Details

analyze493.0ms (6.1%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
23.4%	51.5%	25.1%	7
24.2%	50.7%	25.1%	8
24.6%	50.3%	25.1%	9
36.9%	25.5%	37.6%	10
37.2%	25.3%	37.6%	11
37.3%	25.1%	37.6%	12
43.5%	12.7%	43.8%	13
43.6%	12.6%	43.8%	14

Compiler

Compiled 32 to 21 computations (34.4% saved)

sample1.7s (21.6%)

Infinites

0% of outputs are infinite.

Symmetry

(sort re im)

Results

1.4s	8256×	body	128	valid
183.0ms	1081×	body	128	invalid

Compiler

Compiled 95 to 62 computations (34.7% saved)

simplify99.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

666×	`fma-def_binary64`
620×	`associate-/l/_binary64`
557×	`cube-prod_binary64`
533×	`sqr-pow_binary64`
502×	`pow-sqr_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	22
1	28	21
2	34	21
3	45	14
4	62	11
5	65	11
6	176	11
7	479	11
8	769	11
9	839	11
10	1233	11
11	1523	11
12	2341	11
13	3455	11
14	4399	11
15	4874	11
16	4872	11

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	29.4b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
▶	0.4b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

Status

Error

Program

29.4b

(/.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) (log.f64 base)) (*.f64 (atan2.f64 im re) 0)) (+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 0 0)))

▶

0.4b

(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

Compiler

Compiled 120 to 77 computations (35.8% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 re im)
✓	0.4b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

series637.0ms (7.9%)

Counts

2 → 60

Calls

2 calls:

620.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
17.0ms	(hypot.f64 re im)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`times-frac_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
12×	`pow1_binary64`

Counts

2 → 48

Calls

2 calls:

3.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
0.0ms	(hypot.f64 re im)

simplify86.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

787×	`times-frac_binary64`
599×	`fma-neg_binary64`
441×	`associate-/r*_binary64`
410×	`associate-/l*_binary64`
341×	`fma-def_binary64`

Counts

108 → 142

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	194	2481
1	484	2312
2	1291	2236
3	4583	2236
4	4984	2236

prune98.0ms (1.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	130	12	142
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	131	13	144

Error

0.0b

Counts

144 → 13

Alt Table

Status	Error	Program
	36.0b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	29.4b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
	1.3b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base)))
	44.5b	(exp.f64 (-.f64 (log.f64 (log.f64 (hypot.f64 re im))) (log.f64 (log.f64 base))))
	0.9b	(log.f64 (exp.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	1.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (log.f64 base))))
	15.4b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	1.2b	(/.f64 (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (/.f64 (log.f64 base) (cbrt.f64 (log.f64 (hypot.f64 re im)))))
▶	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
	0.5b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
	33.8b	(*.f64 (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	0.6b	(cbrt.f64 (/.f64 (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
	0.7b	(cbrt.f64 (.f64 (.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))

Compiler

Compiled 3112 to 1457 computations (53.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.2b	(/.f64 1 (log.f64 base))
✓	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))

series651.0ms (8.1%)

Counts

2 → 44

Calls

2 calls:

617.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
33.0ms	(/.f64 1 (log.f64 base))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
26×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
16×	`associate-r_binary64`

Counts

2 → 79

Calls

2 calls:

6.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
2.0ms	(/.f64 1 (log.f64 base))

simplify101.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

453×	`div-sub_binary64`
341×	`times-frac_binary64`
295×	`associate-/l*_binary64`
248×	`fma-def_binary64`
229×	`sub-neg_binary64`

Counts

123 → 141

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	2246
1	382	1983
2	984	1943
3	3458	1943
4	4757	1943
5	5751	1943

prune157.0ms (1.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	181	8	189
Fresh	8	4	12
Picked	1	0	1
Done	0	0	0
Total	190	12	202

