Details

analyze679.0ms (7.3%)

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)

sample2.1s (22.1%)

Symmetry

(sort re im)

Results

1.8s	8256×	body	128	valid
190.0ms	1004×	body	128	invalid

Compiler

Compiled 95 to 62 computations (34.7% saved)

simplify93.0ms (1%)

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%)

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
	33.3b	(/.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

33.3b

(/.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 1 expressions with local error:

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

series526.0ms (5.6%)

Counts

1 → 36

Calls

1 calls:

526.0ms

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

rewrite42.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

713×	`log1p-expm1-u_binary64`
713×	`expm1-log1p-u_binary64`
145×	`expm1-udef_binary64`
145×	`log1p-udef_binary64`
80×	`add-sqr-sqrt_binary64`

Counts

1 → 34

Calls

1 calls:

41.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	156	11
2	1874	11
3	5030	11
0	0	0
1	0	0

simplify70.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

890×	`fma-neg_binary64`
428×	`associate-/l/_binary64`
294×	`times-frac_binary64`
277×	`div-sub_binary64`
222×	`fma-def_binary64`

Counts

70 → 77

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	96	1148
1	263	1052
2	690	1012
3	2594	992
4	4861	992
5	5436	992

prune54.0ms (0.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	69	8	77
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	69	10	79

Error

0.0b

Counts

79 → 10

Alt Table

Status	Error	Program
▶	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
	0.6b	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base))))
	33.3b	(/.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)))
	0.6b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 3))
	21.6b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))) 1)
	35.2b	(pow.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 3) 1/3)
	17.0b	(*.f64 (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 base))))
✓	0.4b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
	1.2b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) 2) (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	1.2b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) 2) 1) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (log.f64 base)))

Compiler

Compiled 1832 to 937 computations (48.9% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series536.0ms (5.7%)

Counts

2 → 44

Calls

2 calls:

505.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
31.0ms	(/.f64 1 (log.f64 base))

rewrite44.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

782×	`log1p-expm1-u_binary64`
782×	`expm1-log1p-u_binary64`
93×	`add-sqr-sqrt_binary64`
88×	`add-log-exp_binary64`
86×	`add-exp-log_binary64`

Counts

2 → 50

Calls

2 calls:

43.0ms	(/.f64 1 (log.f64 base))
43.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	192	17
2	2095	17
3	4978	17
0	0	0
1	0	0

simplify69.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

890×	`fma-neg_binary64`
428×	`associate-/l/_binary64`
294×	`times-frac_binary64`
277×	`div-sub_binary64`
222×	`fma-def_binary64`

Counts

94 → 95

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	1212
1	265	1116
2	692	1060
3	2596	1040
4	4862	1040
5	5437	1040

prune64.0ms (0.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	94	11	105

Error

0.0b

Counts

105 → 11

Alt Table

Status	Error	Program
✓	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
	0.6b	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base))))
	21.6b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))) 1)
	1.2b	(.f64 (log.f64 (hypot.f64 re im)) (.f64 (pow.f64 (pow.f64 (cbrt.f64 (log.f64 base)) 2) -1) (pow.f64 (cbrt.f64 (log.f64 base)) -1)))
	33.3b	(/.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)))
▶	0.6b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 3))
	35.2b	(pow.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 3) 1/3)
	17.0b	(*.f64 (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 base))))
✓	0.4b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
	1.2b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) 2) (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	1.2b	(/.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) 2) (/.f64 (log.f64 base) (cbrt.f64 (log.f64 (hypot.f64 re im)))))

Compiler

Compiled 2025 to 1067 computations (47.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.4b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
✓	0.5b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 3))
✓	0.7b	(pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 3)

series1.3s (13.5%)

Counts

2 → 72

Calls

2 calls:

694.0ms	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 3))
564.0ms	(pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 3)

rewrite56.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

904×	`log1p-expm1-u_binary64`
904×	`expm1-log1p-u_binary64`
99×	`add-sqr-sqrt_binary64`
95×	`add-log-exp_binary64`
94×	`add-exp-log_binary64`

Counts

2 → 84

Calls

2 calls:

54.0ms	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 3))
54.0ms	(pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	206	25
2	2365	25
3	5639	25
0	0	0
1	0	0

simplify316.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

500×	`times-frac_binary64`
374×	`associate-/r*_binary64`
325×	`fma-neg_binary64`
259×	`sub-neg_binary64`
251×	`associate-/l*_binary64`

