Details

analyze477.0ms (9.6%)

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)

sample41.0ms (0.8%)

Algorithm

1×

intervals

Results

13.0ms	187×	body	128	valid
8.0ms	21×	body	4096	valid
6.0ms	19×	body	2048	valid
3.0ms	12×	body	1024	valid
1.0ms	8×	body	512	valid
1.0ms	9×	body	256	valid

Compiler

Compiled 37 to 27 computations (27% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`distribute-lft-in_binary64`
2×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	23	23
2	23	23
3	23	23

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

36.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	36.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Compiler

Compiled 51 to 36 computations (29.4% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

1.7b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
27.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite39.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

36.6b

Rules

5×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64`
3×	`sqrt-prod_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 27

Calls

2 calls:

6.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
3.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 641 to 227 computations (64.6% saved)

series57.0ms (1.1%)

Error

9.8b

Counts

2 → 26

Calls

2 calls:

24.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
18.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)

Compiler

Compiled 984 to 784 computations (20.3% saved)

simplify92.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

561×	`cancel-sign-sub-inv_binary64`
366×	`distribute-rgt-in_binary64`
304×	`unswap-sqr_binary64`
265×	`distribute-rgt-neg-in_binary64`
251×	`distribute-lft-neg-in_binary64`

Counts

53 → 34

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	90	820
1	244	779
2	638	767
3	2385	764
4	4664	764
5	4984	764
6	4936	764

prune28.0ms (0.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	28	6	34
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	6	35

Error

11.0b

Counts

35 → 6

Alt Table

Status	Error	Program
	59.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (neg.f64 re) re))))
	50.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re))))
▶	40.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))))
	46.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 im im) re) -1/2))))
	48.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re 2))))

Compiler

Compiled 738 to 430 computations (41.7% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
6.6b	(sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
21.6b	(/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))
27.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite78.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

10.1b

Rules

21×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
8×	`add-cube-cbrt_binary64`

Counts

4 → 73

Calls

4 calls:

11.0ms	(sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
10.0ms	(/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))
6.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
3.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 1976 to 584 computations (70.4% saved)

series122.0ms (2.4%)

Error

9.7b

Counts

4 → 56

Calls

4 calls:

33.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
21.0ms	(/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))
19.0ms	(sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Compiler

Compiled 2323 to 1767 computations (23.9% saved)

simplify112.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

578×	`times-frac_binary64`
516×	`associate-/l*_binary64`
392×	`associate-l_binary64`
242×	`associate-/r*_binary64`
209×	`associate-*l/_binary64`

Counts

129 → 79

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	180	2551
1	446	2349
2	1306	2323
3	4870	2323
4	4961	2323

prune41.0ms (0.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	75	4	79
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	78	7	85

Error

9.4b

Counts

85 → 7

Alt Table

Status	Error	Program
	48.7b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	50.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re))))
▶	39.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 im (/.f64 im (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))))))
	48.9b	(.f64 1/2 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 (.f64 re (sqrt.f64 (/.f64 1 im))) 1/2))))
	46.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 im im) re) -1/2))))
	40.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (/.f64 (.f64 (/.f64 im (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))) im) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))))

Compiler

Compiled 1479 to 751 computations (49.2% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 im (/.f64 im (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.5b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
6.6b	(sqrt.f64 (.f64 2 (.f64 im (/.f64 im (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))))
27.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite99.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

9.4b

Rules

39×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
24×	`associate-r_binary64`
19×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`

Counts

4 → 88

Calls

4 calls:

12.0ms	(.f64 im (/.f64 im (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
10.0ms	(sqrt.f64 (.f64 2 (.f64 im (/.f64 im (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))))
7.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
3.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 2366 to 714 computations (69.8% saved)

series124.0ms (2.5%)

Error

6.7b

Counts

4 → 56

Calls

4 calls:

33.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
20.0ms	(sqrt.f64 (.f64 2 (.f64 im (/.f64 im (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))))
20.0ms	(.f64 im (/.f64 im (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))

Compiler

Compiled 2323 to 1789 computations (23% saved)

simplify116.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

801×	`times-frac_binary64`
572×	`associate-/l*_binary64`
267×	`associate-/r*_binary64`
260×	`associate-*l/_binary64`
161×	`div-sub_binary64`

Counts

144 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	203	2805
1	511	2582
2	1572	2556
3	4601	2542
4	4938	2542

prune43.0ms (0.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	89	7	96

Error

6.7b

Counts

96 → 7

Alt Table

Status	Error	Program
✓	39.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 im (/.f64 im (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))))))
	51.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 im (/.f64 im (.f64 re -2))))))
	48.7b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	46.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 im (/.f64 im (-.f64 (+.f64 im (.f64 1/2 (/.f64 (*.f64 re re) im))) re))))))
	48.9b	(.f64 1/2 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 (.f64 re (sqrt.f64 (/.f64 1 im))) 1/2))))
	46.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
▶	40.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (/.f64 (.f64 (/.f64 im (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))) im) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))))

