Details

analyze458.0ms (12%)

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)

sample41.0ms (1.1%)

Algorithm

1×

intervals

Results

12.0ms	202×	body	128	valid
5.0ms	16×	body	1024	valid
5.0ms	16×	body	2048	valid
4.0ms	13×	body	4096	valid
4.0ms	256×	pre	128	true
2.0ms	9×	body	512	valid

Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify33.0ms (0.9%)

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

prune5.0ms (0.1%)

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

11.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	11.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	38.0b	(.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)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
6×	`pow1_binary64`

Counts

3 → 55

Calls

3 calls:

6.0ms	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
3.0ms	(-.f64 (hypot.f64 re im) re)
0.0ms	(hypot.f64 re im)

series68.0ms (1.8%)

Counts

3 → 56

Calls

3 calls:

40.0ms	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
16.0ms	(-.f64 (hypot.f64 re im) re)
12.0ms	(hypot.f64 re im)

simplify101.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

994×	`fma-neg_binary64`
747×	`times-frac_binary64`
413×	`cancel-sign-sub-inv_binary64`
173×	`fma-def_binary64`
158×	`sub-neg_binary64`

Counts

111 → 183

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	2332
1	611	2069
2	2078	1999
3	4466	1989
4	5015	1989

prune90.0ms (2.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	178	5	183
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	179	6	185

Error

0.1b

Counts

185 → 6

Alt Table

Status	Error	Program
	54.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
✓	11.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	53.8b	(.f64 1/2 (fma.f64 (sqrt.f64 1/2) (.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (.f64 (/.f64 (.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 1/2)) -1/16))))
	49.6b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
▶	11.6b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re))))
	48.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (fma.f64 1 (hypot.f64 re im) (neg.f64 (.f64 (sqrt.f64 re) (sqrt.f64 re)))) (fma.f64 (neg.f64 (sqrt.f64 re)) (sqrt.f64 re) (.f64 (sqrt.f64 re) (sqrt.f64 re)))))))

Compiler

Compiled 3342 to 2186 computations (34.6% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
17×	`sqrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
8×	`associate-r_binary64`
7×	`add-cube-cbrt_binary64`

Counts

2 → 56

Calls

2 calls:

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

series68.0ms (1.8%)

Counts

2 → 16

Calls

2 calls:

42.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))
26.0ms	(sqrt.f64 (-.f64 (hypot.f64 re im) re))

simplify90.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

778×	`fma-def_binary64`
344×	`associate-/l*_binary64`
291×	`times-frac_binary64`
285×	`fma-neg_binary64`
275×	`associate-*l/_binary64`

Counts

72 → 103

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	202	1877
1	534	1832
2	1757	1756
3	4935	1754
4	5005	1754

prune123.0ms (3.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	248	3	251
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	250	7	257

Error

0.1b

Counts

257 → 7

Alt Table

Status	Error	Program
	49.6b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
	54.9b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 1/2 (/.f64 (.f64 im im) re)))))
	54.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
✓	11.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
▶	11.6b	(.f64 1/2 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))))
	48.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (fma.f64 1 (hypot.f64 re im) (neg.f64 (.f64 (sqrt.f64 re) (sqrt.f64 re)))) (fma.f64 (neg.f64 (sqrt.f64 re)) (sqrt.f64 re) (.f64 (sqrt.f64 re) (sqrt.f64 re)))))))
	49.6b	(.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re)))))

Compiler

Compiled 4747 to 3085 computations (35% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite24.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`
13×	`sqrt-prod_binary64`
10×	`cbrt-prod_binary64`

Counts

2 → 64

Calls

2 calls:

12.0ms

(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (hypot.f64 re im) re))))

8.0ms

(*.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))

series97.0ms (2.5%)

Counts

2 → 16

Calls

2 calls:

55.0ms

(*.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))

42.0ms

(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (hypot.f64 re im) re))))

simplify133.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

556×	`times-frac_binary64`
387×	`fma-neg_binary64`
374×	`cancel-sign-sub-inv_binary64`
330×	`associate-r_binary64`
305×	`associate-l_binary64`

Counts

80 → 132

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	231	2516
1	631	2300
2	2453	2189
3	4526	2185
4	4987	2185
5	4926	2185

prune165.0ms (4.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	427	1	428
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	427	8	435

Error

0.1b

Counts

435 → 8

Alt Table

Status	Error	Program
	49.6b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
	54.9b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 1/2 (/.f64 (.f64 im im) re)))))
	54.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
✓	11.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
✓	11.6b	(.f64 1/2 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))))
	49.6b	(.f64 1/2 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (.f64 im (sqrt.f64 1/2)) (.f64 (sqrt.f64 (/.f64 1 re)) (cbrt.f64 (sqrt.f64 2))))))
▶	48.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (fma.f64 1 (hypot.f64 re im) (neg.f64 (.f64 (sqrt.f64 re) (sqrt.f64 re)))) (fma.f64 (neg.f64 (sqrt.f64 re)) (sqrt.f64 re) (.f64 (sqrt.f64 re) (sqrt.f64 re)))))))
	49.6b	(.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re)))))

