Details

analyze943.0ms (15%)

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)

sample78.0ms (1.2%)

Algorithm

1×

intervals

Results

23.0ms	189×	body	128	valid
17.0ms	25×	body	2048	valid
10.0ms	14×	body	4096	valid
6.0ms	13×	body	1024	valid
3.0ms	8×	body	512	valid
2.0ms	7×	body	256	valid

Compiler

Compiled 37 to 27 computations (27% saved)

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
4×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`distribute-lft-in_binary64`
2×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	25	15
2	29	15
3	31	15
4	31	15

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

15.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 51 to 37 computations (27.5% saved)

localize16.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.0b	(+.f64 re (hypot.f64 re im))

series27.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

27.0ms

(+.f64 re (hypot.f64 re im))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64`
3×	`add-log-exp_binary64`
3×	`fma-def_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`

Counts

1 → 17

Calls

1 calls:

5.0ms

(+.f64 re (hypot.f64 re im))

simplify88.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

609×	`fma-neg_binary64`
513×	`cancel-sign-sub-inv_binary64`
257×	`associate-/r/_binary64`
248×	`distribute-rgt-neg-in_binary64`
241×	`distribute-lft-neg-in_binary64`

Counts

41 → 48

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	81	623
1	237	598
2	604	590
3	2282	590
4	4708	590
5	5107	590

prune68.0ms (1.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	43	5	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	6	49

Error

9.4b

Counts

49 → 6

Alt Table

Status	Error	Program
▶	15.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))))
	17.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))
	49.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	45.3b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	15.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 1030 to 687 computations (33.3% saved)

localize16.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
	1.0b	(+.f64 re (hypot.f64 re im))

series25.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

25.0ms

(*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im))))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`sqrt-prod_binary64`
25×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
16×	`pow1_binary64`
12×	`sqrt-div_binary64`

Counts

1 → 66

Calls

1 calls:

18.0ms

(*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im))))

simplify150.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

513×	`cancel-sign-sub-inv_binary64`
424×	`fma-neg_binary64`
309×	`associate-l_binary64`
299×	`unswap-sqr_binary64`
271×	`associate-r_binary64`

Counts

90 → 103

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	127	1504
1	295	1366
2	808	1322
3	2969	1275
4	4871	1265
5	4993	1265
6	4931	1265

prune259.0ms (4.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	199	6	205

Error

9.4b

Counts

205 → 6

Alt Table

Status	Error	Program
✓	15.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))))
▶	17.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))
	49.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	45.3b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	15.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 5111 to 2421 computations (52.6% saved)

localize20.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
✓	0.6b	(cbrt.f64 re)
✓	16.6b	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))

series195.0ms (3.1%)

Counts

3 → 48

Calls

3 calls:

74.0ms	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
71.0ms	(cbrt.f64 re)
50.0ms	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
10×	`pow1_binary64`

Counts

3 → 65

Calls

3 calls:

10.0ms	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
1.0ms	(cbrt.f64 re)
1.0ms	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))

simplify142.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

749×	`times-frac_binary64`
486×	`fma-neg_binary64`
403×	`associate-/r*_binary64`
393×	`distribute-neg-frac_binary64`
314×	`fma-def_binary64`

Counts

113 → 127

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	118	1156
1	267	1039
2	861	983
3	3718	968
4	4753	956
5	4987	956
6	4914	956

prune234.0ms (3.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	165	6	171

Error

9.4b

Counts

171 → 6

Alt Table

Status	Error	Program
▶	17.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))) (cbrt.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))))
	45.3b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	15.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))))
	49.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	15.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 3429 to 1652 computations (51.8% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))) (cbrt.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))))
	0.5b	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
	0.6b	(cbrt.f64 re)
	16.6b	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))

series149.0ms (2.4%)

Counts

1 → 24

Calls

1 calls:

149.0ms

(*.f64 (cbrt.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))) (cbrt.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
16×	`cbrt-prod_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`
8×	`pow1_binary64`

Counts

1 → 42

Calls

1 calls:

10.0ms

(*.f64 (cbrt.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))) (cbrt.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))))

simplify124.0ms (2%)

Algorithm

1×	egg-herbie

Rules

340×	`times-frac_binary64`
298×	`associate-/l*_binary64`
234×	`associate-/r*_binary64`
233×	`cancel-sign-sub-inv_binary64`
226×	`associate-*l/_binary64`

Counts

66 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	217	2996
1	582	1940
2	1972	1780
3	4984	1780

prune633.0ms (10.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	600	1	601
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	601	6	607

Error

9.4b

Counts

607 → 6

Alt Table

Status	Error	Program
	20.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (exp.f64 (log.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))) (cbrt.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))))
✓	15.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))))
	49.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	45.3b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	15.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 28605 to 7385 computations (74.2% saved)

regimes456.0ms (7.3%)

Accuracy

Total 2.6b remaining (25.8%)

Threshold costs 0b (0%)

Counts

22 → 2

Compiler

Compiled 3622 to 2194 computations (39.4% saved)

bsearch2.0ms (0%)

Compiler: Compiled 15 to 10 computations (33.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	58
1	37	58
2	37	58

end2.0ms (0%)

Compiler: Compiled 40 to 30 computations (25% saved)

sample2.5s (40.1%)

Algorithm

1×

intervals

Results

763.0ms	6037×	body	128	valid
425.0ms	675×	body	2048	valid
375.0ms	490×	body	4096	valid
221.0ms	436×	body	1024	valid
90.0ms	239×	body	512	valid
32.0ms	123×	body	256	valid

Compiler

Compiled 170 to 108 computations (36.5% saved)

Details

analyze943.0ms (15%)

sample78.0ms (1.2%)

simplify13.0ms (0.2%)

prune6.0ms (0.1%)

localize16.0ms (0.3%)

series27.0ms (0.4%)

rewrite6.0ms (0.1%)

simplify88.0ms (1.4%)

prune68.0ms (1.1%)

localize16.0ms (0.3%)

series25.0ms (0.4%)

rewrite32.0ms (0.5%)

simplify150.0ms (2.4%)

prune259.0ms (4.1%)

localize20.0ms (0.3%)

series195.0ms (3.1%)

rewrite18.0ms (0.3%)

simplify142.0ms (2.3%)

prune234.0ms (3.7%)

localize27.0ms (0.4%)

series149.0ms (2.4%)

rewrite26.0ms (0.4%)

simplify124.0ms (2%)

prune633.0ms (10.1%)

regimes456.0ms (7.3%)

bsearch2.0ms (0%)

simplify5.0ms (0.1%)

end2.0ms (0%)

sample2.5s (40.1%)

Profiling