Details

analyze508.0ms (12.9%)

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)

sample62.0ms (1.6%)

Algorithm

1×

intervals

Results

12.0ms	191×	body	128	valid
6.0ms	16×	body	4096	valid
6.0ms	19×	body	2048	valid
4.0ms	15×	body	1024	valid
1.0ms	8×	body	512	valid
1.0ms	7×	body	256	valid

Compiler

Compiled 37 to 27 computations (27% saved)

simplify12.0ms (0.3%)

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

prune4.0ms (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

14.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 51 to 37 computations (27.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
✓	1.3b	(+.f64 re (hypot.f64 re im))

series74.0ms (1.9%)

Counts

2 → 32

Calls

2 calls:

58.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
17.0ms	(+.f64 re (hypot.f64 re im))

rewrite8.0ms (0.2%)

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:

4.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
3.0ms	(+.f64 re (hypot.f64 re im))

simplify79.0ms (2%)

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 → 79

Iterations

Useful iterations: 2 (0.0ms)

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

prune83.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	72	7	79
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	72	8	80

Error

7.3b

Counts

80 → 8

Alt Table

Status	Error	Program
	48.8b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	45.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	57.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 (/.f64 (.f64 im im) re) -1/2 (.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16))))))
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	14.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
▶	14.3b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))
	14.6b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im))))) (sqrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))))
	14.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))))

Compiler

Compiled 1940 to 1332 computations (31.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 re (hypot.f64 re im)))
✓	0.3b	(*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
	1.3b	(+.f64 re (hypot.f64 re im))

series95.0ms (2.4%)

Counts

2 → 16

Calls

2 calls:

56.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
39.0ms	(sqrt.f64 (+.f64 re (hypot.f64 re im)))

rewrite14.0ms (0.4%)

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:

8.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
3.0ms	(sqrt.f64 (+.f64 re (hypot.f64 re im)))

simplify87.0ms (2.2%)

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 → 84

Iterations

Useful iterations: 2 (0.0ms)

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

prune121.0ms (3.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	133	7	140

Error

7.3b

Counts

140 → 7

Alt Table

Status	Error	Program
	48.8b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
▶	14.3b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im))))))
✓	14.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	57.5b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 (/.f64 (.f64 im im) re) -1/2 (.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16))))))
	45.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	14.3b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 3204 to 2113 computations (34.1% saved)

localize11.0ms (0.3%)

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)) (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))
✓	0.3b	(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
	1.3b	(+.f64 re (hypot.f64 re im))

series111.0ms (2.8%)

Counts

2 → 16

Calls

2 calls:

57.0ms	(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
53.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))

rewrite34.0ms (0.9%)

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:

18.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))
9.0ms	(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im))))

simplify111.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

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

Counts

93 → 117

Iterations

Useful iterations: 2 (0.0ms)

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

prune185.0ms (4.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	196	3	199
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	198	8	206

Error

7.3b

Counts

206 → 8

Alt Table

Status	Error	Program
✓	14.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	57.5b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 (/.f64 (.f64 im im) re) -1/2 (.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16))))))
✓	14.3b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))
	48.9b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im))))
✓	14.3b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im))))))
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	54.2b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (.f64 (/.f64 (*.f64 im im) re) -1/2)))))
▶	45.8b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (neg.f64 im)))))

Compiler

Compiled 5624 to 4008 computations (28.7% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (neg.f64 im)))
✓	0.2b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (neg.f64 im))))

series22.0ms (0.6%)

Counts

2 → 0

Calls

2 calls:

12.0ms	(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (neg.f64 im)))
9.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (neg.f64 im))))

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`sqrt-prod_binary64`
40×	`add-sqr-sqrt_binary64`
18×	`associate-l_binary64`
16×	`rem-sqrt-square_binary64`
14×	`associate-r_binary64`

Counts

2 → 79

Calls

2 calls:

13.0ms	(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (neg.f64 im)))
10.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (neg.f64 im))))

simplify85.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

945×	`neg-mul-1_binary64`
839×	`fma-def_binary64`
573×	`distribute-rgt-neg-out_binary64`
571×	`distribute-lft-neg-out_binary64`
358×	`neg-sub0_binary64`

Counts

79 → 87

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	86	1182
1	172	1105
2	480	1105
3	859	1105
4	1745	1105
5	4115	1105
6	5370	1105

prune58.0ms (1.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	4	4
Picked	1	0	1
Done	0	3	3
Total	86	9	95

Error

7.3b

Counts

95 → 9

Alt Table

Status	Error	Program
✓	14.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	57.5b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 (/.f64 (.f64 im im) re) -1/2 (.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16))))))
✓	14.3b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))
	48.9b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im))))
✓	14.3b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im))))))
	50.0b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (cbrt.f64 (.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (neg.f64 im))) (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (neg.f64 im)))) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (neg.f64 im)))))))
	47.1b	(*.f64 1/2 (exp.f64 (+.f64 (log.f64 (sqrt.f64 (sqrt.f64 2))) (+.f64 (log.f64 (sqrt.f64 (sqrt.f64 2))) (log.f64 (sqrt.f64 (neg.f64 im)))))))
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	54.2b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (.f64 (/.f64 (*.f64 im im) re) -1/2)))))

Compiler

Compiled 1736 to 1362 computations (21.5% saved)

regimes633.0ms (16.1%)

Accuracy

Total 3.0b remaining (30%)

Threshold costs 0b (0%)

Counts

57 → 3

Compiler

Compiled 6908 to 5657 computations (18.1% saved)

bsearch2.0ms (0%)

Compiler: Compiled 12 to 7 computations (41.7% 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	98
1	45	98
2	45	98

end1.0ms (0%)

Compiler: Compiled 66 to 38 computations (42.4% saved)

sample1.5s (37.6%)

Algorithm

1×

intervals

Results

464.0ms	6065×	body	128	valid
212.0ms	619×	body	2048	valid
200.0ms	519×	body	4096	valid
109.0ms	431×	body	1024	valid
49.0ms	244×	body	512	valid
19.0ms	122×	body	256	valid

Compiler

Compiled 261 to 198 computations (24.1% saved)

Details

analyze508.0ms (12.9%)

sample62.0ms (1.6%)

simplify12.0ms (0.3%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

series74.0ms (1.9%)

rewrite8.0ms (0.2%)

simplify79.0ms (2%)

prune83.0ms (2.1%)

localize8.0ms (0.2%)

series95.0ms (2.4%)

rewrite14.0ms (0.4%)

simplify87.0ms (2.2%)

prune121.0ms (3.1%)

localize11.0ms (0.3%)

series111.0ms (2.8%)

rewrite34.0ms (0.9%)

simplify111.0ms (2.8%)

prune185.0ms (4.7%)

localize7.0ms (0.2%)

series22.0ms (0.6%)

rewrite29.0ms (0.7%)

simplify85.0ms (2.2%)

prune58.0ms (1.5%)

regimes633.0ms (16.1%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.5s (37.6%)

Profiling