Details

analyze341.0ms (6.7%)

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)

sample34.0ms (0.7%)

Algorithm

1×

intervals

Results

10.0ms	200×	body	128	valid
5.0ms	23×	body	2048	valid
4.0ms	14×	body	4096	valid
4.0ms	256×	pre	128	true
2.0ms	12×	body	1024	valid
1.0ms	6×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify108.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	249	23
1	249	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

Error

39.2b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize14.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.5b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
31.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_441`
7×	`*-un-lft-identity_binary64_419` `pow1_binary64_480`
5×	`add-log-exp_binary64_458` `add-cube-cbrt_binary64_454` `sqrt-prod_binary64_435`
4×	`sqrt-div_binary64_436`
3×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `sqrt-pow1_binary64_437` `cancel-sign-sub-inv_binary64_385`
2×	`difference-of-squares_binary64_388` `pow1/2_binary64_499` `flip3--_binary64_423` `associate-*r/_binary64_361` `flip--_binary64_394`
1×	`flip3-+_binary64_422` `pow-prod-down_binary64_490` `sub-neg_binary64_412` `distribute-lft-out--_binary64_371` `flip-+_binary64_393` `diff-log_binary64_511` `rem-sqrt-square_binary64_432`

Counts

3 → 45

Calls

3 calls:

9.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series237.0ms (4.6%)

Counts

3 → 32

Calls

3 calls:

85.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
77.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
75.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))

Compiler

Compiled 857 to 786 computations (8.3% saved)

simplify70.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4975	1187
1	4975	1187

prune87.0ms (1.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	71	6	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	6	78

Error

0.4b

Counts

78 → 6

Compiler

Compiled 1445 to 702 computations (51.4% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow1_binary64_480`
2×	`sqrt-div_binary64_436` `associate-*r/_binary64_361` `sqrt-pow1_binary64_437`
1×	`*-un-lft-identity_binary64_419` `pow-prod-down_binary64_490` `add-log-exp_binary64_458` `add-cube-cbrt_binary64_454` `pow1/2_binary64_499` `add-sqr-sqrt_binary64_441` `flip3--_binary64_423` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `flip--_binary64_394` `sqrt-prod_binary64_435`

Counts

1 → 13

Calls

1 calls:

5.0ms

(sqrt.f64 (*.f64 2 (-.f64 im re)))

series50.0ms (1%)

Counts

1 → 7

Calls

1 calls:

50.0ms

(sqrt.f64 (*.f64 2 (-.f64 im re)))

Compiler

Compiled 198 to 189 computations (4.5% saved)

simplify105.0ms (2%)

Algorithm

1×	egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	4981	216
1	4981	216

prune18.0ms (0.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	20	0	20
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	20	6	26

Error

0.4b

Counts

26 → 6

Compiler

Compiled 294 to 219 computations (25.5% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))
0.5b	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
28.5b	(sqrt.f64 (.f64 (.f64 im im) 2))
31.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite37.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64_419`
32×	`sqrt-prod_binary64_435`
28×	`times-frac_binary64_425`
24×	`add-sqr-sqrt_binary64_441`
23×	`add-cube-cbrt_binary64_454`
11×	`pow1_binary64_480`
7×	`associate-/r*_binary64_363`
6×	`add-log-exp_binary64_458` `distribute-lft-out_binary64_370` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
4×	`sqrt-div_binary64_436` `sqrt-pow1_binary64_437` `associate-/l*_binary64_364`
3×	`flip3-+_binary64_422` `pow-prod-down_binary64_490` `flip-+_binary64_393`
2×	`pow1/2_binary64_499` `associate-/r/_binary64_365`
1×	`clear-num_binary64_418` `sqrt-undiv_binary64_440` `div-inv_binary64_416` `sum-log_binary64_510` `frac-2neg_binary64_430` `rem-sqrt-square_binary64_432` `+-commutative_binary64_349` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

4 → 93

Calls

4 calls:

13.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))
6.0ms	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
4.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series254.0ms (5%)

Counts

4 → 32

Calls

4 calls:

