Details

analyze631.0ms (8.2%)

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)

sample1.9s (24.5%)

Symmetry

(sort re im)

Results

1.6s	8256×	body	128	valid
217.0ms	1114×	body	128	invalid

Compiler

Compiled 95 to 62 computations (34.7% saved)

simplify38.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

567×	`associate-/l/_binary64`
526×	`cube-prod_binary64`
434×	`times-frac_binary64`
365×	`sqr-pow_binary64`
291×	`pow-sqr_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	22
1	31	21
2	38	21
3	49	14
4	66	11
5	75	11
6	218	11
7	1196	11
8	1804	11
9	2015	11
10	2509	11
11	2992	11
12	3869	11

Stop Event

1×	node limit

Counts

1 → 2

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
▶	0.3b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
	33.6b	(/.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))

33.6b

(/.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 1 expressions with local error:

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

series515.0ms (6.7%)

Counts

1 → 36

Calls

1 calls:

514.0ms

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

rewrite40.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	158	11
2	1965	11

Stop Event

1×	node limit

Counts

1 → 33

Calls

1 calls:

39.0ms

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

simplify41.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

890×	`fma-neg_binary64`
294×	`times-frac_binary64`
219×	`sub-neg_binary64`
210×	`fma-def_binary64`
198×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	96	1148
1	263	1052
2	730	1012
3	3018	992

Stop Event

1×	node limit

Counts

69 → 76

prune62.0ms (0.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	65	11	76
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	66	12	78

Error

0.0b

Counts

78 → 12

Alt Table

Status	Error	Program
✓	0.3b	(/.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))))
	0.9b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	14.9b	(.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 1 (log.f64 base))))
	0.6b	(cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (pow.f64 (log.f64 base) 3)))
	1.3b	(.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) 2) (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 1 (log.f64 base))))
	0.6b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 3))
▶	0.4b	(pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) -1)
	32.4b	(pow.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 3) 1/3)
	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))))
	1.3b	(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (/.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (log.f64 base))))
	18.3b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))

Compiler

Compiled 1841 to 977 computations (46.9% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series1.2s (15%)

Counts

2 → 72

Calls

2 calls:

600.0ms	(pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) -1)
558.0ms	(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))

rewrite50.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	200	22
2	2429	22

Stop Event

1×	node limit

Counts

2 → 76

Calls

2 calls:

49.0ms	(pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) -1)
49.0ms	(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))

simplify52.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

465×	`times-frac_binary64`
386×	`associate-/r*_binary64`
283×	`associate-/l*_binary64`
248×	`fma-def_binary64`
193×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	352	3790
1	1280	3520

Stop Event

1×	node limit

Counts

148 → 179

prune168.0ms (2.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	176	3	179
Fresh	3	7	10
Picked	1	0	1
Done	1	0	1
Total	181	10	191

Error

Counts

191 → 10

Alt Table

Status	Error	Program
	0.9b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	14.9b	(.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 1 (log.f64 base))))
	0.6b	(cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (pow.f64 (log.f64 base) 3)))
	1.3b	(.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) 2) (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 1 (log.f64 base))))
	0.7b	(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (log.f64 base) 3) (pow.f64 (log.f64 (hypot.f64 re im)) 3))) -1)
	0.6b	(pow.f64 (log.f64 (pow.f64 base (/.f64 1 (log.f64 (hypot.f64 re im))))) -1)
	32.4b	(pow.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 3) 1/3)
	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))))
▶	0.4b	(*.f64 (/.f64 1 (log.f64 base)) (log.f64 (hypot.f64 re im)))
	18.3b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))

Compiler

Compiled 5854 to 3321 computations (43.3% 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 (/.f64 1 (log.f64 base)) (log.f64 (hypot.f64 re im)))

series518.0ms (6.7%)

Counts

2 → 44

Calls

2 calls:

486.0ms	(*.f64 (/.f64 1 (log.f64 base)) (log.f64 (hypot.f64 re im)))
32.0ms	(/.f64 1 (log.f64 base))

rewrite43.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

779×	`log1p-expm1-u_binary64`
779×	`expm1-log1p-u_binary64`
94×	`add-sqr-sqrt_binary64`
87×	`add-log-exp_binary64`
86×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	192	17
2	2224	17

Stop Event

1×	node limit

Counts

2 → 49

Calls

2 calls:

42.0ms	(/.f64 1 (log.f64 base))
42.0ms	(*.f64 (/.f64 1 (log.f64 base)) (log.f64 (hypot.f64 re im)))

simplify42.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

890×	`fma-neg_binary64`
294×	`times-frac_binary64`
217×	`sub-neg_binary64`
210×	`fma-def_binary64`
199×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	1212
1	265	1116
2	732	1060
3	3016	1040

