Details

analyze547.0ms (5.4%)

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 (21.3%)

Symmetry

(sort re im)

Results

1.8s	8256×	body	128	valid
248.0ms	1035×	body	128	invalid

Compiler

Compiled 95 to 62 computations (34.7% saved)

simplify92.0ms (0.9%)

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
	34.7b	(/.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)))
▶	0.3b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

Status

Error

Program

34.7b

(/.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)))

▶

0.3b

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

series757.0ms (7.5%)

Counts

2 → 60

Calls

2 calls:

741.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
15.0ms	(hypot.f64 re im)

rewrite49.0ms (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

2 → 54

Calls

2 calls:

48.0ms	(hypot.f64 re im)
48.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	156	15
2	1874	15
3	5030	15
0	0	0
1	0	0

simplify71.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

779×	`fma-neg_binary64`
762×	`times-frac_binary64`
408×	`associate-/r*_binary64`
365×	`associate-/l*_binary64`
340×	`fma-def_binary64`

Counts

114 → 129

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	133	1684
1	392	1570
2	1116	1490
3	4752	1490
4	5342	1490

prune102.0ms (1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	116	13	129
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	117	14	131

Error

0.0b

Counts

131 → 14

Alt Table

Status	Error	Program
	1.3b	(/.f64 (log.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) 2)) (cbrt.f64 (log.f64 (hypot.f64 re im))))) (log.f64 base))
	0.6b	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base))))
	44.8b	(/.f64 (log.f64 (pow.f64 (pow.f64 (hypot.f64 re im) 3) 1/3)) (log.f64 base))
	34.7b	(/.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)))
	16.0b	(/.f64 (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 (hypot.f64 re im)))) (sqrt.f64 (log.f64 (hypot.f64 re im))))) (log.f64 base))
	19.8b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))) 1)
	0.4b	(pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) -1)
▶	0.3b	(/.f64 (log.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 3)) (log.f64 base))
	16.5b	(*.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))))
	1.3b	(*.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 1 (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (/.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (log.f64 base))))
	1.3b	(*.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (pow.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) 2))
	0.6b	(cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (pow.f64 (log.f64 base) 3)))
	0.7b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 3))

Compiler

Compiled 2828 to 1522 computations (46.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.3b	(/.f64 (log.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 3)) (log.f64 base))
✓	0.6b	(cbrt.f64 (hypot.f64 re im))
✓	0.8b	(pow.f64 (cbrt.f64 (hypot.f64 re im)) 3)

series1.8s (18%)

Counts

3 → 84

Calls

3 calls:

1.7s	(/.f64 (log.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 3)) (log.f64 base))
69.0ms	(pow.f64 (cbrt.f64 (hypot.f64 re im)) 3)
40.0ms	(cbrt.f64 (hypot.f64 re im))

rewrite58.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

3 → 81

Calls

3 calls:

56.0ms	(/.f64 (log.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 3)) (log.f64 base))
56.0ms	(cbrt.f64 (hypot.f64 re im))
56.0ms	(pow.f64 (cbrt.f64 (hypot.f64 re im)) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	205	21
2	2360	21
3	5613	21
0	0	0
1	0	0

simplify381.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

762×	`times-frac_binary64`
637×	`fma-def_binary64`
355×	`associate-/l*_binary64`
353×	`fma-neg_binary64`
298×	`cancel-sign-sub-inv_binary64`

Counts

165 → 179

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	2418
1	586	2294
2	1746	2202
3	4787	2202
4	4946	2202
5	4950	2202

prune173.0ms (1.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	225	5	230
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	232	12	244

Error

Counts

244 → 12

Alt Table

Status	Error	Program
	34.3b	(*.f64 (/.f64 3 (sqrt.f64 (log.f64 base))) (/.f64 (log.f64 (cbrt.f64 (hypot.f64 re im))) (sqrt.f64 (log.f64 base))))
	33.9b	(/.f64 (log.f64 (pow.f64 (pow.f64 im 1/3) 3)) (log.f64 base))
	1.3b	(/.f64 (log.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) 2)) (cbrt.f64 (log.f64 (hypot.f64 re im))))) (log.f64 base))
	0.6b	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base))))
	1.2b	(*.f64 (/.f64 3 (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (/.f64 (log.f64 (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 base))))
▶	0.4b	(pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) -1)
	32.4b	(fma.f64 1/2 (/.f64 (.f64 im im) (.f64 (*.f64 re re) (log.f64 base))) (/.f64 (log.f64 (neg.f64 re)) (log.f64 base)))
	1.3b	(*.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (pow.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) 2))
	34.7b	(/.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)))
	0.4b	(/.f64 (log.f64 (pow.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (hypot.f64 re im)))) 3)) (log.f64 base))
	0.6b	(cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (pow.f64 (log.f64 base) 3)))
	16.0b	(/.f64 (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 (hypot.f64 re im)))) (sqrt.f64 (log.f64 (hypot.f64 re im))))) (log.f64 base))

Compiler

Compiled 4819 to 2761 computations (42.7% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series1.8s (17.5%)

Counts

2 → 72

Calls

2 calls:

1.0s	(pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) -1)
750.0ms	(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))

rewrite61.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

861×	`log1p-expm1-u_binary64`
861×	`expm1-log1p-u_binary64`
99×	`add-sqr-sqrt_binary64`
93×	`add-log-exp_binary64`
92×	`add-exp-log_binary64`

Counts

2 → 76

Calls

2 calls:

59.0ms	(pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) -1)
59.0ms	(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	198	22
2	2262	22
3	5438	22
0	0	0
1	0	0

simplify100.0ms (1%)

Algorithm

1×	egg-herbie

Rules

472×	`fma-neg_binary64`
465×	`times-frac_binary64`
386×	`associate-/r*_binary64`
284×	`associate-/l*_binary64`
248×	`fma-def_binary64`