81.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))
75.0ms	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
67.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
30.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))

Compiler

Compiled 1034 to 884 computations (14.5% saved)

simplify85.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4944	3092
1	4944	3092

prune137.0ms (2.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	119	6	125
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	121	10	131

Error

0.3b

Counts

131 → 10

Compiler

Compiled 3444 to 1358 computations (60.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
0.5b	(*.f64 im (sqrt.f64 2))
0.5b	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
31.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite34.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64_419`
17×	`add-sqr-sqrt_binary64_441`
15×	`sqrt-prod_binary64_435`
12×	`add-cube-cbrt_binary64_454`
11×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
7×	`times-frac_binary64_425` `associate-/r*_binary64_363` `pow1_binary64_480`
6×	`add-log-exp_binary64_458` `associate-r_binary64_359`
4×	`sqrt-div_binary64_436`
3×	`flip3-+_binary64_422` `distribute-lft-out_binary64_370` `associate-l_binary64_360` `flip-+_binary64_393`
2×	`unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-/r/_binary64_365` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`pow-prod-down_binary64_490` `clear-num_binary64_418` `pow1/2_binary64_499` `div-inv_binary64_416` `sum-log_binary64_510` `-commutative_binary64_350` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `+-commutative_binary64_349` `associate-/l_binary64_364`

Counts

4 → 80

Calls

4 calls:

11.0ms	(/.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
6.0ms	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
6.0ms	(*.f64 im (sqrt.f64 2))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series310.0ms (6.1%)

Counts

4 → 40

Calls

4 calls:

105.0ms	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
88.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
88.0ms	(/.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
29.0ms	(*.f64 im (sqrt.f64 2))

Compiler

Compiled 1236 to 1076 computations (12.9% saved)

simplify78.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4977	2028
1	4977	2028

prune117.0ms (2.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	115	5	120
Fresh	4	4	8
Picked	1	0	1
Done	0	1	1
Total	120	10	130

Error

0.3b

Counts

130 → 10

Compiler

Compiled 2609 to 1160 computations (55.5% saved)

regimes950.0ms (18.6%)

Accuracy

Total 13.1b remaining (97.4%)

Threshold costs 0b (0%)

Compiler

Compiled 7536 to 5354 computations (29% saved)

bsearch86.0ms (1.7%)

Steps

Iters	Range		Point
10	2.635159266582253e+77	2.6985934216437893e+88	6.477992946618128e+80
8	-2.512837136916818e-40	-5.64568761212097e-43	-5.707305022353321e-43
9	-2.1144374507539735e+129	-1.8148107878303114e+123	-6.500985051720089e+126

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	87
1	58	87

end0.0ms (0%)

sample1.9s (36.8%)

Algorithm

1×

intervals

Results

311.0ms	6111×	body	128	valid
156.0ms	530×	body	4096	valid
142.0ms	601×	body	2048	valid
115.0ms	8000×	pre	128	true
82.0ms	408×	body	1024	valid
36.0ms	236×	body	512	valid
13.0ms	114×	body	256	valid

Compiler

Compiled 1021 to 729 computations (28.6% saved)

Details

analyze341.0ms (6.7%)

sample34.0ms (0.7%)

simplify108.0ms (2.1%)

prune3.0ms (0.1%)

localize14.0ms (0.3%)

rewrite25.0ms (0.5%)

series237.0ms (4.6%)

simplify70.0ms (1.4%)

prune87.0ms (1.7%)

localize8.0ms (0.2%)

rewrite6.0ms (0.1%)

series50.0ms (1%)

simplify105.0ms (2%)

prune18.0ms (0.4%)

localize15.0ms (0.3%)

rewrite37.0ms (0.7%)

series254.0ms (5%)

simplify85.0ms (1.7%)

prune137.0ms (2.7%)

localize12.0ms (0.2%)

rewrite34.0ms (0.7%)

series310.0ms (6.1%)

simplify78.0ms (1.5%)

prune117.0ms (2.3%)

regimes950.0ms (18.6%)

bsearch86.0ms (1.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.9s (36.8%)

Profiling