Details

analyze946.0ms (19.7%)

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

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample78.0ms (1.6%)

Algorithm

1×

intervals

Results

28.0ms	202×	body	128	valid
15.0ms	15×	body	4096	valid
10.0ms	16×	body	2048	valid
7.0ms	15×	body	1024	valid
2.0ms	5×	body	512	valid
1.0ms	3×	body	256	valid

Compiler

Compiled 37 to 27 computations (27% saved)

simplify22.0ms (0.5%)

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

prune10.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

12.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	38.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
▶	12.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 85 to 61 computations (28.2% saved)

localize13.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
✓	0.3b	(+.f64 re (hypot.f64 re im))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`fma-def_binary64`

Counts

2 → 32

Calls

2 calls:

8.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
5.0ms	(+.f64 re (hypot.f64 re im))

series120.0ms (2.5%)

Counts

2 → 32

Calls

2 calls:

88.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
31.0ms	(+.f64 re (hypot.f64 re im))

simplify132.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

862×	`fma-neg_binary64`
517×	`fma-def_binary64`
437×	`associate-r_binary64`
361×	`associate-l_binary64`
244×	`cancel-sign-sub-inv_binary64`

Counts

64 → 99

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	161	1270
1	435	1196
2	1255	1148
3	4683	1148
4	5413	1148

prune120.0ms (2.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	93	6	99
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	95	6	101

Error

6.3b

Counts

101 → 6

Alt Table

Status	Error	Program
	12.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (cbrt.f64 (+.f64 re (hypot.f64 re im))) (cbrt.f64 (+.f64 re (hypot.f64 re im)))) (cbrt.f64 (+.f64 re (hypot.f64 re im)))))))
	27.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 re) (sqrt.f64 re) (hypot.f64 re im)))))
	48.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	45.4b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
▶	12.1b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 1862 to 1265 computations (32.1% saved)

localize14.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 re (hypot.f64 re im)))
	0.3b	(+.f64 re (hypot.f64 re im))
✓	0.4b	(*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im))))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
15×	`sqrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
7×	`associate-r_binary64`
7×	`add-cube-cbrt_binary64`

Counts

2 → 55

Calls

2 calls:

15.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
5.0ms	(sqrt.f64 (+.f64 re (hypot.f64 re im)))

series140.0ms (2.9%)

Counts

2 → 16

Calls

2 calls:

87.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
53.0ms	(sqrt.f64 (+.f64 re (hypot.f64 re im)))

simplify125.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

608×	`fma-neg_binary64`
601×	`fma-def_binary64`
441×	`times-frac_binary64`
335×	`associate-/l*_binary64`
318×	`cancel-sign-sub-inv_binary64`

Counts

71 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	181	1642
1	461	1585
2	1487	1518
3	4539	1518
4	4997	1518

prune109.0ms (2.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	164	3	167
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	166	7	173

Error

6.2b

Counts

173 → 7

Alt Table

Status	Error	Program
	55.8b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (/.f64 (.f64 im im) re) -1/2))))
	27.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 re) (sqrt.f64 re) (hypot.f64 re im)))))
	48.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	12.8b	(.f64 1/2 (.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2))) (.f64 (sqrt.f64 (cbrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im))))))
▶	12.1b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im))))))
	45.4b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))

Compiler

Compiled 3186 to 2101 computations (34.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 re (hypot.f64 re im)))
✓	0.2b	(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
✓	0.2b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))
	0.3b	(+.f64 re (hypot.f64 re im))

rewrite27.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
36×	`sqrt-prod_binary64`
18×	`associate-l_binary64`
16×	`rem-sqrt-square_binary64`
14×	`pow1_binary64`

Counts

2 → 77

Calls

2 calls:

11.0ms	(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
11.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))

series86.0ms (1.8%)

Counts

2 → 16

Calls

2 calls:

44.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))
41.0ms	(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im))))

simplify105.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

591×	`fma-def_binary64`
440×	`fma-neg_binary64`
341×	`cancel-sign-sub-inv_binary64`
263×	`associate-+l+_binary64`
215×	`associate-r_binary64`

Counts

93 → 153

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	218	2355
1	541	2218
2	1749	2162
3	4834	2162
4	5136	2162

prune169.0ms (3.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	316	6	322
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	320	9	329

