Details

analyze847.0ms (12.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
25%	25%	50%	2
25%	25%	50%	3
31.2%	18.7%	50%	4
31.2%	18.7%	50%	5
34.3%	15.6%	50%	6
34.3%	15.6%	50%	7
35.9%	14%	50%	8
35.9%	14%	50%	9
36.7%	13.3%	50%	10
36.7%	13.3%	50%	11
37.1%	12.9%	50%	12
37.1%	12.9%	50%	13
37.3%	12.7%	50%	14

Compiler

Compiled 20 to 14 computations (30% saved)

sample3.5s (49.9%)

Results

1.5s	6233×	body	128	valid
743.0ms	585×	body	4096	valid
617.0ms	635×	body	2048	valid
352.0ms	462×	body	1024	valid
125.0ms	208×	body	512	valid
59.0ms	133×	body	256	valid

Compiler

Compiled 57 to 40 computations (29.8% saved)

simplify55.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

203×	`fma-def_binary64`
142×	`fma-neg_binary64`
51×	`distribute-rgt-in_binary64`
42×	`cancel-sign-sub-inv_binary64`
28×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	50	15
4	69	15
5	98	15
6	151	15
7	211	15
8	263	15
9	305	15
10	343	15
11	379	15
12	396	15
13	415	15
14	428	15
15	465	15
16	477	15
17	486	15
18	449	15

prune13.0ms (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

16.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	16.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	40.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Compiler

Compiled 85 to 61 computations (28.2% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 re im)
✓	0.6b	(-.f64 (hypot.f64 re im) re)

series44.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

24.0ms	(hypot.f64 re im)
20.0ms	(-.f64 (hypot.f64 re im) re)

rewrite142.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

578×	`log1p-expm1-u_binary64`
578×	`expm1-log1p-u_binary64`
410×	`prod-diff_binary64`
329×	`fma-udef_binary64`
205×	`fma-def_binary64`

Counts

2 → 103

Calls

2 calls:

138.0ms	(hypot.f64 re im)
138.0ms	(-.f64 (hypot.f64 re im) re)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	111	11
2	1427	11
3	4856	11
4	4826	11
5	4979	11
0	0	0
1	0	0

simplify104.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

313×	`distribute-rgt-neg-in_binary64`
308×	`distribute-lft-neg-in_binary64`
288×	`sub-neg_binary64`
280×	`distribute-neg-frac_binary64`
256×	`associate-/l/_binary64`

Counts

151 → 160

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	80	973
1	260	947
2	769	923
3	2933	923
4	4807	923
5	4946	923

prune173.0ms (2.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	158	4	162

Error

9.6b

Counts

162 → 4

Alt Table

Status	Error	Program
✓	16.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	53.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
	40.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
▶	33.0b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))

Compiler

Compiled 3185 to 1896 computations (40.5% saved)

localize7.0ms (0.1%)

prune9.0ms (0.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	1	1
Total	4	4

Error

9.6b

Counts

4 → 4

Alt Table

Status	Error	Program
✓	16.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	53.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
▶	40.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
✓	33.0b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))

Compiler

Compiled 82 to 64 computations (22% saved)

localize17.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 re re) (.f64 im im))
✓	0.6b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
✓	28.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series56.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

24.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
21.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
11.0ms	(+.f64 (.f64 re re) (.f64 im im))

rewrite100.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

918×	`log1p-expm1-u_binary64`
918×	`expm1-log1p-u_binary64`
104×	`egg-rr`
89×	`add-sqr-sqrt_binary64`
85×	`add-log-exp_binary64`

Counts

3 → 104

Calls

3 calls:

96.0ms	(+.f64 (.f64 re re) (.f64 im im))
96.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
96.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	180	18
2	2274	18
3	5496	18
0	0	0
1	0	0

simplify117.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

313×	`distribute-rgt-neg-in_binary64`
308×	`distribute-lft-neg-in_binary64`
288×	`sub-neg_binary64`
280×	`distribute-neg-frac_binary64`
256×	`associate-/l/_binary64`

Counts

176 → 166

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	81	1177
1	262	1115
2	773	1091
3	2937	1091
4	4811	1091
5	4950	1091

prune189.0ms (2.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	166	4	170

Error

9.6b

Counts

170 → 4

Alt Table

Status	Error	Program
✓	16.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
▶	53.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
✓	40.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
✓	33.0b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))

Compiler

Compiled 3222 to 2111 computations (34.5% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 1/2 (/.f64 (pow.f64 im 2) re)))
✓	0.4b	(*.f64 1/2 (/.f64 (pow.f64 im 2) re))
✓	6.7b	(/.f64 (pow.f64 im 2) re)
✓	17.2b	(sqrt.f64 (.f64 2 (.f64 1/2 (/.f64 (pow.f64 im 2) re))))

series95.0ms (1.4%)

