Details

analyze326.0ms (8.1%)

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)

sample33.0ms (0.8%)

Algorithm

1×

intervals

Results

9.0ms	193×	body	128	valid
5.0ms	20×	body	4096	valid
5.0ms	22×	body	2048	valid
3.0ms	256×	pre	128	true
2.0ms	11×	body	1024	valid
1.0ms	6×	body	512	valid
0.0ms	4×	body	256	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify108.0ms (2.7%)

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

41.1b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize14.0ms (0.3%)

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)))
0.9b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
32.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite31.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_441`
8×	`*-un-lft-identity_binary64_419` `add-log-exp_binary64_458` `pow1_binary64_480`
6×	`add-cube-cbrt_binary64_454`
5×	`sqrt-prod_binary64_435`
4×	`sqrt-div_binary64_436` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`sqrt-pow1_binary64_437` `cancel-sign-sub-inv_binary64_385`
2×	`flip3-+_binary64_422` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `flip3--_binary64_423` `associate-*r/_binary64_361` `flip-+_binary64_393` `flip--_binary64_394`
1×	`pow-prod-down_binary64_490` `sub-neg_binary64_412` `sum-log_binary64_510` `distribute-lft-out--_binary64_371` `diff-log_binary64_511` `rem-sqrt-square_binary64_432` `+-commutative_binary64_349`

Counts

4 → 56

Calls

4 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)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))

series180.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

107.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
27.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
26.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
20.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify86.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4930	1140
1	4930	1140

prune87.0ms (2.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	59	9	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	9	69

Error

11.6b

Counts

69 → 9

Compiler

Compiled 1525 to 679 computations (55.5% saved)

localize6.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune9.0ms (0.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	8	8
Picked	1	1
Done	0	0
Total	9	9

Error

11.6b

Counts

9 → 9

Compiler

Compiled 163 to 99 computations (39.3% saved)

localize12.0ms (0.3%)

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)))))
6.7b	(-.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)
32.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
32.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite67.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`sqrt-prod_binary64_435`
60×	`add-sqr-sqrt_binary64_441`
34×	`sqrt-pow1_binary64_437`
29×	`pow1_binary64_480`
28×	`sqrt-div_binary64_436`
19×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
18×	`pow1/2_binary64_499`
15×	`swap-sqr_binary64_386`
10×	`rem-sqrt-square_binary64_432`
9×	`associate-r_binary64_359` `unswap-sqr_binary64_387` `associate-l_binary64_360` `pow-prod-up_binary64_489`
8×	`flip3-+_binary64_422` `flip-+_binary64_393`
6×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
5×	`pow-prod-down_binary64_490` `pow-sqr_binary64_392`
4×	`sqr-abs_binary64_434` `frac-times_binary64_429`
3×	`cancel-sign-sub-inv_binary64_385`
2×	`associate-l/_binary64_362` `associate-r/_binary64_361`
1×	`sub-neg_binary64_412` `difference-of-squares_binary64_388` `sqrt-unprod_binary64_439` `rem-square-sqrt_binary64_431` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `flip3--_binary64_423` `pow-plus_binary64_482` `*-commutative_binary64_350` `diff-log_binary64_511` `flip--_binary64_394` `pow2_binary64_500`

Counts

4 → 132

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)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series102.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

32.0ms	(-.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)
25.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
23.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
21.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify88.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4995	2304
1	4995	2304

prune146.0ms (3.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	144	9	153

Error

11.6b

Counts

153 → 9

Compiler

Compiled 3877 to 1340 computations (65.4% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

32.8b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))) (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))
33.8b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
33.8b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
33.8b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite49.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`cbrt-div_binary64_451`
30×	`flip3-+_binary64_422` `flip-+_binary64_393`
28×	`frac-times_binary64_429`
26×	`sqrt-div_binary64_436`
24×	`pow1_binary64_480`
15×	`sqrt-pow1_binary64_437`
14×	`associate-*l/_binary64_362`
12×	`pow1/3_binary64_501`
9×	`cbrt-prod_binary64_450` `pow-prod-up_binary64_489`
8×	`associate-*r/_binary64_361`
7×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
6×	`pow-plus_binary64_482`
5×	`pow-prod-down_binary64_490`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`pow-sqr_binary64_392`
2×	`pow2_binary64_500`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `pow3_binary64_502`

Counts

4 → 89

Calls

4 calls:

20.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))) (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series246.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

76.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
73.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
68.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))) (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))

simplify104.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4917	2950
1	4917	2950

prune139.0ms (3.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	101	9	110

Error

11.6b

Counts

110 → 9

Compiler

Compiled 3977 to 1537 computations (61.4% saved)

regimes599.0ms (14.9%)

Accuracy

Total 9.8b remaining (49.7%)

Threshold costs 0b (0%)

Compiler

Compiled 4081 to 2859 computations (29.9% saved)

bsearch155.0ms (3.9%)

Steps

Iters	Range		Point
8	3.515987312526627e+208	1.2557948101261e+213	5.416764675562037e+209
10	8.195474808994166e+155	5.162022484262054e+173	1.8587874195533764e+169
8	1.5071718097111723e+34	1.4747740085390362e+38	1.7496279647313789e+34
6	-2.6098805793203997e-119	-1.862896324376759e-120	-3.703126325438035e-120
8	-6.605379369491444e+151	-3.792679072512062e+148	-3.846513651338927e+148

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	92	128
1	92	128

end0.0ms (0%)

sample1.4s (34.9%)

Algorithm

1×

intervals

Results

279.0ms	6101×	body	128	valid
147.0ms	542×	body	4096	valid
139.0ms	615×	body	2048	valid
115.0ms	8000×	pre	128	true
74.0ms	430×	body	1024	valid
27.0ms	210×	body	512	valid
9.0ms	102×	body	256	valid

Compiler

Compiled 534 to 371 computations (30.5% saved)

Details

analyze326.0ms (8.1%)

sample33.0ms (0.8%)

simplify108.0ms (2.7%)

prune3.0ms (0.1%)

localize14.0ms (0.3%)

rewrite31.0ms (0.8%)

series180.0ms (4.5%)

simplify86.0ms (2.1%)

prune87.0ms (2.2%)

localize6.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify9.0ms (0.2%)

prune9.0ms (0.2%)

localize12.0ms (0.3%)

rewrite67.0ms (1.7%)

series102.0ms (2.5%)

simplify88.0ms (2.2%)

prune146.0ms (3.6%)

localize17.0ms (0.4%)

rewrite49.0ms (1.2%)

series246.0ms (6.1%)

simplify104.0ms (2.6%)

prune139.0ms (3.4%)

regimes599.0ms (14.9%)

bsearch155.0ms (3.9%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (34.9%)

Profiling