Error

6.2b

Counts

329 → 9

Alt Table

Status	Error	Program
✓	12.1b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im))))))
	45.5b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im))))
▶	12.0b	(.f64 1/2 (pow.f64 (.f64 2 (+.f64 re (hypot.f64 re im))) (/.f64 1 2)))
	48.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	45.4b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (*.f64 (sqrt.f64 2) im))))
	55.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	48.5b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (neg.f64 im)))))
	55.8b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (.f64 -1/2 (/.f64 (pow.f64 im 2) re))))))
	12.8b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im))))) (cbrt.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))) (cbrt.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im))))))))

Compiler

Compiled 5681 to 4049 computations (28.7% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))) (/.f64 1 2))
	0.3b	(+.f64 re (hypot.f64 re im))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`pow-unpow_binary64`
9×	`times-frac_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`

Counts

1 → 29

Calls

1 calls:

7.0ms

(pow.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))) (/.f64 1 2))

series34.0ms (0.7%)

Counts

1 → 24

Calls

1 calls:

33.0ms

(pow.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))) (/.f64 1 2))

simplify63.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

860×	`times-frac_binary64`
453×	`associate-/l*_binary64`
394×	`fma-def_binary64`
367×	`associate-/r*_binary64`
155×	`cancel-sign-sub-inv_binary64`

Counts

53 → 100

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	196	1736
1	505	1655
2	1496	1557
3	5141	1557

prune110.0ms (2.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	356	4	360
Fresh	5	2	7
Picked	0	1	1
Done	0	1	1
Total	361	8	369

Error

1.8b

Counts

369 → 8

Alt Table

Status	Error	Program
	55.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	55.9b	(.f64 1/2 (-.f64 (exp.f64 (.f64 1/2 (+.f64 (log.f64 (/.f64 -1 re)) (log.f64 (pow.f64 im 2))))) (.f64 1/8 (/.f64 (.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 (/.f64 -1 re)) (log.f64 (pow.f64 im 2))))) (pow.f64 im 2)) (pow.f64 re 2)))))
✓	12.0b	(.f64 1/2 (pow.f64 (.f64 2 (+.f64 re (hypot.f64 re im))) (/.f64 1 2)))
	49.6b	(*.f64 1/2 (sqrt.f64 (exp.f64 (-.f64 (log.f64 2) (log.f64 (/.f64 -1 im))))))
	55.7b	(.f64 1/2 (fma.f64 (.f64 (/.f64 (.f64 im im) (.f64 re re)) (.f64 (pow.f64 (/.f64 -1 re) 1/2) (exp.f64 (log.f64 im)))) -1/8 (.f64 (pow.f64 (/.f64 -1 re) 1/2) (exp.f64 (log.f64 im)))))
	55.1b	(.f64 1/2 (.f64 (pow.f64 (/.f64 -1 re) 1/2) (exp.f64 (log.f64 im))))
	55.8b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (.f64 -1/2 (/.f64 (pow.f64 im 2) re))))))
✓	12.1b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im))))))

Compiler

Compiled 3682 to 2718 computations (26.2% saved)

regimes942.0ms (19.6%)

Accuracy

Total 7.6b remaining (69.6%)

Threshold costs 0b (0%)

Compiler

Compiled 9781 to 7879 computations (19.4% saved)

bsearch3.0ms (0.1%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	95
1	45	95
2	45	95

end1.0ms (0%)

Compiler: Compiled 63 to 43 computations (31.7% saved)

sample1.4s (28.4%)

Algorithm

1×

intervals

Results

387.0ms	6068×	body	128	valid
220.0ms	651×	body	2048	valid
194.0ms	529×	body	4096	valid
100.0ms	412×	body	1024	valid
37.0ms	221×	body	512	valid
14.0ms	119×	body	256	valid

Compiler

Compiled 247 to 193 computations (21.9% saved)

Details

analyze946.0ms (19.7%)

sample78.0ms (1.6%)

simplify22.0ms (0.5%)

prune10.0ms (0.2%)

localize13.0ms (0.3%)

rewrite16.0ms (0.3%)

series120.0ms (2.5%)

simplify132.0ms (2.7%)

prune120.0ms (2.5%)

localize14.0ms (0.3%)

rewrite28.0ms (0.6%)

series140.0ms (2.9%)

simplify125.0ms (2.6%)

prune109.0ms (2.3%)

localize9.0ms (0.2%)

rewrite27.0ms (0.6%)

series86.0ms (1.8%)

simplify105.0ms (2.2%)

prune169.0ms (3.5%)

localize9.0ms (0.2%)

rewrite8.0ms (0.2%)

series34.0ms (0.7%)

simplify63.0ms (1.3%)

prune110.0ms (2.3%)

regimes942.0ms (19.6%)

bsearch3.0ms (0.1%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.4s (28.4%)

Profiling