Details

analyze320.0ms (7.5%)

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample30.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	186×	body	128	valid
5.0ms	25×	body	2048	valid
5.0ms	19×	body	4096	valid
2.0ms	13×	body	512	valid
1.0ms	8×	body	1024	valid
0.0ms	5×	body	256	valid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	23
1	23	23

prune3.0ms (0.1%)

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: 39.2b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.5b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
29.1b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 38

Calls

3 calls:

7.0ms	(+.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))

series139.0ms (3.2%)

Counts

3 → 9

Calls

3 calls:

54.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
50.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
35.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify86.0ms (2%)

Algorithm

1×	egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4935	690
1	4935	690

prune174.0ms (4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	40	7	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	8	48

Merged error: 16.4b

Counts

48 → 8

Compiler

Compiled 3092 to 1832 computations (40.8% 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)))))
9.5b	(+.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)
29.1b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
29.1b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite64.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`sqrt-prod_binary64`
58×	`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`
10×	`rem-sqrt-square_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×	`sqr-abs_binary64` `frac-times_binary64`
2×	`associate-r/_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 → 128

Calls

4 calls:

19.0ms	(+.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)
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)))))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series202.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(+.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)
48.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
41.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
41.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify56.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5160	2274

prune162.0ms (3.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	141	7	148

Merged error: 16.4b

Counts

148 → 7

Compiler

Compiled 3980 to 1515 computations (61.9% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.9b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.5b	(sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
23.5b	(/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))
29.1b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite44.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64` `add-cube-cbrt_binary64`
7×	`sqrt-prod_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `difference-of-squares_binary64` `times-frac_binary64`
3×	`cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `distribute-lft-out--_binary64` `sqrt-div_binary64`
2×	`pow1/2_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `div-exp_binary64` `flip--_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `flip-+_binary64`

Counts

4 → 73

Calls

4 calls:

12.0ms	(/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))
12.0ms	(sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (-.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)))

series369.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

166.0ms	(sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
108.0ms	(/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))
55.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
40.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify55.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4921	1730
1	4921	1730

prune237.0ms (5.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	81	4	85
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	83	9	92

Merged error: 12.3b

Counts

92 → 9

Compiler

Compiled 4865 to 2554 computations (47.5% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 im (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re) im))
0.9b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.5b	(sqrt.f64 (.f64 2 (/.f64 im (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re) im))))
29.1b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite63.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
122×	`add-sqr-sqrt_binary64`
95×	`*-un-lft-identity_binary64`
69×	`add-cube-cbrt_binary64`
26×	`difference-of-squares_binary64`
22×	`associate-/r*_binary64`
17×	`sqrt-prod_binary64`
13×	`distribute-lft-out--_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64`
5×	`div-inv_binary64`
3×	`cbrt-undiv_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `associate-/l*_binary64` `div-exp_binary64` `sqrt-div_binary64`
2×	`pow1/2_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 150

Calls

4 calls:

15.0ms	(/.f64 im (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re) im))
15.0ms	(sqrt.f64 (.f64 2 (/.f64 im (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re) im))))
9.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series380.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

187.0ms	(sqrt.f64 (.f64 2 (/.f64 im (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re) im))))
98.0ms	(/.f64 im (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re) im))
54.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
40.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify100.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5724	4959

prune295.0ms (6.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	159	3	162
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	163	8	171

Merged error: 10.1b

Counts

171 → 8

Compiler

Compiled 6986 to 2879 computations (58.8% saved)

regimes261.0ms (6.1%)

Compiler: Compiled 1045 to 838 computations (19.8% saved)

bsearch75.0ms (1.7%)

Steps

Iters	Range		Point
5	5.986396324260378e+56	1.4869382962924306e+57	1.4701524095992479e+57
5	7.948621037828916e-171	1.640089953357148e-170	8.017246655510101e-171
4	-2.180064213946696e-206	-1.496833524932593e-206	-1.6035883200910468e-206
9	-4.1084924497129085e+118	-1.2482836422540047e+110	-4.015762233969269e+118

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	74	126
1	74	126

end0.0ms (0%)

sample1.1s (25.6%)

Algorithm

1×

intervals

Results

292.0ms	6065×	body	128	valid
159.0ms	547×	body	4096	valid
149.0ms	660×	body	2048	valid
64.0ms	367×	body	1024	valid
35.0ms	242×	body	512	valid
11.0ms	119×	body	256	valid

Compiler

Compiled 262 to 192 computations (26.7% saved)

Details

analyze320.0ms (7.5%)

sample30.0ms (0.7%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

rewrite19.0ms (0.5%)

series139.0ms (3.2%)

simplify86.0ms (2%)

prune174.0ms (4%)

localize12.0ms (0.3%)

rewrite64.0ms (1.5%)

series202.0ms (4.7%)

simplify56.0ms (1.3%)

prune162.0ms (3.8%)

localize11.0ms (0.3%)

rewrite44.0ms (1%)

series369.0ms (8.6%)

simplify55.0ms (1.3%)

prune237.0ms (5.5%)

localize12.0ms (0.3%)

rewrite63.0ms (1.5%)

series380.0ms (8.8%)

simplify100.0ms (2.3%)

prune295.0ms (6.9%)

regimes261.0ms (6.1%)

bsearch75.0ms (1.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.1s (25.6%)

Profiling