Counts

148 → 179

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	352	3790
1	1222	3520
2	4786	3520
3	5188	3520

prune198.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	226	4	230
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	232	10	242

Error

Counts

242 → 10

Alt Table

Status	Error	Program
	16.6b	(pow.f64 (expm1.f64 (log1p.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))) -1)
	1.2b	(*.f64 (/.f64 3 (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (/.f64 (log.f64 (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 base))))
	32.4b	(fma.f64 1/2 (/.f64 (.f64 im im) (.f64 (*.f64 re re) (log.f64 base))) (/.f64 (log.f64 (neg.f64 re)) (log.f64 base)))
	1.3b	(*.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (pow.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) 2))
	34.3b	(*.f64 (/.f64 3 (sqrt.f64 (log.f64 base))) (/.f64 (log.f64 (cbrt.f64 (hypot.f64 re im))) (sqrt.f64 (log.f64 base))))
	0.7b	(pow.f64 (log.f64 (pow.f64 base (/.f64 1 (log.f64 (hypot.f64 re im))))) -1)
	2.2b	(pow.f64 (log1p.f64 (expm1.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))) -1)
	0.4b	(/.f64 (log.f64 (pow.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (hypot.f64 re im)))) 3)) (log.f64 base))
▶	0.4b	(*.f64 (/.f64 1 (neg.f64 (log.f64 base))) (neg.f64 (log.f64 (hypot.f64 re im))))
	0.6b	(cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (pow.f64 (log.f64 base) 3)))

Compiler

Compiled 6775 to 3847 computations (43.2% 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 1 (neg.f64 (log.f64 base)))
✓	0.4b	(*.f64 (/.f64 1 (neg.f64 (log.f64 base))) (neg.f64 (log.f64 (hypot.f64 re im))))

series714.0ms (7.1%)

Counts

2 → 48

Calls

2 calls:

679.0ms	(*.f64 (/.f64 1 (neg.f64 (log.f64 base))) (neg.f64 (log.f64 (hypot.f64 re im))))
34.0ms	(/.f64 1 (neg.f64 (log.f64 base)))

rewrite56.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

817×	`log1p-expm1-u_binary64`
817×	`expm1-log1p-u_binary64`
114×	`add-sqr-sqrt_binary64`
106×	`add-log-exp_binary64`
105×	`add-exp-log_binary64`

Counts

2 → 51

Calls

2 calls:

55.0ms	(/.f64 1 (neg.f64 (log.f64 base)))
55.0ms	(*.f64 (/.f64 1 (neg.f64 (log.f64 base))) (neg.f64 (log.f64 (hypot.f64 re im))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	23
1	238	17
2	2193	17
3	5091	17
0	0	0
1	0	0

simplify71.0ms (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

99 → 96

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	99	1220
1	266	1124
2	693	1084
3	2597	1064
4	4863	1064
5	5437	1064

prune88.0ms (0.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	147	10	157

Error

Counts

157 → 10

Alt Table

Status	Error	Program
	16.6b	(pow.f64 (expm1.f64 (log1p.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))) -1)
	1.2b	(*.f64 (/.f64 3 (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (/.f64 (log.f64 (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 base))))
	32.4b	(fma.f64 1/2 (/.f64 (.f64 im im) (.f64 (*.f64 re re) (log.f64 base))) (/.f64 (log.f64 (neg.f64 re)) (log.f64 base)))
	1.3b	(*.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (pow.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) 2))
	34.3b	(*.f64 (/.f64 3 (sqrt.f64 (log.f64 base))) (/.f64 (log.f64 (cbrt.f64 (hypot.f64 re im))) (sqrt.f64 (log.f64 base))))
	0.7b	(pow.f64 (log.f64 (pow.f64 base (/.f64 1 (log.f64 (hypot.f64 re im))))) -1)
	2.2b	(pow.f64 (log1p.f64 (expm1.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))) -1)
	0.4b	(/.f64 (log.f64 (pow.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (hypot.f64 re im)))) 3)) (log.f64 base))
✓	0.4b	(*.f64 (/.f64 1 (neg.f64 (log.f64 base))) (neg.f64 (log.f64 (hypot.f64 re im))))
	0.6b	(cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (pow.f64 (log.f64 base) 3)))

Compiler

Compiled 2871 to 1537 computations (46.5% saved)

regimes640.0ms (6.3%)

Accuracy

Total 0.3b remaining (87.1%)

Threshold costs 0.3b (87.1%)

Counts

131 → 1

Compiler

Compiled 9801 to 7241 computations (26.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	26
1	13	26

end151.0ms (1.5%)

Remove: (sort re im)
Compiler: Compiled 243 to 166 computations (31.7% saved)

Details

analyze547.0ms (5.4%)

sample2.1s (21.3%)

simplify92.0ms (0.9%)

prune5.0ms (0%)

localize7.0ms (0.1%)

series757.0ms (7.5%)

rewrite49.0ms (0.5%)

simplify71.0ms (0.7%)

prune102.0ms (1%)

localize9.0ms (0.1%)

series1.8s (18%)

rewrite58.0ms (0.6%)

simplify381.0ms (3.8%)

prune173.0ms (1.7%)

localize8.0ms (0.1%)

series1.8s (17.5%)

rewrite61.0ms (0.6%)

simplify100.0ms (1%)

prune198.0ms (2%)

localize10.0ms (0.1%)

series714.0ms (7.1%)

rewrite56.0ms (0.6%)

simplify71.0ms (0.7%)

prune88.0ms (0.9%)

regimes640.0ms (6.3%)

simplify2.0ms (0%)

end151.0ms (1.5%)

Profiling