Stop Event

1×	node limit

Counts

93 → 94

prune64.0ms (0.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	94	10	104

Error

Counts

104 → 10

Alt Table

Status	Error	Program
	0.9b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	14.9b	(.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 1 (log.f64 base))))
▶	0.6b	(cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (pow.f64 (log.f64 base) 3)))
	1.3b	(.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) 2) (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 1 (log.f64 base))))
	0.7b	(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (log.f64 base) 3) (pow.f64 (log.f64 (hypot.f64 re im)) 3))) -1)
	0.6b	(pow.f64 (log.f64 (pow.f64 base (/.f64 1 (log.f64 (hypot.f64 re im))))) -1)
	32.4b	(pow.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 3) 1/3)
	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))))
✓	0.4b	(*.f64 (/.f64 1 (log.f64 base)) (log.f64 (hypot.f64 re im)))
	18.3b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))

Compiler

Compiled 1960 to 1057 computations (46.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (pow.f64 (log.f64 base) 3))
✓	0.5b	(cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (pow.f64 (log.f64 base) 3)))
✓	0.7b	(pow.f64 (log.f64 (hypot.f64 re im)) 3)
✓	0.7b	(pow.f64 (log.f64 base) 3)

series1.2s (15.2%)

Counts

4 → 104

Calls

4 calls:

602.0ms	(/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (pow.f64 (log.f64 base) 3))
499.0ms	(cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (pow.f64 (log.f64 base) 3)))
43.0ms	(pow.f64 (log.f64 (hypot.f64 re im)) 3)
28.0ms	(pow.f64 (log.f64 base) 3)

rewrite63.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

558×	`log-prod_binary64`
199×	`expm1-udef_binary64`
199×	`log1p-udef_binary64`
193×	`log-pow_binary64`
137×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	43
1	243	40
2	2927	40

Stop Event

1×	node limit

Counts

4 → 137

Calls

4 calls:

60.0ms	(/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (pow.f64 (log.f64 base) 3))
60.0ms	(cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (pow.f64 (log.f64 base) 3)))
60.0ms	(pow.f64 (log.f64 (hypot.f64 re im)) 3)
60.0ms	(pow.f64 (log.f64 base) 3)

simplify73.0ms (1%)

Algorithm

1×	egg-herbie

Rules

600×	`times-frac_binary64`
433×	`associate-/r*_binary64`
366×	`associate-/l*_binary64`
325×	`fma-def_binary64`
198×	`associate-*r/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	403	5298
1	1414	4954

Stop Event

1×	node limit

Counts

241 → 288

prune245.0ms (3.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	288	0	288
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	288	10	298

Error

Counts

298 → 10

Alt Table

Status	Error	Program
	0.9b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	14.9b	(.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 1 (log.f64 base))))
✓	0.6b	(cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (pow.f64 (log.f64 base) 3)))
	1.3b	(.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) 2) (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 1 (log.f64 base))))
	0.7b	(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (log.f64 base) 3) (pow.f64 (log.f64 (hypot.f64 re im)) 3))) -1)
	0.6b	(pow.f64 (log.f64 (pow.f64 base (/.f64 1 (log.f64 (hypot.f64 re im))))) -1)
	32.4b	(pow.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 3) 1/3)
	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))))
✓	0.4b	(*.f64 (/.f64 1 (log.f64 base)) (log.f64 (hypot.f64 re im)))
	18.3b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))

Compiler

Compiled 8877 to 5422 computations (38.9% saved)

regimes641.0ms (8.3%)

Accuracy

Total 0.3b remaining (88.3%)

Threshold costs 0.3b (88.3%)

Counts

112 → 1

Compiler

Compiled 8756 to 6506 computations (25.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	4294967295
1	15	4294967295

Stop Event

1×

saturated

end163.0ms (2.1%)

Remove: (sort re im)
Compiler: Compiled 217 to 159 computations (26.7% saved)

Details

analyze631.0ms (8.2%)

sample1.9s (24.5%)

simplify38.0ms (0.5%)

prune5.0ms (0.1%)

localize7.0ms (0.1%)

series515.0ms (6.7%)

rewrite40.0ms (0.5%)

simplify41.0ms (0.5%)

prune62.0ms (0.8%)

localize8.0ms (0.1%)

series1.2s (15%)

rewrite50.0ms (0.7%)

simplify52.0ms (0.7%)

prune168.0ms (2.2%)

localize8.0ms (0.1%)

series518.0ms (6.7%)

rewrite43.0ms (0.6%)

simplify42.0ms (0.5%)

prune64.0ms (0.8%)

localize10.0ms (0.1%)

series1.2s (15.2%)

rewrite63.0ms (0.8%)

simplify73.0ms (1%)

prune245.0ms (3.2%)

regimes641.0ms (8.3%)

simplify2.0ms (0%)

end163.0ms (2.1%)

Profiling