Compiler

Compiled 6985 to 5159 computations (26.1% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (sqrt.f64 re) (sqrt.f64 re))
✓	0.2b	(*.f64 (sqrt.f64 re) (sqrt.f64 re))
✓	7.8b	(fma.f64 1 (hypot.f64 re im) (neg.f64 (*.f64 (sqrt.f64 re) (sqrt.f64 re))))
✓	27.8b	(fma.f64 (neg.f64 (sqrt.f64 re)) (sqrt.f64 re) (*.f64 (sqrt.f64 re) (sqrt.f64 re)))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
18×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

3 → 72

Calls

3 calls:

5.0ms	(*.f64 (sqrt.f64 re) (sqrt.f64 re))
0.0ms	(fma.f64 (neg.f64 (sqrt.f64 re)) (sqrt.f64 re) (*.f64 (sqrt.f64 re) (sqrt.f64 re)))
0.0ms	(fma.f64 1 (hypot.f64 re im) (neg.f64 (*.f64 (sqrt.f64 re) (sqrt.f64 re))))

series119.0ms (3.1%)

Counts

3 → 35

Calls

3 calls:

97.0ms	(fma.f64 (neg.f64 (sqrt.f64 re)) (sqrt.f64 re) (*.f64 (sqrt.f64 re) (sqrt.f64 re)))
18.0ms	(fma.f64 1 (hypot.f64 re im) (neg.f64 (*.f64 (sqrt.f64 re) (sqrt.f64 re))))
4.0ms	(*.f64 (sqrt.f64 re) (sqrt.f64 re))

simplify108.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

927×	`fma-neg_binary64`
558×	`times-frac_binary64`
307×	`associate-/r*_binary64`
285×	`associate-l_binary64`
284×	`associate-r_binary64`

Counts

107 → 184

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	122	918
1	250	829
2	759	752
3	3744	738
4	4632	734
5	4959	734
6	4908	734

prune101.0ms (2.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	287	1	288
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	287	9	296

Error

0.1b

Counts

296 → 9

Alt Table

Status	Error	Program
	49.6b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
	54.9b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 1/2 (/.f64 (.f64 im im) re)))))
	54.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
✓	11.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	49.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 re im) re))) (fma.f64 (neg.f64 (sqrt.f64 re)) (sqrt.f64 re) (*.f64 (sqrt.f64 re) (sqrt.f64 re)))))))
✓	11.6b	(.f64 1/2 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))))
	49.6b	(.f64 1/2 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (.f64 im (sqrt.f64 1/2)) (.f64 (sqrt.f64 (/.f64 1 re)) (cbrt.f64 (sqrt.f64 2))))))
✓	48.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (fma.f64 1 (hypot.f64 re im) (neg.f64 (.f64 (sqrt.f64 re) (sqrt.f64 re)))) (fma.f64 (neg.f64 (sqrt.f64 re)) (sqrt.f64 re) (.f64 (sqrt.f64 re) (sqrt.f64 re)))))))
	49.6b	(.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re)))))

Compiler

Compiled 5544 to 2130 computations (61.6% saved)

regimes454.0ms (11.9%)

Accuracy

Total 5.9b remaining (97.6%)

Threshold costs 0b (0%)

Compiler

Compiled 6867 to 5001 computations (27.2% saved)

bsearch2.0ms (0%)

Compiler: Compiled 12 to 7 computations (41.7% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-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	31	73
1	43	73
2	48	73
3	50	73
4	51	73
5	50	73

end1.0ms (0%)

Compiler: Compiled 48 to 38 computations (20.8% saved)

sample1.5s (38.3%)

Algorithm

1×

intervals

Results

370.0ms	6079×	body	128	valid
192.0ms	671×	body	2048	valid
182.0ms	509×	body	4096	valid
111.0ms	8000×	pre	128	true
101.0ms	413×	body	1024	valid
40.0ms	199×	body	512	valid
14.0ms	129×	body	256	valid

Compiler

Compiled 246 to 189 computations (23.2% 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

analyze458.0ms (12%)

sample41.0ms (1.1%)

simplify33.0ms (0.9%)

prune5.0ms (0.1%)

localize7.0ms (0.2%)

rewrite12.0ms (0.3%)

series68.0ms (1.8%)

simplify101.0ms (2.6%)

prune90.0ms (2.4%)

localize7.0ms (0.2%)

rewrite15.0ms (0.4%)

series68.0ms (1.8%)

simplify90.0ms (2.3%)

prune123.0ms (3.2%)

localize11.0ms (0.3%)

rewrite24.0ms (0.6%)

series97.0ms (2.5%)

simplify133.0ms (3.5%)

prune165.0ms (4.3%)

localize13.0ms (0.3%)

rewrite11.0ms (0.3%)

series119.0ms (3.1%)

simplify108.0ms (2.8%)

prune101.0ms (2.6%)

regimes454.0ms (11.9%)

bsearch2.0ms (0%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.5s (38.3%)

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