Details

analyze478.0ms (11.4%)

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 18 to 13 computations (27.8% saved)

sample44.0ms (1%)

Algorithm

1×

intervals

Results

12.0ms	194×	body	128	valid
10.0ms	20×	body	4096	valid
5.0ms	18×	body	2048	valid
4.0ms	15×	body	1024	valid
1.0ms	7×	body	512	valid
0.0ms	2×	body	256	valid

Compiler

Compiled 37 to 27 computations (27% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`distribute-lft-in_binary64`
2×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	23	23
2	23	23
3	23	23

prune2.0ms (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

Error

39.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	39.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Compiler

Compiled 51 to 36 computations (29.4% saved)

localize12.0ms (0.3%)

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)
30.6b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite62.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

39.5b

Rules

7×	`add-log-exp_binary64`
6×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
4×	`pow1_binary64`

Counts

3 → 38

Calls

3 calls:

6.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
3.0ms	(+.f64 (.f64 re re) (.f64 im im))
3.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 907 to 328 computations (63.8% saved)

series102.0ms (2.4%)

Error

7.8b

Counts

3 → 47

Calls

3 calls:

31.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
27.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
22.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 1615 to 1296 computations (19.8% saved)

simplify110.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

469×	`unswap-sqr_binary64`
393×	`distribute-rgt-neg-in_binary64`
379×	`distribute-lft-neg-in_binary64`
284×	`associate-r_binary64`
277×	`distribute-neg-frac_binary64`

Counts

85 → 59

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	99	1277
1	275	1209
2	744	1206
3	2922	1206
4	4948	1206
5	4993	1206
6	4947	1206

prune35.0ms (0.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	52	7	59
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	7	60

Error

9.5b

Counts

60 → 7

Alt Table

Status	Error	Program
	58.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (neg.f64 re) re))))
	49.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re))))
▶	40.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.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))))
	44.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (neg.f64 im) re))))
	47.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 im im) re) -1/2))))
	47.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re 2))))

Compiler

Compiled 958 to 560 computations (41.5% saved)

localize14.0ms (0.3%)

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)))))
5.4b	(+.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)
31.6b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
31.6b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite93.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

9.5b

Rules

47×	`add-sqr-sqrt_binary64`
25×	`cbrt-prod_binary64`
16×	`sqrt-prod_binary64`
16×	`cbrt-div_binary64`
15×	`unswap-sqr_binary64`

Counts

4 → 94

Calls

4 calls:

14.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
13.0ms	(+.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)
3.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
3.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 3657 to 836 computations (77.1% saved)

series195.0ms (4.6%)

Error

9.5b

Counts

4 → 38

Calls

4 calls:

58.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
46.0ms	(+.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)
46.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
31.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 2852 to 2295 computations (19.5% saved)

simplify173.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

524×	`unswap-sqr_binary64`
422×	`*-commutative_binary64`
392×	`difference-of-squares_binary64`
392×	`sub-neg_binary64`
333×	`distribute-rgt-in_binary64`

Counts

132 → 117

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	172	4121
1	396	3146
2	922	2770
3	1675	2761
4	3716	2761
5	4629	2761
6	4946	2761

prune62.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	116	8	124

Error

9.5b

Counts

124 → 8

Alt Table

Status	Error	Program
	58.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (neg.f64 re) re))))
	49.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re))))
✓	40.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.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))))
	55.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (cbrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) (cbrt.f64 im)))))
▶	44.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (neg.f64 im) re))))
	47.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 im im) re) -1/2))))
	47.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re 2))))

Compiler

Compiled 2528 to 1070 computations (57.7% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(sqrt.f64 (*.f64 2 (+.f64 (neg.f64 im) re)))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

9.5b

Rules

4×	`pow1_binary64`
2×	`sqrt-div_binary64`
2×	`associate-*r/_binary64`
2×	`sqrt-pow1_binary64`
1×	`*-un-lft-identity_binary64`

Counts

1 → 13

Calls

1 calls:

5.0ms

(sqrt.f64 (*.f64 2 (+.f64 (neg.f64 im) re)))

Compiler

Compiled 200 to 119 computations (40.5% saved)

series18.0ms (0.4%)

Error

9.5b

Counts

1 → 7

Calls

1 calls:

16.0ms

(sqrt.f64 (*.f64 2 (+.f64 (neg.f64 im) re)))