Compiler

Compiled 1648 to 827 computations (49.8% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

7.3b	(/.f64 (.f64 (/.f64 im (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))) im) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
27.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
27.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
27.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite97.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

6.7b

Rules

22×	`add-sqr-sqrt_binary64`
18×	`add-exp-log_binary64`
15×	`*-un-lft-identity_binary64`
12×	`cbrt-prod_binary64`
12×	`add-cbrt-cube_binary64`

Counts

4 → 85

Calls

4 calls:

28.0ms	(/.f64 (.f64 (/.f64 im (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))) im) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
3.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
3.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
3.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 4510 to 806 computations (82.1% saved)

series134.0ms (2.7%)

Error

6.7b

Counts

4 → 51

Calls

4 calls:

32.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
27.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
25.0ms	(/.f64 (.f64 (/.f64 im (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))) im) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))

Compiler

Compiled 4432 to 2314 computations (47.8% saved)

simplify128.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

656×	`associate-*l/_binary64`
496×	`associate-/r*_binary64`
467×	`associate-l_binary64`
411×	`unswap-sqr_binary64`
368×	`associate-*r/_binary64`

Counts

136 → 107

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	159	4463
1	387	3228
2	1403	3179
3	4158	2808
4	5282	2808

prune60.0ms (1.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	107	7	114

Error

6.7b

Counts

114 → 7

Alt Table

Status	Error	Program
	39.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 im (/.f64 im (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))))))
	51.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 im (/.f64 im (.f64 re -2))))))
	48.7b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	46.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 im (/.f64 im (-.f64 (+.f64 im (.f64 1/2 (/.f64 (*.f64 re re) im))) re))))))
	48.9b	(.f64 1/2 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 (.f64 re (sqrt.f64 (/.f64 1 im))) 1/2))))
	46.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	40.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (/.f64 (.f64 (/.f64 im (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))) im) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))))

Compiler

Compiled 3770 to 1112 computations (70.5% saved)

regimes1.5s (30.4%)

Accuracy

Total 18.2b remaining (75.5%)

Threshold costs 0b (0%)

Compiler

Compiled 16423 to 9919 computations (39.6% saved)

bsearch130.0ms (2.6%)

Steps

Iters	Range		Point
9	2.179546229029429e+78	5.246252109660243e+86	5.110855543795228e+86
8	3.1190159867640562e-149	8.70112074555135e-147	3.398879661315353e-149
2	4.238865701704969e-183	8.6161669899513e-176	2.856357253236775e-181
10	2.6603380082910193e-252	6.939356303039168e-235	3.3257616803601e-235
11	-5.247929021158637e-102	-1.2489492704424938e-124	-1.2662953255596096e-124
5	-6.227796877697633e+142	-1.800427938354411e+142	-5.541738335196269e+142

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

26×	`*-commutative_binary64`
14×	`+-commutative_binary64`
10×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	173
1	101	173
2	114	173
3	133	173
4	143	173
5	151	173
6	154	173
7	155	173
8	153	173

end3.0ms (0.1%)

Compiler: Compiled 116 to 77 computations (33.6% saved)

sample1.4s (27.4%)

Algorithm

1×

intervals

Results

393.0ms	6058×	body	128	valid
222.0ms	557×	body	4096	valid
205.0ms	617×	body	2048	valid
112.0ms	427×	body	1024	valid
41.0ms	226×	body	512	valid
14.0ms	115×	body	256	valid

Compiler

Compiled 274 to 179 computations (34.7% saved)

Iter	Nodes	Cost
0	68	173
1	101	173
2	114	173
3	133	173
4	143	173
5	151	173
6	154	173
7	155	173
8	153	173

Iter	Nodes	Cost
0	68	173
1	101	173
2	114	173
3	133	173
4	143	173
5	151	173
6	154	173
7	155	173
8	153	173

Details

analyze477.0ms (9.6%)

sample41.0ms (0.8%)

simplify10.0ms (0.2%)

prune2.0ms (0%)

localize9.0ms (0.2%)

rewrite39.0ms (0.8%)

series57.0ms (1.1%)

simplify92.0ms (1.8%)

prune28.0ms (0.6%)

localize16.0ms (0.3%)

rewrite78.0ms (1.6%)

series122.0ms (2.4%)

simplify112.0ms (2.2%)

prune41.0ms (0.8%)

localize13.0ms (0.3%)

rewrite99.0ms (2%)

series124.0ms (2.5%)

simplify116.0ms (2.3%)

prune43.0ms (0.9%)

localize20.0ms (0.4%)

rewrite97.0ms (1.9%)

series134.0ms (2.7%)

simplify128.0ms (2.6%)

prune60.0ms (1.2%)

regimes1.5s (30.4%)

bsearch130.0ms (2.6%)

simplify12.0ms (0.2%)

end3.0ms (0.1%)

sample1.4s (27.4%)

Profiling

Iter	Nodes	Cost
0	68	173
1	101	173
2	114	173
3	133	173
4	143	173
5	151	173
6	154	173
7	155	173
8	153	173