Error

0.0b

Counts

202 → 12

Alt Table

Status	Error	Program
	0.8b	(*.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
	1.3b	(.f64 (/.f64 (log.f64 (hypot.f64 im re)) (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 1 (cbrt.f64 (log.f64 base))))
	0.6b	(cbrt.f64 (/.f64 (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
	0.4b	(.f64 (log.f64 (.f64 (*.f64 (cbrt.f64 (hypot.f64 im re)) (cbrt.f64 (hypot.f64 im re))) (cbrt.f64 (hypot.f64 im re)))) (/.f64 1 (log.f64 base)))
	0.9b	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
	36.0b	(.f64 (log.f64 (hypot.f64 re im)) (.f64 (sqrt.f64 (/.f64 1 (log.f64 base))) (sqrt.f64 (/.f64 1 (log.f64 base)))))
	0.8b	(.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))
	0.5b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
	1.2b	(.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 1 (log.f64 base))))
▶	0.4b	(/.f64 (*.f64 (log.f64 (hypot.f64 re im)) 1) (log.f64 base))
	33.8b	(*.f64 (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	0.7b	(cbrt.f64 (.f64 (.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))

Compiler

Compiled 3920 to 2001 computations (49% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.4b	(/.f64 (*.f64 (log.f64 (hypot.f64 re im)) 1) (log.f64 base))

series783.0ms (9.7%)

Counts

1 → 36

Calls

1 calls:

783.0ms

(/.f64 (*.f64 (log.f64 (hypot.f64 re im)) 1) (log.f64 base))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-exp-log_binary64`
6×	`add-cbrt-cube_binary64`
4×	`associate-/r*_binary64`
4×	`times-frac_binary64`
3×	`*-un-lft-identity_binary64`

Counts

1 → 26

Calls

1 calls:

4.0ms

(/.f64 (*.f64 (log.f64 (hypot.f64 re im)) 1) (log.f64 base))

simplify86.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

547×	`div-sub_binary64`
410×	`times-frac_binary64`
329×	`associate-/l*_binary64`
245×	`fma-def_binary64`
237×	`associate-/r*_binary64`

Counts

62 → 82

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	143	1568
1	340	1403
2	895	1363
3	3308	1342
4	4660	1342
5	5904	1342

prune94.0ms (1.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	131	11	142

Error

0.0b

Counts

142 → 11

Alt Table

Status	Error	Program
	0.8b	(*.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
	1.3b	(.f64 (/.f64 (log.f64 (hypot.f64 im re)) (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 1 (cbrt.f64 (log.f64 base))))
	0.5b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
	15.4b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))))
	0.6b	(cbrt.f64 (/.f64 (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
▶	0.4b	(.f64 (log.f64 (.f64 (*.f64 (cbrt.f64 (hypot.f64 im re)) (cbrt.f64 (hypot.f64 im re))) (cbrt.f64 (hypot.f64 im re)))) (/.f64 1 (log.f64 base)))
	0.9b	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
	1.2b	(.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 1 (log.f64 base))))
✓	0.4b	(/.f64 (*.f64 (log.f64 (hypot.f64 re im)) 1) (log.f64 base))
	33.8b	(*.f64 (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	0.7b	(cbrt.f64 (.f64 (.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))

Compiler

Compiled 2886 to 1513 computations (47.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (hypot.f64 im re)) (cbrt.f64 (hypot.f64 im re))) (cbrt.f64 (hypot.f64 im re)))
✓	0.4b	(.f64 (log.f64 (.f64 (*.f64 (cbrt.f64 (hypot.f64 im re)) (cbrt.f64 (hypot.f64 im re))) (cbrt.f64 (hypot.f64 im re)))) (/.f64 1 (log.f64 base)))
✓	0.5b	(*.f64 (cbrt.f64 (hypot.f64 im re)) (cbrt.f64 (hypot.f64 im re)))
✓	0.6b	(cbrt.f64 (hypot.f64 im re))

series765.0ms (9.5%)

Counts

4 → 108

Calls

4 calls:

668.0ms	(.f64 (log.f64 (.f64 (*.f64 (cbrt.f64 (hypot.f64 im re)) (cbrt.f64 (hypot.f64 im re))) (cbrt.f64 (hypot.f64 im re)))) (/.f64 1 (log.f64 base)))
43.0ms	(*.f64 (cbrt.f64 (hypot.f64 im re)) (cbrt.f64 (hypot.f64 im re)))
37.0ms	(cbrt.f64 (hypot.f64 im re))
17.0ms	(.f64 (.f64 (cbrt.f64 (hypot.f64 im re)) (cbrt.f64 (hypot.f64 im re))) (cbrt.f64 (hypot.f64 im re)))

rewrite38.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`pow1_binary64`
41×	`add-sqr-sqrt_binary64`
28×	`associate-r_binary64`
25×	`associate-l_binary64`
25×	`*-un-lft-identity_binary64`