Counts

156 → 188

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	284	3710
1	1006	3418
2	4289	3414
3	5010	3414

prune201.0ms (2.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	262	3	265
Fresh	3	5	8
Picked	0	1	1
Done	0	2	2
Total	265	11	276

Error

0.0b

Counts

276 → 11

Alt Table

Status	Error	Program
✓	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
▶	0.6b	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base))))
	21.6b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))) 1)
	1.2b	(.f64 (log.f64 (hypot.f64 re im)) (.f64 (pow.f64 (pow.f64 (cbrt.f64 (log.f64 base)) 2) -1) (pow.f64 (cbrt.f64 (log.f64 base)) -1)))
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) 2) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	0.6b	(cbrt.f64 (/.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 2) (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))))
	33.3b	(/.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)))
✓	0.6b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 3))
	0.7b	(*.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (pow.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 2) 1/3))
✓	0.4b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
	1.2b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) 2) (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))

Compiler

Compiled 7551 to 4226 computations (44% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.3b	(/.f64 1 (log.f64 base))
✓	0.5b	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base))))
✓	0.5b	(pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base)))

series2.2s (23.7%)

Counts

2 → 72

Calls

2 calls:

1.4s	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base))))
820.0ms	(pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base)))

rewrite48.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

792×	`log1p-expm1-u_binary64`
792×	`expm1-log1p-u_binary64`
96×	`add-sqr-sqrt_binary64`
90×	`add-log-exp_binary64`
89×	`add-exp-log_binary64`

Counts

2 → 47

Calls

2 calls:

47.0ms	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base))))
47.0ms	(pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	195	23
2	2115	23
3	4984	23
0	0	0
1	0	0

simplify138.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

553×	`cancel-sign-sub-inv_binary64`
414×	`unswap-sqr_binary64`
340×	`fma-neg_binary64`
330×	`times-frac_binary64`
282×	`associate-/r*_binary64`

Counts

119 → 135

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	262	3852
1	941	3642
2	3914	3502
3	4348	3486
4	4901	3486
5	4852	3486

prune129.0ms (1.4%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	160	1	161
Fresh	2	5	7
Picked	0	1	1
Done	0	3	3
Total	162	10	172

Error

Counts

172 → 10

Alt Table

Status	Error	Program
✓	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
✓	0.6b	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base))))
	21.6b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))) 1)
	1.2b	(.f64 (log.f64 (hypot.f64 re im)) (.f64 (pow.f64 (pow.f64 (cbrt.f64 (log.f64 base)) 2) -1) (pow.f64 (cbrt.f64 (log.f64 base)) -1)))
	0.6b	(cbrt.f64 (/.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 2) (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))))
	33.3b	(/.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)))
✓	0.6b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 3))
	0.7b	(*.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (pow.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 2) 1/3))
✓	0.4b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
	1.6b	(log.f64 (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base)))) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base)))) 2)))

Compiler

Compiled 4892 to 2785 computations (43.1% saved)

regimes561.0ms (6%)

Accuracy

Total 0.3b remaining (85.6%)

Threshold costs 0.3b (85.6%)

Counts

111 → 1

Compiler

Compiled 9696 to 6901 computations (28.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	8	11

end143.0ms (1.5%)

Remove: (sort re im)
Compiler: Compiled 222 to 151 computations (32% saved)

Details

analyze679.0ms (7.3%)

sample2.1s (22.1%)

simplify93.0ms (1%)

prune5.0ms (0%)

localize7.0ms (0.1%)

series526.0ms (5.6%)

rewrite42.0ms (0.5%)

simplify70.0ms (0.7%)

prune54.0ms (0.6%)

localize8.0ms (0.1%)

series536.0ms (5.7%)

rewrite44.0ms (0.5%)

simplify69.0ms (0.7%)

prune64.0ms (0.7%)

localize9.0ms (0.1%)

series1.3s (13.5%)

rewrite56.0ms (0.6%)

simplify316.0ms (3.4%)

prune201.0ms (2.1%)

localize9.0ms (0.1%)

series2.2s (23.7%)

rewrite48.0ms (0.5%)

simplify138.0ms (1.5%)

prune129.0ms (1.4%)

regimes561.0ms (6%)

simplify2.0ms (0%)

end143.0ms (1.5%)

Profiling