Details

analyze322.0ms (9.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
25%	25%	50%	2
25%	25%	50%	3
31.2%	18.7%	50%	4
31.2%	18.7%	50%	5
34.3%	15.6%	50%	6
34.3%	15.6%	50%	7
35.9%	14%	50%	8
35.9%	14%	50%	9
36.7%	13.3%	50%	10
36.7%	13.3%	50%	11
37.1%	12.9%	50%	12
37.1%	12.9%	50%	13
37.3%	12.7%	50%	14

Compiler

Compiled 18 to 14 computations (22.2% saved)

sample36.0ms (1%)

Algorithm

1×

intervals

Results

11.0ms	194×	body	128	valid
5.0ms	17×	body	4096	valid
4.0ms	256×	pre	128	true
3.0ms	16×	body	2048	valid
2.0ms	12×	body	1024	valid
2.0ms	13×	body	512	valid
0.0ms	4×	body	256	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify160.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	156	23
1	156	23

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

Merged error: 41.2b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.0b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.8b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
31.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite35.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_435`
8×	`pow1_binary64_472` `add-log-exp_binary64_450`
7×	`*-un-lft-identity_binary64_414`
5×	`add-cube-cbrt_binary64_446` `sqrt-prod_binary64_429`
4×	`sqrt-div_binary64_430` `add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
3×	`sqrt-pow1_binary64_431`
2×	`flip3--_binary64_418` `flip3-+_binary64_417` `difference-of-squares_binary64_383` `flip-+_binary64_388` `pow1/2_binary64_491` `flip--_binary64_389` `associate-*r/_binary64_358`
1×	`distribute-lft-out--_binary64_368` `diff-log_binary64_503` `+-commutative_binary64_346` `pow-prod-down_binary64_482` `sub-neg_binary64_407` `sum-log_binary64_502` `rem-sqrt-square_binary64_427`

Counts

4 → 53

Calls

4 calls:

10.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
6.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(+.f64 (.f64 re re) (.f64 im im))

series357.0ms (10.4%)

Counts

4 → 12

Calls

4 calls:

210.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
60.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
52.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
34.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify44.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5171	1116

prune88.0ms (2.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	57	8	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	8	66

Merged error: 9.7b

Counts

66 → 8

Compiler

Compiled 1434 to 644 computations (55.1% saved)

localize6.0ms (0.2%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune8.0ms (0.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	7	7
Picked	1	1
Done	0	0
Total	8	8

Merged error: 9.7b

Counts

8 → 8

Compiler

Compiled 129 to 84 computations (34.9% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
9.0b	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
31.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
31.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite66.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`sqrt-prod_binary64_429`
51×	`add-sqr-sqrt_binary64_435`
34×	`sqrt-pow1_binary64_431`
29×	`pow1_binary64_472`
28×	`sqrt-div_binary64_430`
18×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414` `pow1/2_binary64_491`
15×	`swap-sqr_binary64_381`
9×	`pow-prod-up_binary64_481` `associate-l_binary64_357` `associate-r_binary64_356` `unswap-sqr_binary64_382`
8×	`flip3-+_binary64_417` `flip-+_binary64_388`
6×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447` `add-log-exp_binary64_450`
5×	`pow-prod-down_binary64_482` `pow-sqr_binary64_387`
4×	`frac-times_binary64_424`
2×	`associate-l/_binary64_359` `associate-r/_binary64_358` `rem-sqrt-square_binary64_427`
1×	`pow-plus_binary64_474` `flip3--_binary64_418` `difference-of-squares_binary64_383` `diff-log_binary64_503` `*-commutative_binary64_347` `prod-exp_binary64_460` `sub-neg_binary64_407` `sqrt-unprod_binary64_433` `rem-square-sqrt_binary64_426` `flip--_binary64_389` `cbrt-unprod_binary64_444` `pow2_binary64_492`

Counts

4 → 125

Calls

4 calls:

19.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
18.0ms	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series198.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
54.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
47.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
38.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify79.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4925	2300
1	4925	2300

prune142.0ms (4.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	138	7	145

Merged error: 9.7b

Counts

145 → 7

Compiler

Compiled 3656 to 1295 computations (64.6% saved)

localize24.0ms (0.7%)

Local error

Found 4 expressions with local error:

11.3b	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) 4) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))) re)
31.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
31.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
31.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite51.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_435`
9×	`sqrt-prod_binary64_429`
7×	`pow1_binary64_472` `add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
6×	`sqrt-div_binary64_430` `add-log-exp_binary64_450`
4×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
3×	`flip3-+_binary64_417` `sqrt-pow1_binary64_431` `flip-+_binary64_388` `pow1/2_binary64_491` `rem-sqrt-square_binary64_427`
1×	`flip3--_binary64_418` `diff-log_binary64_503` `sub-neg_binary64_407` `flip--_binary64_389`

Counts

4 → 56

Calls

4 calls:

28.0ms	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) 4) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series198.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) 4) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))) re)
49.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
45.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
41.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify84.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4863	967
1	4863	967

prune93.0ms (2.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	68	7	75

Merged error: 9.7b

Counts

75 → 7

Compiler

Compiled 2718 to 908 computations (66.6% saved)

regimes152.0ms (4.4%)

Compiler: Compiled 476 to 348 computations (26.9% saved)

bsearch96.0ms (2.8%)

Steps

Iters	Range		Point
6	1.205250905625099e+97	5.996556376730269e+97	3.680960150483854e+97
6	1.7833455385765348e-75	7.651139367441543e-75	2.416279663740342e-75
9	1.0385190483911067e-160	2.0691959923605614e-154	2.0790220575817727e-160
6	3.9628412093824493e-174	5.281612055965653e-173	5.188805611596897e-173

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	73	153
1	73	153

end0.0ms (0%)

sample1.2s (33.9%)

Algorithm

1×

intervals

Results

281.0ms	6096×	body	128	valid
142.0ms	616×	body	2048	valid
137.0ms	497×	body	4096	valid
113.0ms	8000×	pre	128	true
71.0ms	414×	body	1024	valid
33.0ms	236×	body	512	valid
12.0ms	141×	body	256	valid

Compiler

Compiled 234 to 157 computations (32.9% saved)

Details

analyze322.0ms (9.4%)

sample36.0ms (1%)

simplify160.0ms (4.6%)

prune3.0ms (0.1%)

localize14.0ms (0.4%)

rewrite35.0ms (1%)

series357.0ms (10.4%)

simplify44.0ms (1.3%)

prune88.0ms (2.6%)

localize6.0ms (0.2%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.2%)

prune8.0ms (0.2%)

localize12.0ms (0.4%)

rewrite66.0ms (1.9%)

series198.0ms (5.7%)

simplify79.0ms (2.3%)

prune142.0ms (4.1%)

localize24.0ms (0.7%)

rewrite51.0ms (1.5%)

series198.0ms (5.8%)

simplify84.0ms (2.4%)

prune93.0ms (2.7%)

regimes152.0ms (4.4%)

bsearch96.0ms (2.8%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.2s (33.9%)

Profiling