Details

analyze543.0ms (10.6%)

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)

sample32.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	198×	body	128	valid
5.0ms	17×	body	4096	valid
5.0ms	21×	body	2048	valid
1.0ms	8×	body	1024	valid
1.0ms	7×	body	512	valid
0.0ms	5×	body	256	valid

Compiler

Compiled 37 to 27 computations (27% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

prune3.0ms (0.1%)

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

40.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	40.0b	(.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)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.0b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
1.2b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
31.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite128.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

39.9b

Rules

8×	`pow1_binary64` `add-log-exp_binary64`
7×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `flip3-+_binary64` `sqrt-div_binary64` `flip-+_binary64` `sqrt-prod_binary64`

Counts

4 → 51

Calls

4 calls:

8.0ms	(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)))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 1237 to 435 computations (64.8% saved)

series153.0ms (3%)

Error

8.0b

Counts

4 → 50

Calls

4 calls:

43.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
32.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
28.0ms	(+.f64 (.f64 re re) (.f64 im im))
21.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))

Compiler

Compiled 1800 to 1462 computations (18.8% saved)

simplify114.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

493×	`unswap-sqr_binary64`
353×	`associate-r_binary64`
328×	`associate-l_binary64`
292×	`distribute-neg-frac_binary64`
276×	`div-sub_binary64`

Counts

101 → 71

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	125	1583
1	328	1493
2	874	1478
3	3350	1475
4	4678	1475
5	5146	1475

prune55.0ms (1.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	64	7	71
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	64	8	72

Error

7.4b

Counts

72 → 8

Alt Table

Status	Error	Program
✓	40.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
	45.7b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	45.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
▶	42.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (neg.f64 im) re))))
	50.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re))))
	56.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 im im) re) -1/2))))
	60.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (neg.f64 re) re))))
	43.5b	(.f64 1/2 (/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))))

Compiler

Compiled 1169 to 641 computations (45.2% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(sqrt.f64 (*.f64 2 (+.f64 (neg.f64 im) re)))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

7.4b

Rules

4×	`pow1_binary64`
2×	`sqrt-pow1_binary64` `associate-*r/_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `pow-prod-down_binary64` `flip3-+_binary64` `flip-+_binary64` `sqrt-prod_binary64` `*-un-lft-identity_binary64`

Counts

1 → 13

Calls

1 calls:

6.0ms

(sqrt.f64 (*.f64 2 (+.f64 (neg.f64 im) re)))

Compiler

Compiled 200 to 119 computations (40.5% saved)

series25.0ms (0.5%)

Error

7.4b

Counts

1 → 7

Calls

1 calls:

22.0ms

(sqrt.f64 (*.f64 2 (+.f64 (neg.f64 im) re)))

Compiler

Compiled 259 to 211 computations (18.5% saved)

simplify142.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

817×	`times-frac_binary64`
590×	`unsub-neg_binary64`
446×	`sub-neg_binary64`
370×	`distribute-rgt-neg-in_binary64`
360×	`neg-sub0_binary64` `unswap-sqr_binary64`

Counts

20 → 15

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	254
1	118	224
2	268	224
3	647	219
4	1454	219
5	2191	219
6	3441	219
7	4213	219
8	4849	219
9	4909	219
10	5581	219

prune19.0ms (0.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	14	1	15
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	14	9	23

Error

7.4b

Counts

23 → 9

Alt Table

Status	Error	Program
✓	40.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
	45.5b	(.f64 1/2 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 (neg.f64 im)) (*.f64 re (/.f64 1/2 (sqrt.f64 (neg.f64 im)))))))
	45.7b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	45.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
✓	42.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (neg.f64 im) re))))
	50.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re))))
	56.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 im im) re) -1/2))))
	60.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (neg.f64 re) re))))
▶	43.5b	(.f64 1/2 (/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))))

Compiler

Compiled 387 to 278 computations (28.2% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
0.6b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.3b	(sqrt.f64 (.f64 2 (.f64 im im)))
31.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite127.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

7.4b

Rules

51×	`add-sqr-sqrt_binary64`
50×	`sqrt-prod_binary64`
38×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
26×	`add-cube-cbrt_binary64`

Counts

4 → 108

Calls

4 calls:

15.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(sqrt.f64 (.f64 2 (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 2950 to 960 computations (67.5% saved)

series119.0ms (2.3%)

Error

2.5b

Counts

4 → 36

Calls

4 calls:

40.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
26.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
26.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
9.0ms	(sqrt.f64 (.f64 2 (.f64 im im)))

Compiler

Compiled 1677 to 1260 computations (24.9% saved)

simplify156.0ms (3%)

Algorithm

1×	egg-herbie

Rules

403×	`times-frac_binary64`
359×	`unswap-sqr_binary64`
351×	`associate-r_binary64`
330×	`associate-l_binary64`
313×	`associate-/l*_binary64`

Counts

144 → 84

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	194	4049
1	403	3885
2	1019	3844
3	4101	3833
4	5016	3833

prune60.0ms (1.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	79	5	84
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	81	12	93

Error

2.5b

Counts

93 → 12

Alt Table

Status	Error	Program
	48.4b	(.f64 1/2 (/.f64 (.f64 (neg.f64 im) (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
✓	40.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
	45.5b	(.f64 1/2 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 (neg.f64 im)) (*.f64 re (/.f64 1/2 (sqrt.f64 (neg.f64 im)))))))
	53.4b	(.f64 1/2 (/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)) im)))
	45.7b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	45.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
✓	42.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (neg.f64 im) re))))
	50.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re))))
▶	43.6b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 im im)))) (/.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 im im)))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))))
	56.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 im im) re) -1/2))))
	49.7b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 im)))
	53.4b	(.f64 1/2 (/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (.f64 re -2))))

