Details

analyze164.0ms (10.1%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
56.2%	43.7%	0.1%	7
65.6%	34.3%	0.1%	8
76.5%	23.4%	0.1%	9
82%	18%	0.1%	10
87.8%	12.1%	0.1%	11
90.7%	9.2%	0.1%	12
93.8%	6.1%	0.1%	13
95.3%	4.6%	0.1%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample24.0ms (1.5%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 23 to 15 computations (34.8% saved)

simplify10.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	8	12
2	8	12

prune1.0ms (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

31.3b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	31.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 20 to 12 computations (40% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

29.4b

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

rewrite9.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

31.3b

Rules

3×	`sqrt-prod_binary64`
3×	`add-sqr-sqrt_binary64`
2×	`*-un-lft-identity_binary64`
2×	`sqrt-div_binary64`
2×	`add-cube-cbrt_binary64`

Counts

1 → 15

Calls

1 calls:

3.0ms

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

Compiler

Compiled 247 to 55 computations (77.7% saved)

series23.0ms (1.4%)

Error

0.1b

Counts

1 → 12

Calls

1 calls:

18.0ms

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

Compiler

Compiled 313 to 233 computations (25.6% saved)

simplify61.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

469×	`cancel-sign-sub-inv_binary64`
298×	`unswap-sqr_binary64`
260×	`associate-/r/_binary64`
251×	`neg-mul-1_binary64`
248×	`associate-/l/_binary64`

Counts

27 → 14

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	62	395
1	160	378
2	452	378
3	1911	378
4	4512	378
5	5030	378

prune11.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	12	2	14
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	12	3	15

Error

1.3b

Counts

15 → 3

Alt Table

Status	Error	Program
✓	31.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
	33.0b	(neg.f64 re)
▶	30.7b	(+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im)))

Compiler

Compiled 193 to 99 computations (48.7% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im)))
5.9b	(/.f64 (*.f64 re re) im)

rewrite22.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 32

Calls

2 calls:

3.0ms	(/.f64 (*.f64 re re) im)
2.0ms	(+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im)))

Compiler

Compiled 520 to 223 computations (57.1% saved)

series33.0ms (2%)

Error

1.3b

Counts

2 → 18

Calls

2 calls:

19.0ms	(+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im)))
12.0ms	(/.f64 (*.f64 re re) im)

Compiler

Compiled 328 to 238 computations (27.4% saved)

simplify87.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

302×	`associate-*l/_binary64`
293×	`associate-*r/_binary64`
242×	`distribute-rgt-in_binary64`
228×	`associate-l_binary64`
217×	`associate-/l*_binary64`

Counts

50 → 32

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	71	649
1	186	571
2	581	571
3	2415	568
4	4132	568
5	4891	568
6	4926	568

prune10.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	31	1	32
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	32	3	35

Error

0.1b

Counts

35 → 3

Alt Table

Status	Error	Program
▶	29.4b	(+.f64 im (.f64 1/2 (.f64 re (/.f64 re im))))
✓	31.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
	33.0b	(neg.f64 re)

Compiler

Compiled 271 to 137 computations (49.4% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 im (.f64 1/2 (.f64 re (/.f64 re im))))
0.1b	(*.f64 re (/.f64 re im))

rewrite27.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

15×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
10×	`times-frac_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

2 → 43

Calls

2 calls:

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

Compiler

Compiled 701 to 290 computations (58.6% saved)

series33.0ms (2%)

Error

0.1b

Counts

2 → 18

Calls

2 calls:

20.0ms	(+.f64 im (.f64 1/2 (.f64 re (/.f64 re im))))
10.0ms	(*.f64 re (/.f64 re im))

Compiler

Compiled 328 to 238 computations (27.4% saved)

simplify80.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

295×	`associate-*r/_binary64`
289×	`associate-*l/_binary64`
266×	`unswap-sqr_binary64`
264×	`associate-/l*_binary64`
243×	`times-frac_binary64`

Counts

61 → 45

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	785
1	239	689
2	844	686
3	2507	675
4	4152	675
5	4915	675

prune13.0ms (0.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	45	0	45
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	45	3	48

Error

0.1b

Counts

48 → 3

Alt Table

Status	Error	Program
✓	29.4b	(+.f64 im (.f64 1/2 (.f64 re (/.f64 re im))))
✓	31.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
▶	33.0b	(neg.f64 re)

Compiler

Compiled 425 to 199 computations (53.2% saved)

localize1.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 0.1b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify8.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune2.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	2	2
Total	3	3

Error

0.1b

Counts

3 → 3

Alt Table

Status	Error	Program
	29.4b	(+.f64 im (.f64 1/2 (.f64 re (/.f64 re im))))
	31.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
	33.0b	(neg.f64 re)

Compiler

Compiled 25 to 16 computations (36% saved)

regimes163.0ms (10.1%)

Accuracy

Total 7.0b remaining (96.8%)

Threshold costs 0b (0%)

Compiler

Compiled 1007 to 634 computations (37% saved)

bsearch33.0ms (2%)

Steps

Iters	Range		Point
8	1.6810848822855357e+112	6.023912510660256e+115	2.5184939753787586e+113
6	4.750208550312806e-165	6.5215288627863926e-164	4.776300407843372e-164

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	28
1	20	28
2	22	28
3	23	28
4	23	28

end6.0ms (0.4%)

Compiler: Compiled 63 to 39 computations (38.1% saved)

sample783.0ms (48.3%)

Algorithm

1×

intervals

Results

316.0ms

8000×

body

128

valid

Compiler

Compiled 59 to 38 computations (35.6% saved)

Details

analyze164.0ms (10.1%)

sample24.0ms (1.5%)

simplify10.0ms (0.6%)

prune1.0ms (0.1%)

localize5.0ms (0.3%)

rewrite9.0ms (0.5%)

series23.0ms (1.4%)

simplify61.0ms (3.7%)

prune11.0ms (0.7%)

localize5.0ms (0.3%)

rewrite22.0ms (1.3%)

series33.0ms (2%)

simplify87.0ms (5.4%)

prune10.0ms (0.6%)

localize5.0ms (0.3%)

rewrite27.0ms (1.7%)

series33.0ms (2%)

simplify80.0ms (4.9%)

prune13.0ms (0.8%)

localize1.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify8.0ms (0.5%)

prune2.0ms (0.1%)

regimes163.0ms (10.1%)

bsearch33.0ms (2%)

simplify4.0ms (0.2%)

end6.0ms (0.4%)

sample783.0ms (48.3%)

Profiling