Counts

4 → 149

Calls

4 calls:

14.0ms	(.f64 (log.f64 (.f64 (*.f64 (cbrt.f64 (hypot.f64 im re)) (cbrt.f64 (hypot.f64 im re))) (cbrt.f64 (hypot.f64 im re)))) (/.f64 1 (log.f64 base)))
8.0ms	(.f64 (.f64 (cbrt.f64 (hypot.f64 im re)) (cbrt.f64 (hypot.f64 im re))) (cbrt.f64 (hypot.f64 im re)))
5.0ms	(*.f64 (cbrt.f64 (hypot.f64 im re)) (cbrt.f64 (hypot.f64 im re)))
1.0ms	(cbrt.f64 (hypot.f64 im re))

simplify164.0ms (2%)

Algorithm

1×	egg-herbie

Rules

790×	`times-frac_binary64`
689×	`fma-neg_binary64`
230×	`associate-r_binary64`
207×	`associate-l_binary64`
189×	`unswap-sqr_binary64`

Counts

257 → 328

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	377	5395
1	1001	4956
2	2918	4759
3	4979	4743
4	5355	4743

prune392.0ms (4.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	434	4	438
Fresh	4	5	9
Picked	1	0	1
Done	0	1	1
Total	439	10	449

Error

Counts

449 → 10

Alt Table

Status	Error	Program
	0.5b	(.f64 (log.f64 (exp.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (hypot.f64 im re)) (cbrt.f64 (hypot.f64 im re)))) (log.f64 (cbrt.f64 (hypot.f64 im re)))))) (/.f64 1 (log.f64 base)))
	1.2b	(.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 1 (log.f64 base))))
	33.8b	(*.f64 (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	0.6b	(.f64 1/3 (/.f64 (.f64 3 (log.f64 (hypot.f64 re im))) (log.f64 base)))
	0.5b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
✓	0.4b	(/.f64 (*.f64 (log.f64 (hypot.f64 re im)) 1) (log.f64 base))
	0.9b	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
	0.5b	(*.f64 3 (/.f64 (log.f64 (cbrt.f64 (hypot.f64 re im))) (log.f64 base)))
	0.5b	(.f64 3 (.f64 (log.f64 (cbrt.f64 (hypot.f64 im re))) (/.f64 1 (log.f64 base))))
	0.7b	(cbrt.f64 (.f64 (.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))

Compiler

Compiled 12308 to 5451 computations (55.7% saved)

regimes1.5s (18.5%)

Accuracy

Total 0.3b remaining (91.8%)

Threshold costs 0.3b (91.8%)

Counts

261 → 1

Compiler

Compiled 26326 to 16836 computations (36% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	13	11
2	12	11

end132.0ms (1.6%)

Remove: (sort re im)
Compiler: Compiled 216 to 134 computations (38% saved)

Details

analyze493.0ms (6.1%)

sample1.7s (21.6%)

simplify99.0ms (1.2%)

prune5.0ms (0.1%)

localize7.0ms (0.1%)

series637.0ms (7.9%)

rewrite5.0ms (0.1%)

simplify86.0ms (1.1%)

prune98.0ms (1.2%)

localize8.0ms (0.1%)

series651.0ms (8.1%)

rewrite18.0ms (0.2%)

simplify101.0ms (1.2%)

prune157.0ms (1.9%)

localize8.0ms (0.1%)

series783.0ms (9.7%)

rewrite5.0ms (0.1%)

simplify86.0ms (1.1%)

prune94.0ms (1.2%)

localize13.0ms (0.2%)

series765.0ms (9.5%)

rewrite38.0ms (0.5%)

simplify164.0ms (2%)

prune392.0ms (4.8%)

regimes1.5s (18.5%)

simplify2.0ms (0%)

end132.0ms (1.6%)

Profiling