Counts

4 → 36

Calls

4 calls:

28.0ms	(sqrt.f64 (.f64 2 (.f64 1/2 (/.f64 (pow.f64 im 2) re))))
23.0ms	(*.f64 1/2 (/.f64 (pow.f64 im 2) re))
23.0ms	(/.f64 (pow.f64 im 2) re)
21.0ms	(.f64 2 (.f64 1/2 (/.f64 (pow.f64 im 2) re)))

rewrite103.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

810×	`log1p-expm1-u_binary64`
810×	`expm1-log1p-u_binary64`
130×	`egg-rr`
89×	`add-sqr-sqrt_binary64`
85×	`add-log-exp_binary64`

Counts

4 → 130

Calls

4 calls:

99.0ms	(.f64 2 (.f64 1/2 (/.f64 (pow.f64 im 2) re)))
99.0ms	(*.f64 1/2 (/.f64 (pow.f64 im 2) re))
99.0ms	(/.f64 (pow.f64 im 2) re)
99.0ms	(sqrt.f64 (.f64 2 (.f64 1/2 (/.f64 (pow.f64 im 2) re))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	33
1	194	30
2	2135	30
3	4984	30
0	0	0
1	0	0

simplify105.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

688×	`fma-def_binary64`
564×	`fma-neg_binary64`
489×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
423×	`associate-*r/_binary64`

Counts

166 → 117

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	284
1	23	284
2	40	284
3	73	284
4	154	284
5	407	284
6	1269	284
7	2910	284
8	3967	284
9	4874	284
10	4864	284

prune710.0ms (10.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	113	4	117
Fresh	0	0	0
Picked	1	0	1
Done	1	2	3
Total	115	6	121

Error

0.1b

Counts

121 → 6

Alt Table

Status	Error	Program
	43.4b	(*.f64 1/2 (expm1.f64 (log1p.f64 (/.f64 im (sqrt.f64 re)))))
✓	16.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	50.6b	(*.f64 1/2 (sqrt.f64 (/.f64 im (/.f64 re im))))
	43.5b	(.f64 1/2 (.f64 (sqrt.f64 2) (*.f64 (/.f64 im (sqrt.f64 re)) (sqrt.f64 1/2))))
✓	40.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
	43.3b	(.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 re)) im))

Compiler

Compiled 1745 to 1072 computations (38.6% saved)

regimes406.0ms (5.8%)

Accuracy

Total 6.3b remaining (97.8%)

Threshold costs 0b (0%)

Counts

21 → 2

Compiler

Compiled 1900 to 1473 computations (22.5% saved)

bsearch1.0ms (0%)

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
4×	`+-commutative_binary64`
3×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	49
1	32	49
2	37	49
3	39	49
4	40	49
5	40	49

end167.0ms (2.4%)

Compiler: Compiled 141 to 104 computations (26.2% saved)

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	50	15
4	69	15
5	98	15
6	151	15
7	211	15
8	263	15
9	305	15
10	343	15
11	379	15
12	396	15
13	415	15
14	428	15
15	465	15
16	477	15
17	486	15
18	449	15

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	50	15
4	69	15
5	98	15
6	151	15
7	211	15
8	263	15
9	305	15
10	343	15
11	379	15
12	396	15
13	415	15
14	428	15
15	465	15
16	477	15
17	486	15
18	449	15

Details

analyze847.0ms (12.2%)

sample3.5s (49.9%)

simplify55.0ms (0.8%)

prune13.0ms (0.2%)

localize12.0ms (0.2%)

series44.0ms (0.6%)

rewrite142.0ms (2%)

simplify104.0ms (1.5%)

prune173.0ms (2.5%)

localize7.0ms (0.1%)

prune9.0ms (0.1%)

localize17.0ms (0.3%)

series56.0ms (0.8%)

rewrite100.0ms (1.4%)

simplify117.0ms (1.7%)

prune189.0ms (2.7%)

localize15.0ms (0.2%)

series95.0ms (1.4%)

rewrite103.0ms (1.5%)

simplify105.0ms (1.5%)

prune710.0ms (10.2%)

regimes406.0ms (5.8%)

bsearch1.0ms (0%)

simplify6.0ms (0.1%)

end167.0ms (2.4%)

Profiling

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	50	15
4	69	15
5	98	15
6	151	15
7	211	15
8	263	15
9	305	15
10	343	15
11	379	15
12	396	15
13	415	15
14	428	15
15	465	15
16	477	15
17	486	15
18	449	15