Details

analyze324.0ms (11.7%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

sample35.0ms (1.3%)

Algorithm

1×

intervals

Results

9.0ms	189×	body	80	valid
8.0ms	21×	body	2560	valid
5.0ms	21×	body	1280	valid
2.0ms	7×	body	5120	valid
2.0ms	9×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	22	15
1	22	15

prune5.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 41.2b

Counts

2 → 1

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.0b	(sqrt.f64 (.f64 2.0 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
1.0b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite27.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64` `pow1_binary64`
7×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64` `flip-+_binary64` `sqrt-div_binary64`
3×	`sqrt-pow1_binary64`
2×	`pow1/2_binary64` `associate-*r/_binary64` `+-commutative_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `distribute-lft-out_binary64` `rem-sqrt-square_binary64`

Counts

4 → 51

Calls

4 calls:

9.0ms	(sqrt.f64 (.f64 2.0 (+.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	(+.f64 (.f64 re re) (.f64 im im))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series59.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt.f64 (.f64 2.0 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
10.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
7.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify36.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5008	690

prune114.0ms (4.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	54	9	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	9	64

Merged error: 21.3b

Counts

64 → 9

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)))))
7.0b	(+.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)
30.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
30.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite50.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`sqrt-prod_binary64`
50×	`add-sqr-sqrt_binary64`
34×	`sqrt-pow1_binary64`
29×	`pow1_binary64`
28×	`sqrt-div_binary64`
18×	`*-un-lft-identity_binary64` `pow1/2_binary64` `add-cube-cbrt_binary64`
15×	`swap-sqr_binary64`
9×	`flip3-+_binary64` `associate-r_binary64` `pow-prod-up_binary64` `associate-l_binary64` `unswap-sqr_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-down_binary64` `pow-sqr_binary64`
4×	`frac-times_binary64`
2×	`associate-r/_binary64` `rem-sqrt-square_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 124

Calls

4 calls:

17.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
16.0ms	(+.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)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series33.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

10.0ms	(+.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)
8.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify70.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4944	1470
1	4944	1470

prune162.0ms (5.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	136	9	145

Merged error: 21.3b

Counts

145 → 9

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
6.5b	(+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
31.2b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
31.2b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite30.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `cbrt-prod_binary64`
9×	`associate-r_binary64`
8×	`sqrt-prod_binary64`
6×	`cbrt-div_binary64` `add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`flip3-+_binary64` `flip-+_binary64`
3×	`associate-l_binary64` `unswap-sqr_binary64`
2×	`associate-*r/_binary64` `pow1/3_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 65

Calls

4 calls:

10.0ms	(+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
9.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (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)))

series121.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
33.0ms	(+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
25.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
23.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify67.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4945	1404
1	4945	1404

prune108.0ms (3.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	76	10	86

Merged error: 21.3b

Counts

86 → 10

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

11.4b	(+.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) re)
30.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
30.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
30.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite39.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `sqrt-div_binary64`
4×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`+-commutative_binary64` `sum-log_binary64`

Counts

4 → 56

Calls

4 calls:

24.0ms	(+.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (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)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series35.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(+.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) re)
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify59.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5310	612

prune76.0ms (2.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	68	10	78

Merged error: 21.3b

Counts

78 → 10

regimes303.0ms (10.9%)

Accuracy

Total 9.4b remaining (34.8%)

Threshold costs 0b (0%)

bsearch41.0ms (1.5%)

Steps

Iters	Range		Point
0	1.6562206752772235e+136	1.6741129710535287e+136	1.665166823165376e+136
9	3.928784151661965e-254	3.1808294008083687e-249	3.98296718739982e-254
8	1.2597963522294294e-278	1.3174351383314836e-275	1.3032785344699448e-275
6	-3.1400830244957616e-298	-3.828280990086513e-299	-1.8219756175958796e-298

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	64	79
1	64	79

end0.0ms (0%)

sample917.0ms (33.1%)

Algorithm

1×

intervals

Results

291.0ms	6023×	body	80	valid
195.0ms	714×	body	2560	valid
101.0ms	301×	body	5120	valid
100.0ms	443×	body	1280	valid
51.0ms	286×	body	640	valid
20.0ms	155×	body	320	valid
7.0ms	78×	body	160	valid

Details

analyze324.0ms (11.7%)

sample35.0ms (1.3%)

simplify6.0ms (0.2%)

prune5.0ms (0.2%)

localize10.0ms (0.4%)

rewrite27.0ms (1%)

series59.0ms (2.1%)

simplify36.0ms (1.3%)

prune114.0ms (4.1%)

localize12.0ms (0.4%)

rewrite50.0ms (1.8%)

series33.0ms (1.2%)

simplify70.0ms (2.5%)

prune162.0ms (5.9%)

localize13.0ms (0.5%)

rewrite30.0ms (1.1%)

series121.0ms (4.4%)

simplify67.0ms (2.4%)

prune108.0ms (3.9%)

localize14.0ms (0.5%)

rewrite39.0ms (1.4%)

series35.0ms (1.3%)

simplify59.0ms (2.1%)

prune76.0ms (2.7%)

regimes303.0ms (10.9%)

bsearch41.0ms (1.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample917.0ms (33.1%)

Profiling