Details

analyze382.0ms (9.2%)

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)

sample42.0ms (1%)

Algorithm

1×

intervals

Results

9.0ms	190×	body	128	valid
6.0ms	20×	body	4096	valid
4.0ms	19×	body	2048	valid
3.0ms	256×	pre	128	true
3.0ms	18×	body	1024	valid
1.0ms	7×	body	512	valid
0.0ms	2×	body	256	valid

Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify27.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

51×	`distribute-rgt-in_binary64`
42×	`cancel-sign-sub-inv_binary64`
37×	`sub-neg_binary64`
27×	`neg-mul-1_binary64` `unsub-neg_binary64`
26×	`distribute-lft-in_binary64` `associate--r+_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	18	23
2	29	23
3	43	23
4	57	23
5	82	23
6	122	23
7	163	23
8	190	23
9	216	23
10	229	23
11	231	23
12	242	23
13	255	23
14	267	23
15	288	23
16	285	23
17	286	23
18	249	23

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

37.5b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	37.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Compiler

Compiled 34 to 24 computations (29.4% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.3b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
28.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite94.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

37.3b

Rules

10×	`add-sqr-sqrt_binary64`
7×	`pow1_binary64` `*-un-lft-identity_binary64`
5×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
4×	`sqrt-div_binary64`
3×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `cancel-sign-sub-inv_binary64`

Counts

3 → 45

Calls

3 calls:

9.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
7.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 1063 to 371 computations (65.1% saved)

series119.0ms (2.9%)

Error

0.2b

Counts

3 → 37

Calls

3 calls:

35.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
33.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))

Compiler

Compiled 1464 to 1196 computations (18.3% saved)

simplify100.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

384×	`distribute-rgt-neg-in_binary64`
379×	`associate-r_binary64`
362×	`associate-l_binary64`
292×	`unswap-sqr_binary64`
200×	`div-sub_binary64`

Counts

82 → 44

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	140	1421
1	328	1357
2	811	1333
3	3150	1327
4	4603	1327
5	4922	1327

prune42.0ms (1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	38	6	44
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	6	45

Error

8.7b

Counts

45 → 6

Alt Table

Status	Error	Program
	46.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) 3)) re))))
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 1/2 (/.f64 (.f64 im im) re)))))
	48.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re -2))))
	39.7b	(.f64 1/2 (/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))
▶	32.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re))))
	45.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) 3) (pow.f64 re 3)) (+.f64 (.f64 im im) (.f64 re (+.f64 re (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))))))))

Compiler

Compiled 853 to 502 computations (41.1% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im)))
6.1b	(/.f64 (*.f64 re re) im)
10.1b	(sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (/.f64 (*.f64 re re) im))) re)))

rewrite72.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

7.5b

Rules

8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64`
5×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
3×	`times-frac_binary64` `associate-/r*_binary64`
2×	`sqrt-pow1_binary64` `associate-*r/_binary64` `sqrt-div_binary64` `div-exp_binary64` `cbrt-undiv_binary64`

Counts

3 → 45

Calls

3 calls:

9.0ms	(sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (/.f64 (*.f64 re re) im))) re)))
5.0ms	(/.f64 (*.f64 re re) im)
4.0ms	(+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im)))

Compiler

Compiled 1096 to 611 computations (44.3% saved)

series95.0ms (2.3%)

Error

7.3b

Counts

3 → 27

Calls

3 calls:

33.0ms	(+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im)))
32.0ms	(sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (/.f64 (*.f64 re re) im))) re)))
21.0ms	(/.f64 (*.f64 re re) im)

Compiler

Compiled 1053 to 859 computations (18.4% saved)

simplify148.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

417×	`associate-l_binary64`
365×	`associate-*l/_binary64`
363×	`associate-r_binary64`
338×	`associate-*r/_binary64`
333×	`associate-/l*_binary64`

Counts

72 → 40

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	124	1171
1	307	1102
2	997	1090
3	4438	1087
4	4932	1087
5	4983	1087
6	4976	1087
7	4948	1087

prune33.0ms (0.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	40	6	46

Error

7.3b

Counts

46 → 6

Alt Table

Status	Error	Program
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 1/2 (/.f64 (.f64 im im) re)))))
▶	30.1b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 im)))
	48.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re -2))))
	30.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (.f64 re (/.f64 re im)))) re))))
	39.7b	(.f64 1/2 (/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))
	45.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) 3) (pow.f64 re 3)) (+.f64 (.f64 im im) (.f64 re (+.f64 re (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))))))))

Compiler

Compiled 700 to 456 computations (34.9% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.5b	(*.f64 (sqrt.f64 2) (sqrt.f64 im))

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

7.3b

Rules

15×	`add-sqr-sqrt_binary64`
10×	`sqrt-prod_binary64`
6×	`associate-l_binary64` `associate-r_binary64`
5×	`pow1_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
4×	`unswap-sqr_binary64`

Counts

1 → 31

Calls

1 calls:

7.0ms

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

Compiler

Compiled 294 to 220 computations (25.2% saved)

series11.0ms (0.3%)

Error

7.3b

Counts

1 → 3

Calls

1 calls:

10.0ms

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

Compiler

Compiled 81 to 73 computations (9.9% saved)

simplify86.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

564×	`log-div_binary64`
359×	`associate-l_binary64`
296×	`associate-*l/_binary64`
288×	`unswap-sqr_binary64`
259×	`*-commutative_binary64`

Counts

34 → 13

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	46	367
1	83	361
2	199	361
3	251	361
4	360	361
5	590	361
6	1218	361
7	2923	361
8	4877	361
9	5212	361

prune24.0ms (0.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	9	4	13
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	11	8	19

