Details

analyze410.0ms (10.7%)

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)

sample87.0ms (2.3%)

Algorithm

1×

intervals

Results

11.0ms	190×	body	128	valid
7.0ms	23×	body	2048	valid
5.0ms	16×	body	4096	valid
4.0ms	256×	pre	128	true
3.0ms	13×	body	1024	valid
2.0ms	10×	body	512	valid
0.0ms	4×	body	256	valid

Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify29.0ms (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

prune3.0ms (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

14.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))

Compiler

Compiled 51 to 37 computations (27.5% saved)

localize6.0ms (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)))
✓	0.6b	(-.f64 (hypot.f64 re im) re)

series73.0ms (1.9%)

Counts

3 → 56

Calls

3 calls:

46.0ms	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
14.0ms	(-.f64 (hypot.f64 re im) re)
12.0ms	(hypot.f64 re im)

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)

simplify83.0ms (2.2%)

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 → 136

Iterations

Useful iterations: 3 (0.0ms)

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

prune87.0ms (2.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	132	4	136
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	132	5	137

Error

0.2b

Counts

137 → 5

Alt Table

Status	Error	Program
▶	32.6b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 im)))
	53.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
	51.8b	(.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))))
✓	14.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	46.4b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))

Compiler

Compiled 3295 to 2162 computations (34.4% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (sqrt.f64 2) (sqrt.f64 im))

series8.0ms (0.2%)

Counts

1 → 0

Calls

1 calls:

8.0ms

(*.f64 (sqrt.f64 2) (sqrt.f64 im))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
10×	`sqrt-prod_binary64`
6×	`associate-r_binary64`
6×	`associate-l_binary64`
5×	`*-un-lft-identity_binary64`

Counts

1 → 33

Calls

1 calls:

5.0ms

(*.f64 (sqrt.f64 2) (sqrt.f64 im))

simplify60.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

564×	`log-div_binary64`
346×	`log-prod_binary64`
337×	`associate-l_binary64`
288×	`unswap-sqr_binary64`
251×	`associate-*l/_binary64`

Counts

33 → 32

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	363
1	76	357
2	176	357
3	227	357
4	307	357
5	493	357
6	978	357
7	2532	357
8	4121	357
9	4984	357

prune22.0ms (0.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	31	1	32
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	32	5	37

Error

0.2b

Counts

37 → 5

Alt Table

Status	Error	Program
	53.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
▶	32.7b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im))))
	51.8b	(.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))))
✓	14.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	46.4b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))

Compiler

Compiled 552 to 438 computations (20.7% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series18.0ms (0.5%)

Counts

2 → 0

Calls

2 calls:

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

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 72

Calls

2 calls:

9.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im)))
7.0ms	(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im))

simplify78.0ms (2%)

Algorithm

1×	egg-herbie

Rules

455×	`log-div_binary64`
454×	`cube-div_binary64`
383×	`associate-l_binary64`
382×	`log-prod_binary64`
370×	`cube-prod_binary64`

Counts

72 → 80

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	68	938
1	137	877
2	370	877
3	558	877
4	656	877
5	901	877
6	2176	877
7	3633	877
8	5039	877

prune46.0ms (1.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	80	5	85

Error

0.2b

Counts

85 → 5

Alt Table

Status	Error	Program
	53.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
✓	32.7b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im))))
	51.8b	(.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))))
✓	14.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
▶	46.4b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))

Compiler

Compiled 1485 to 1255 computations (15.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 re))
✓	0.1b	(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
✓	0.4b	(*.f64 (sqrt.f64 2) im)
✓	0.4b	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im))

series37.0ms (1%)

Counts

4 → 0

Calls

4 calls:

23.0ms	(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
5.0ms	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im))
5.0ms	(sqrt.f64 (/.f64 1 re))
4.0ms	(*.f64 (sqrt.f64 2) im)

rewrite28.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`sqrt-prod_binary64`
32×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64`
22×	`pow1_binary64`

Counts

4 → 114

Calls

4 calls:

11.0ms	(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
5.0ms	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im))
4.0ms	(*.f64 (sqrt.f64 2) im)
2.0ms	(sqrt.f64 (/.f64 1 re))

simplify93.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

468×	`associate-/l*_binary64`
416×	`*-commutative_binary64`
403×	`unswap-sqr_binary64`
271×	`sqr-pow_binary64`
214×	`associate-l_binary64`

Counts

114 → 123

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	121	1600
1	239	1498
2	789	1498
3	1286	1498
4	2620	1498
5	3060	1498
6	4473	1498
7	5012	1498

prune106.0ms (2.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	115	8	123
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	117	11	128

Error

0.1b

Counts

128 → 11

Alt Table

Status	Error	Program
	46.4b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (pow.f64 re -1/2)))
	46.5b	(.f64 1/2 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 re) (cbrt.f64 re))))) (sqrt.f64 (/.f64 1 (cbrt.f64 re)))))
	53.6b	(.f64 1/2 (.f64 (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) 3)) (sqrt.f64 (/.f64 1 re))))
✓	32.7b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im))))
	46.3b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im))) (sqrt.f64 (/.f64 1 re))))
✓	14.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	46.4b	(.f64 1/2 (.f64 (sqrt.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))) (sqrt.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))))
	46.5b	(.f64 1/2 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))))
	46.5b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) im)) (cbrt.f64 (.f64 (sqrt.f64 2) im))) (cbrt.f64 (.f64 (sqrt.f64 2) im)))) (sqrt.f64 (/.f64 1 re))))
	47.3b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (exp.f64 (log.f64 (.f64 (sqrt.f64 2) im)))) (sqrt.f64 (/.f64 1 re))))
	53.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 2763 to 2340 computations (15.3% saved)

regimes1.0s (26.6%)

Accuracy

Total 7.6b remaining (98.6%)

Threshold costs 0b (0%)

Counts

102 → 2

Compiler

Compiled 14234 to 12288 computations (13.7% saved)

bsearch47.0ms (1.2%)

Steps

Iters	Range		Point
10	3.7595623274743217e+24	2.9303186338222314e+37	2.352210546064473e+37

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	52
1	36	52
2	40	52
3	42	52
4	43	52
5	42	52

end1.0ms (0%)

Compiler: Compiled 35 to 29 computations (17.1% saved)

sample1.4s (37.3%)

Algorithm

1×

intervals

Results

358.0ms	6072×	body	128	valid
202.0ms	686×	body	2048	valid
166.0ms	493×	body	4096	valid
117.0ms	8000×	pre	128	true
92.0ms	416×	body	1024	valid
36.0ms	222×	body	512	valid
12.0ms	111×	body	256	valid

Compiler

Compiled 301 to 255 computations (15.3% 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

analyze410.0ms (10.7%)

sample87.0ms (2.3%)

simplify29.0ms (0.8%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series73.0ms (1.9%)

rewrite12.0ms (0.3%)

simplify83.0ms (2.2%)

prune87.0ms (2.3%)

localize4.0ms (0.1%)

series8.0ms (0.2%)

rewrite6.0ms (0.2%)

simplify60.0ms (1.6%)

prune22.0ms (0.6%)

localize6.0ms (0.2%)

series18.0ms (0.5%)

rewrite20.0ms (0.5%)

simplify78.0ms (2%)

prune46.0ms (1.2%)

localize9.0ms (0.2%)

series37.0ms (1%)

rewrite28.0ms (0.7%)

simplify93.0ms (2.4%)

prune106.0ms (2.8%)

regimes1.0s (26.6%)

bsearch47.0ms (1.2%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.4s (37.3%)

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