computations (14.3% saved)

simplify75.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4996	1435
1	4996	1435

prune60.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	34	7	41
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	34	8	42

Error

0.1b

Counts

42 → 8

Compiler

Compiled 1067 to 409 computations (61.7% saved)

localize12.0ms (0.3%)

Local error

Found 8 expressions with local error:

32.4b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
0.0b	(sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
0.0b	(sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
0.0b	(sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
32.4b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
32.4b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite59.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`sqrt-prod_binary64_20400`
62×	`add-sqr-sqrt_binary64_20406`
38×	`sqrt-pow1_binary64_20402`
32×	`sqrt-div_binary64_20401`
31×	`pow1_binary64_20445`
20×	`*-un-lft-identity_binary64_20384` `pow1/2_binary64_20464` `add-cube-cbrt_binary64_20419`
15×	`swap-sqr_binary64_20351`
12×	`rem-sqrt-square_binary64_20397`
9×	`flip3-+_binary64_20387` `pow-prod-up_binary64_20454` `flip-+_binary64_20358` `unswap-sqr_binary64_20352` `associate-r_binary64_20324` `associate-l_binary64_20325`
6×	`add-cbrt-cube_binary64_20420` `add-exp-log_binary64_20422`
5×	`pow-prod-down_binary64_20455` `pow-sqr_binary64_20357`
4×	`add-log-exp_binary64_20423` `sqr-abs_binary64_20399` `frac-times_binary64_20394`
2×	`associate-r/_binary64_20326` `associate-l/_binary64_20327`
1×	`cbrt-unprod_binary64_20417` `rem-square-sqrt_binary64_20396` `*-commutative_binary64_20315` `pow-plus_binary64_20447` `prod-exp_binary64_20433` `sqrt-unprod_binary64_20404` `pow2_binary64_20465`

Counts

4 → 138

Calls

8 calls:

22.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
6.0ms	(sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
6.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
6.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
0.0ms	(sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))

series1.4s (30.5%)

Counts

4 → 100

Calls

4 calls:

479.0ms	(sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
315.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
313.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
311.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

Compiler

Compiled 6056 to 4861 computations (19.7% saved)

simplify107.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5235	7937

prune252.0ms (5.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	238	8	246

Error

0.1b

Counts

246 → 8

Compiler

Compiled 8187 to 1849 computations (77.4% saved)

localize1.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune3.0ms (0.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	5	5
Picked	1	1
Done	2	2
Total	8	8

Error

0.1b

Counts

8 → 8

Compiler

Compiled 8 to 18 computations (-125% saved)

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune1.0ms (0%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	3	3
Total	8	8

Error

0.1b

Counts

8 → 8

Compiler

Compiled 0 to 0 computations (0% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	138	213
1	138	213

regimes352.0ms (7.6%)

Accuracy

Total 25.1b remaining (98.3%)

Threshold costs 0b (0%)

Compiler

Compiled 1541 to 1258 computations (18.4% saved)

bsearch33.0ms (0.7%)

Steps

Iters	Range		Point
8	1.9256591861854557e+109	6.529267025614804e+111	6.450989484237564e+111
9	-2.6490716385674418e+40	-1.1723182602190305e+34	-2.604223501683959e+40

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	34
1	27	34

end0.0ms (0%)

sample1.4s (29.1%)

Algorithm

1×

intervals

Results

323.0ms

8000×

body

128

valid

Compiler

Compiled 517 to 409 computations (20.9% saved)

Pareto

0.208586765345169

Details

analyze468.0ms (10%)

sample20.0ms (0.4%)

simplify102.0ms (2.2%)

prune2.0ms (0%)

localize8.0ms (0.2%)

rewrite8.0ms (0.2%)

series297.0ms (6.4%)

simplify75.0ms (1.6%)

prune60.0ms (1.3%)

localize12.0ms (0.3%)

rewrite59.0ms (1.3%)

series1.4s (30.5%)

simplify107.0ms (2.3%)

prune252.0ms (5.4%)

localize1.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize2.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.1%)

prune1.0ms (0%)

simplify6.0ms (0.1%)

regimes352.0ms (7.6%)

bsearch33.0ms (0.7%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.4s (29.1%)

Profiling