Details

analyze23.0ms (1.1%)

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
74.9%	25%	0.1%	3
87.4%	12.5%	0.1%	4
93.7%	6.2%	0.1%	5
96.8%	3.1%	0.1%	6
98.3%	1.6%	0.1%	7
99.1%	0.8%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample26.0ms (1.2%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

128

valid

Compiler

Compiled 25 to 17 computations (32% saved)

simplify8.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	9	14
2	9	14

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

31.1b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	31.1b	(log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))

Compiler

Compiled 22 to 14 computations (36.4% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
29.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite30.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

31.1b

Rules

4×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64` `*-un-lft-identity_binary64`
2×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `flip3-+_binary64` `sqrt-div_binary64` `flip-+_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

2 → 26

Calls

2 calls:

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

Compiler

Compiled 461 to 115 computations (75.1% saved)

series73.0ms (3.4%)

Error

0.3b

Counts

2 → 29

Calls

2 calls:

34.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
27.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 701 to 547 computations (22% saved)

simplify78.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

689×	`cancel-sign-sub-inv_binary64`
499×	`unswap-sqr_binary64`
278×	`associate-r_binary64`
275×	`times-frac_binary64`
257×	`associate-l_binary64`

Counts

55 → 35

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	82	775
1	219	735
2	657	735
3	2800	735
4	4899	735
5	5052	735

prune22.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	33	2	35
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	3	36

Error

1.4b

Counts

36 → 3

Alt Table

Status	Error	Program
▶	28.9b	(log.f64 (neg.f64 re))
	34.7b	(log.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))))
✓	31.1b	(log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))

Compiler

Compiled 364 to 192 computations (47.3% saved)

localize3.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

1.4b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 1.4b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune3.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

1.4b

Counts

3 → 3

Alt Table

Status	Error	Program
✓	28.9b	(log.f64 (neg.f64 re))
▶	34.7b	(log.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))))
✓	31.1b	(log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))

Compiler

Compiled 40 to 27 computations (32.5% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im)))
5.1b	(/.f64 (*.f64 re re) im)
8.5b	(log.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))))

rewrite49.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

9×	`add-exp-log_binary64`
8×	`add-cbrt-cube_binary64`
6×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`
4×	`pow1_binary64`

Counts

3 → 46

Calls

3 calls:

5.0ms	(/.f64 (*.f64 re re) im)
3.0ms	(+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im)))
3.0ms	(log.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))))

Compiler

Compiled 835 to 386 computations (53.8% saved)

series94.0ms (4.4%)

Error

0.3b

Counts

3 → 29

Calls

3 calls:

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

Compiler

Compiled 814 to 637 computations (21.7% saved)

simplify123.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

336×	`associate-*l/_binary64`
324×	`associate-*r/_binary64`
296×	`cancel-sign-sub-inv_binary64`
270×	`times-frac_binary64`
259×	`associate-l_binary64`

Counts

75 → 45

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	119	1223
1	280	1075
2	785	1069
3	3237	1061
4	4747	1061
5	4991	1057
6	4961	1057

prune19.0ms (0.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	44	1	45
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	45	3	48

Error

0.2b

Counts

48 → 3

Alt Table

Status	Error	Program
✓	28.9b	(log.f64 (neg.f64 re))
▶	33.3b	(log.f64 (+.f64 im (.f64 1/2 (.f64 re (/.f64 re im)))))
✓	31.1b	(log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))

Compiler

Compiled 389 to 212 computations (45.5% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 im (.f64 1/2 (.f64 re (/.f64 re im))))
0.1b	(*.f64 re (/.f64 re im))
8.5b	(log.f64 (+.f64 im (.f64 1/2 (.f64 re (/.f64 re im)))))

rewrite61.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

17×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
12×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
10×	`times-frac_binary64`
9×	`add-exp-log_binary64`

Counts

3 → 57

Calls

3 calls:

7.0ms	(*.f64 re (/.f64 re im))
5.0ms	(log.f64 (+.f64 im (.f64 1/2 (.f64 re (/.f64 re im)))))
3.0ms	(+.f64 im (.f64 1/2 (.f64 re (/.f64 re im))))

Compiler

Compiled 1025 to 462 computations (54.9% saved)

series93.0ms (4.3%)

Error

0.2b

Counts

3 → 29

Calls

3 calls:

33.0ms	(+.f64 im (.f64 1/2 (.f64 re (/.f64 re im))))
32.0ms	(log.f64 (+.f64 im (.f64 1/2 (.f64 re (/.f64 re im)))))
18.0ms	(*.f64 re (/.f64 re im))

Compiler

Compiled 814 to 637 computations (21.7% saved)

simplify107.0ms (5%)

Algorithm

1×	egg-herbie

Rules

367×	`times-frac_binary64`
316×	`associate-*r/_binary64`
306×	`associate-*l/_binary64`
290×	`associate-/l*_binary64`
268×	`cancel-sign-sub-inv_binary64`

Counts

86 → 67

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	138	1341
1	336	1199
2	1039	1187
3	3261	1168
4	4588	1154
5	4940	1154

prune27.0ms (1.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	67	3	70

Error

0.2b

Counts

70 → 3

Alt Table

Status	Error	Program
	28.9b	(log.f64 (neg.f64 re))
	33.3b	(log.f64 (+.f64 im (.f64 1/2 (.f64 re (/.f64 re im)))))
	31.1b	(log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))

Compiler

Compiled 700 to 353 computations (49.6% saved)

regimes332.0ms (15.5%)

Accuracy

Total 6.8b remaining (97.6%)

Threshold costs 0b (0%)

Compiler

Compiled 1596 to 1034 computations (35.2% saved)

bsearch35.0ms (1.6%)

Steps

Iters	Range		Point
8	-1.0823865483161492e-133	-6.998594982616266e-138	-7.144782444788284e-138
8	-8.105875244160862e+151	-7.041673353714045e+148	-7.143276769119883e+148

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	46
1	30	46
2	32	46
3	33	46
4	33	46

end8.0ms (0.4%)

Compiler: Compiled 96 to 63 computations (34.4% saved)

sample893.0ms (41.7%)

Algorithm

1×

intervals

Results

364.0ms

8000×

body

128

valid

Compiler

Compiled 74 to 50 computations (32.4% saved)

Details

analyze23.0ms (1.1%)

sample26.0ms (1.2%)

simplify8.0ms (0.4%)

prune2.0ms (0.1%)

localize7.0ms (0.3%)

rewrite30.0ms (1.4%)

series73.0ms (3.4%)

simplify78.0ms (3.6%)

prune22.0ms (1%)

localize3.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0.3%)

prune3.0ms (0.1%)

localize8.0ms (0.4%)

rewrite49.0ms (2.3%)

series94.0ms (4.4%)

simplify123.0ms (5.8%)

prune19.0ms (0.9%)

localize8.0ms (0.4%)

rewrite61.0ms (2.8%)

series93.0ms (4.3%)

simplify107.0ms (5%)

prune27.0ms (1.3%)

regimes332.0ms (15.5%)

bsearch35.0ms (1.6%)

simplify4.0ms (0.2%)

end8.0ms (0.4%)

sample893.0ms (41.7%)

Profiling