Compiler

Compiled 1738 to 827 computations (52.4% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.3b	(sqrt.f64 (.f64 2 (.f64 im im)))
30.3b	(sqrt.f64 (.f64 2 (.f64 im im)))
31.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite73.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

2.5b

Rules

17×	`pow1_binary64`
11×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
7×	`sqrt-pow1_binary64`
6×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64` `pow-prod-down_binary64`

Counts

4 → 56

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(sqrt.f64 (.f64 2 (.f64 im im)))
4.0ms	(sqrt.f64 (.f64 2 (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 1827 to 813 computations (55.5% saved)

series114.0ms (2.2%)

Error

2.5b

Counts

4 → 33

Calls

4 calls:

44.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
31.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
10.0ms	(sqrt.f64 (.f64 2 (.f64 im im)))
9.0ms	(sqrt.f64 (.f64 2 (.f64 im im)))

Compiler

Compiled 2257 to 1600 computations (29.1% saved)

simplify105.0ms (2%)

Algorithm

1×	egg-herbie

Rules

442×	`distribute-rgt-neg-in_binary64`
338×	`unswap-sqr_binary64`
304×	`div-sub_binary64`
299×	`distribute-neg-frac_binary64`
297×	`associate-r_binary64`

Counts

89 → 44

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	110	1181
1	261	1130
2	674	1118
3	2921	1115
4	4658	1115
5	5157	1115

prune43.0ms (0.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	0	9	9
Picked	1	0	1
Done	0	2	2
Total	44	12	56

Error

2.5b

Counts

56 → 12

Alt Table

Status	Error	Program
	48.4b	(.f64 1/2 (/.f64 (.f64 (neg.f64 im) (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
	40.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
	45.5b	(.f64 1/2 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 (neg.f64 im)) (*.f64 re (/.f64 1/2 (sqrt.f64 (neg.f64 im)))))))
	53.4b	(.f64 1/2 (/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)) im)))
	45.7b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	45.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	42.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (neg.f64 im) re))))
	50.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re))))
	56.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 im im) re) -1/2))))
	49.7b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 im)))
	53.4b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 im im)))) (/.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 im im)))) (sqrt.f64 (*.f64 re -2)))))
	53.4b	(.f64 1/2 (/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (.f64 re -2))))

Compiler

Compiled 1199 to 691 computations (42.4% saved)

regimes1.6s (31.9%)

Accuracy

Total 21.0b remaining (89.7%)

Threshold costs 0b (0%)

Compiler

Compiled 13562 to 8809 computations (35% saved)

bsearch155.0ms (3%)

Steps

Iters	Range		Point
8	9.243350754054082e+108	9.694393391630773e+112	1.5184799493309332e+111
9	5.794919433678647e+28	6.843109950795625e+33	5.860124411478432e+28
9	6.740563255653875e-15	8.120091894691637e-09	2.379531245742764e-10
8	4.131415020528795e-168	1.7064403722675033e-163	4.4753072681602385e-164
8	-9.004886839848612e-303	-5.348202176127388e-307	-9.515876010320053e-305
7	-1.2264227270703035e-112	-4.115438435678444e-114	-7.594043707095321e-114
7	-1.8315404530098413e+53	-1.0398718362009602e+52	-1.6284670281102737e+53

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

21×	`*-commutative_binary64`
12×	`+-commutative_binary64`
7×	`neg-mul-1_binary64` `neg-sub0_binary64` `sub-neg_binary64`
2×	`distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`
1×	`unsub-neg_binary64` `cancel-sign-sub-inv_binary64` `distribute-frac-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	208
1	88	206
2	101	206
3	115	204
4	126	204
5	130	204
6	131	204
7	130	204

end3.0ms (0.1%)

Compiler: Compiled 135 to 76 computations (43.7% saved)

sample1.2s (24.1%)

Algorithm

1×

intervals

Results

290.0ms	6089×	body	128	valid
164.0ms	515×	body	4096	valid
146.0ms	627×	body	2048	valid
80.0ms	409×	body	1024	valid
30.0ms	222×	body	512	valid
13.0ms	138×	body	256	valid

Compiler

Compiled 339 to 231 computations (31.9% saved)

Details

analyze543.0ms (10.6%)

sample32.0ms (0.6%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

rewrite128.0ms (2.5%)

series153.0ms (3%)

simplify114.0ms (2.2%)

prune55.0ms (1.1%)

localize7.0ms (0.1%)

rewrite16.0ms (0.3%)

series25.0ms (0.5%)

simplify142.0ms (2.8%)

prune19.0ms (0.4%)

localize15.0ms (0.3%)

rewrite127.0ms (2.5%)

series119.0ms (2.3%)

simplify156.0ms (3%)

prune60.0ms (1.2%)

localize17.0ms (0.3%)

rewrite73.0ms (1.4%)

series114.0ms (2.2%)

simplify105.0ms (2%)

prune43.0ms (0.8%)

regimes1.6s (31.9%)

bsearch155.0ms (3%)

simplify13.0ms (0.2%)

end3.0ms (0.1%)

sample1.2s (24.1%)

Profiling