Details

analyze1.9s (21.6%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	74.9%	25.1%	7
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
0%	62.4%	37.6%	10
0%	62.4%	37.6%	11
0%	62.4%	37.6%	12
0%	56.2%	43.8%	13
0%	56.2%	43.8%	14

Compiler

Compiled 32 to 21 computations (34.4% saved)

sample2.3s (26.3%)

Symmetry

(sort re im)

Results

2.0s	8256×	body	128	valid
190.0ms	992×	body	128	invalid

Compiler

Compiled 63 to 41 computations (34.9% saved)

simplify103.0ms (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

prune6.0ms (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
▶	0.3b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
	33.7b	(/.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)))

Status

Error

Program

▶

0.3b

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

33.7b

(/.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)))

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)
✓	0.3b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

series778.0ms (8.9%)

Counts

2 → 60

Calls

2 calls:

766.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
12.0ms	(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)

simplify96.0ms (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

prune109.0ms (1.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	132	10	142
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	134	10	144

Error

0.0b

Counts

144 → 10

Alt Table

Status	Error	Program
▶	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
	0.7b	(log.f64 (exp.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	32.5b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 base))) (sqrt.f64 (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))))
	16.6b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	15.7b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	1.3b	(.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (cbrt.f64 (log.f64 (hypot.f64 im re)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	28.3b	(*.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 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
	1.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))

Compiler

Compiled 3000 to 1377 computations (54.1% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.3b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
✓	0.3b	(/.f64 1 (log.f64 base))

series762.0ms (8.8%)

Counts

2 → 44

Calls

2 calls:

728.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
34.0ms	(/.f64 1 (log.f64 base))

rewrite17.0ms (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:

11.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
3.0ms	(/.f64 1 (log.f64 base))

simplify111.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

453×	`div-sub_binary64`
341×	`times-frac_binary64`
294×	`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	4563	1943
5	5555	1943

prune146.0ms (1.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	186	3	189
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	190	9	199

Error

0.0b

Counts

199 → 9

Alt Table

Status	Error	Program
	32.5b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 base))) (sqrt.f64 (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))))
	0.7b	(.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)))))
▶	0.3b	(/.f64 (*.f64 (log.f64 (hypot.f64 re im)) 1) (log.f64 base))
	15.7b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	1.3b	(.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (cbrt.f64 (log.f64 (hypot.f64 im re)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	0.7b	(log.f64 (pow.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 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
	1.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))

Compiler

Compiled 3806 to 1921 computations (49.5% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.3b	(/.f64 (*.f64 (log.f64 (hypot.f64 re im)) 1) (log.f64 base))

series706.0ms (8.1%)

Counts

1 → 36

Calls

1 calls:

705.0ms

(/.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))

simplify87.0ms (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

prune89.0ms (1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	130	9	139

Error

0.0b

Counts

139 → 9

Alt Table

Status	Error	Program
	32.5b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 base))) (sqrt.f64 (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))))
▶	0.7b	(.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)))))
✓	0.3b	(/.f64 (*.f64 (log.f64 (hypot.f64 re im)) 1) (log.f64 base))
	15.7b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	1.3b	(.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (cbrt.f64 (log.f64 (hypot.f64 im re)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	0.7b	(log.f64 (pow.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 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
	1.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))

Compiler

Compiled 2832 to 1475 computations (47.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series149.0ms (1.7%)

Counts

4 → 48

Calls

4 calls:

60.0ms	(/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))
33.0ms	(cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
30.0ms	(.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))
25.0ms	(*.f64 (log.f64 base) (log.f64 base))

rewrite43.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

125×	`add-exp-log_binary64`
91×	`prod-exp_binary64`
50×	`add-cbrt-cube_binary64`
39×	`1-exp_binary64`
37×	`pow1_binary64`

Counts

4 → 149

Calls

4 calls:

12.0ms	(/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))
9.0ms	(cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
6.0ms	(.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))
4.0ms	(*.f64 (log.f64 base) (log.f64 base))

simplify162.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

734×	`times-frac_binary64`
514×	`div-sub_binary64`
409×	`fma-neg_binary64`
336×	`distribute-rgt-in_binary64`
309×	`log-prod_binary64`

Counts

197 → 186

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	126	2108
1	213	1793
2	640	1721
3	2385	1646
4	3606	1522
5	4665	1522
6	4985	1522
7	4883	1522

prune136.0ms (1.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	184	2	186
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	186	9	195

Error

Counts

195 → 9

Alt Table

Status	Error	Program
	0.9b	(.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (exp.f64 (log.f64 (*.f64 (log.f64 base) (log.f64 base)))) (log.f64 base)))))
✓	0.7b	(.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)))))
✓	0.3b	(/.f64 (*.f64 (log.f64 (hypot.f64 re im)) 1) (log.f64 base))
	1.0b	(.f64 (log.f64 (hypot.f64 re im)) (.f64 (cbrt.f64 (/.f64 (.f64 1 1) (.f64 (log.f64 base) (log.f64 base)))) (cbrt.f64 (/.f64 1 (log.f64 base)))))
	15.7b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	1.3b	(.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (cbrt.f64 (log.f64 (hypot.f64 im re)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	0.7b	(log.f64 (pow.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 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
	1.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))

Compiler

Compiled 4683 to 2222 computations (52.6% saved)

regimes849.0ms (9.8%)

Accuracy

Total 0.3b remaining (89.3%)

Threshold costs 0.3b (89.3%)

Counts

168 → 1

Compiler

Compiled 14551 to 10296 computations (29.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	10	21

end135.0ms (1.5%)

Remove: (sort re im)
Compiler: Compiled 256 to 146 computations (43% saved)

Details

analyze1.9s (21.6%)

sample2.3s (26.3%)

simplify103.0ms (1.2%)

prune6.0ms (0.1%)

localize7.0ms (0.1%)

series778.0ms (8.9%)

rewrite5.0ms (0.1%)

simplify96.0ms (1.1%)

prune109.0ms (1.3%)

localize10.0ms (0.1%)

series762.0ms (8.8%)

rewrite17.0ms (0.2%)

simplify111.0ms (1.3%)

prune146.0ms (1.7%)

localize8.0ms (0.1%)

series706.0ms (8.1%)

rewrite5.0ms (0.1%)

simplify87.0ms (1%)

prune89.0ms (1%)

localize13.0ms (0.2%)

series149.0ms (1.7%)

rewrite43.0ms (0.5%)

simplify162.0ms (1.9%)

prune136.0ms (1.6%)

regimes849.0ms (9.8%)

simplify2.0ms (0%)

end135.0ms (1.5%)

Profiling