Compiler

Compiled 259 to 211 computations (18.5% saved)

simplify115.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

774×	`unsub-neg_binary64`
480×	`sub-neg_binary64`
469×	`div-sub_binary64`
421×	`distribute-rgt-in_binary64`
370×	`distribute-rgt-neg-in_binary64`

Counts

20 → 14

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	47	254
1	118	224
2	268	224
3	647	224
4	1454	219
5	2511	219
6	3659	219
7	4340	219
8	4952	219
9	4949	219

prune13.0ms (0.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	13	1	14
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	13	9	22

Error

9.5b

Counts

22 → 9

Alt Table

Status	Error	Program
	58.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (neg.f64 re) re))))
	49.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re))))
	47.5b	(.f64 1/2 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 (neg.f64 im)) (*.f64 re (/.f64 1/2 (sqrt.f64 (neg.f64 im)))))))
✓	40.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.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))))
	55.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (cbrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) (cbrt.f64 im)))))
✓	44.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (neg.f64 im) re))))
▶	47.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 im im) re) -1/2))))
	47.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re 2))))

Compiler

Compiled 386 to 278 computations (28% saved)

localize5.0ms (0.1%)

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

9.5b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 9.5b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune6.0ms (0.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	6	6
Picked	1	1
Done	2	2
Total	9	9

Error

9.5b

Counts

9 → 9

Alt Table

Status	Error	Program
	58.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (neg.f64 re) re))))
	49.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re))))
	47.5b	(.f64 1/2 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 (neg.f64 im)) (*.f64 re (/.f64 1/2 (sqrt.f64 (neg.f64 im)))))))
	40.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.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))))
	55.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (cbrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) (cbrt.f64 im)))))
	44.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (neg.f64 im) re))))
	47.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 im im) re) -1/2))))
	47.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re 2))))

Compiler

Compiled 137 to 100 computations (27% saved)

regimes1.2s (28.1%)

Accuracy

Total 18.9b remaining (68.9%)

Threshold costs 0b (0%)

Compiler

Compiled 14579 to 8782 computations (39.8% saved)

bsearch155.0ms (3.7%)

Steps

Iters	Range		Point
9	1.1107198801759568e+27	5.902805000671261e+32	1.649882945586574e+32
9	9.2898760545009e-68	7.869996475844399e-63	9.645579323198895e-68
9	3.4654197333607543e-109	9.330131861504284e-104	6.386439438427647e-106
10	1.0710232480950635e-301	9.570600952865459e-287	1.1023411135196444e-294
7	-6.568790375525752e-81	-1.284272536042574e-82	-4.0810855285811026e-82

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
8×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	50	150
1	73	148
2	79	148
3	82	148
4	83	148
5	83	148

end3.0ms (0.1%)

Compiler: Compiled 100 to 62 computations (38% saved)

sample1.3s (30.6%)

Algorithm

1×

intervals

Results

377.0ms	6049×	body	128	valid
193.0ms	519×	body	4096	valid
192.0ms	655×	body	2048	valid
100.0ms	428×	body	1024	valid
42.0ms	240×	body	512	valid
13.0ms	109×	body	256	valid

Compiler

Compiled 257 to 177 computations (31.1% saved)

Details

analyze478.0ms (11.4%)

sample44.0ms (1%)

simplify9.0ms (0.2%)

prune2.0ms (0.1%)

localize12.0ms (0.3%)

rewrite62.0ms (1.5%)

series102.0ms (2.4%)

simplify110.0ms (2.6%)

prune35.0ms (0.8%)

localize14.0ms (0.3%)

rewrite93.0ms (2.2%)

series195.0ms (4.6%)

simplify173.0ms (4.1%)

prune62.0ms (1.5%)

localize6.0ms (0.1%)

rewrite11.0ms (0.3%)

series18.0ms (0.4%)

simplify115.0ms (2.7%)

prune13.0ms (0.3%)

localize5.0ms (0.1%)

rewrite2.0ms (0%)

series0.0ms (0%)

simplify8.0ms (0.2%)

prune6.0ms (0.1%)

regimes1.2s (28.1%)

bsearch155.0ms (3.7%)

simplify7.0ms (0.2%)

end3.0ms (0.1%)

sample1.3s (30.6%)

Profiling