Error

7.3b

Counts

19 → 8

Alt Table

Status	Error	Program
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 1/2 (/.f64 (.f64 im im) re)))))
	30.2b	(.f64 1/2 (.f64 (*.f64 (sqrt.f64 2) (fabs.f64 (cbrt.f64 im))) (sqrt.f64 (cbrt.f64 im))))
	30.1b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 im) (sqrt.f64 (sqrt.f64 2)))))
	48.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re -2))))
▶	29.8b	(.f64 1/2 (sqrt.f64 (.f64 im 2)))
	36.5b	(.f64 1/2 (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im)) 3)))
	39.7b	(.f64 1/2 (/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))
	45.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) 3) (pow.f64 re 3)) (+.f64 (.f64 im im) (.f64 re (+.f64 re (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))))))))

Compiler

Compiled 373 to 282 computations (24.4% saved)

localize4.0ms (0.1%)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

7.3b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 7.3b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune7.0ms (0.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	7	7
Picked	1	1
Done	0	0
Total	8	8

Error

7.3b

Counts

8 → 8

Alt Table

Status	Error	Program
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 1/2 (/.f64 (.f64 im im) re)))))
	30.2b	(.f64 1/2 (.f64 (*.f64 (sqrt.f64 2) (fabs.f64 (cbrt.f64 im))) (sqrt.f64 (cbrt.f64 im))))
	30.1b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 im) (sqrt.f64 (sqrt.f64 2)))))
	48.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re -2))))
	29.8b	(.f64 1/2 (sqrt.f64 (.f64 im 2)))
	36.5b	(.f64 1/2 (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im)) 3)))
	39.7b	(.f64 1/2 (/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))
	45.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) 3) (pow.f64 re 3)) (+.f64 (.f64 im im) (.f64 re (+.f64 re (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))))))))

Compiler

Compiled 134 to 97 computations (27.6% saved)

regimes1.3s (32%)

Accuracy

Total 6.9b remaining (48.7%)

Threshold costs 0b (0%)

Compiler

Compiled 10467 to 7287 computations (30.4% saved)

bsearch104.0ms (2.5%)

Steps

Iters	Range		Point
7	1.3371076402346294e+41	4.389203064517121e+42	1.5600440620400777e+41
9	2.956407643163521e-29	4.666412025916379e-21	1.1214730224820804e-28
8	3.832709135152997e-90	1.2236473642876516e-85	3.229385886304382e-86
8	-3.3000480317782867e-107	-3.93968302309732e-110	-3.990259720622686e-110
9	-1.5644502912601568e+112	-2.2960385614445762e+107	-5.935554961352542e+109

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
7×	`+-commutative_binary64`
5×	`sub-neg_binary64`
2×	`neg-mul-1_binary64` `neg-sub0_binary64`
1×	`if-if-or-not_binary64` `unpow1_binary64` `1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	130
1	84	130
2	92	130
3	96	130
4	98	130
5	97	130

end3.0ms (0.1%)

Compiler: Compiled 86 to 66 computations (23.3% saved)

sample1.4s (32.6%)

Algorithm

1×

intervals

Results

288.0ms	6029×	body	128	valid
166.0ms	652×	body	2048	valid
146.0ms	505×	body	4096	valid
100.0ms	8000×	pre	128	true
80.0ms	445×	body	1024	valid
32.0ms	231×	body	512	valid
16.0ms	138×	body	256	valid

Compiler

Compiled 242 to 179 computations (26% saved)

Iter	Nodes	Cost
0	13	23
1	18	23
2	29	23
3	43	23
4	57	23
5	82	23
6	122	23
7	163	23
8	190	23
9	216	23
10	229	23
11	231	23
12	242	23
13	255	23
14	267	23
15	288	23
16	285	23
17	286	23
18	249	23

Iter	Nodes	Cost
0	13	23
1	18	23
2	29	23
3	43	23
4	57	23
5	82	23
6	122	23
7	163	23
8	190	23
9	216	23
10	229	23
11	231	23
12	242	23
13	255	23
14	267	23
15	288	23
16	285	23
17	286	23
18	249	23

Details

analyze382.0ms (9.2%)

sample42.0ms (1%)

simplify27.0ms (0.7%)

prune2.0ms (0.1%)

localize11.0ms (0.3%)

rewrite94.0ms (2.3%)

series119.0ms (2.9%)

simplify100.0ms (2.4%)

prune42.0ms (1%)

localize10.0ms (0.2%)

rewrite72.0ms (1.7%)

series95.0ms (2.3%)

simplify148.0ms (3.6%)

prune33.0ms (0.8%)

localize5.0ms (0.1%)

rewrite29.0ms (0.7%)

series11.0ms (0.3%)

simplify86.0ms (2.1%)

prune24.0ms (0.6%)

localize4.0ms (0.1%)

rewrite1.0ms (0%)

series0.0ms (0%)

simplify9.0ms (0.2%)

prune7.0ms (0.2%)

regimes1.3s (32%)

bsearch104.0ms (2.5%)

simplify7.0ms (0.2%)

end3.0ms (0.1%)

sample1.4s (32.6%)

Profiling

Iter	Nodes	Cost
0	13	23
1	18	23
2	29	23
3	43	23
4	57	23
5	82	23
6	122	23
7	163	23
8	190	23
9	216	23
10	229	23
11	231	23
12	242	23
13	255	23
14	267	23
15	288	23
16	285	23
17	286	23
18	249	23