Details

analyze607.0ms (9.5%)

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)

sample2.0s (30.7%)

Symmetry

(sort re im)

Results

1.7s	8256×	body	128	valid
201.0ms	1008×	body	128	invalid

Compiler

Compiled 95 to 62 computations (34.7% saved)

simplify39.0ms (0.6%)

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

prune4.0ms (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
	34.2b	(/.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

34.2b

(/.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))

series522.0ms (8.2%)

Counts

2 → 60

Calls

2 calls:

509.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
13.0ms	(hypot.f64 re im)

rewrite45.0ms (0.7%)

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	15
1	158	15
2	1965	15

Stop Event

1×	node limit

Counts

2 → 54

Calls

2 calls:

44.0ms	(hypot.f64 re im)
44.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

simplify37.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

762×	`times-frac_binary64`
406×	`associate-/r*_binary64`
360×	`associate-/l*_binary64`
332×	`fma-def_binary64`
209×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	133	1684
1	394	1570
2	1188	1490

Stop Event

1×	node limit

Counts

114 → 129

prune95.0ms (1.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	117	12	129
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	118	13	131

Error

0.0b

Counts

131 → 13

Alt Table

Status	Error	Program
	0.6b	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base))))
	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
▶	0.4b	(pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) -1)
	34.2b	(/.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)))
	1.4b	(*.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))
	14.5b	(/.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))
	1.4b	(pow.f64 (cbrt.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)
	34.3b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.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))))
	14.5b	(*.f64 (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) 1) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (log.f64 base)))
	0.7b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	0.7b	(cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (pow.f64 (log.f64 base) 3)))

Compiler

Compiled 2766 to 1487 computations (46.2% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.2b	(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)))

series1.1s (17.7%)

Counts

2 → 72

Calls

2 calls:

598.0ms	(pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) -1)
532.0ms	(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))

rewrite48.0ms (0.8%)

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:

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

simplify49.0ms (0.8%)

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

prune188.0ms (2.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	225	5	230
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	231	12	243

Error

Counts

243 → 12

Alt Table

Status	Error	Program
	0.6b	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base))))
	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
	35.3b	(*.f64 (pow.f64 (sqrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) -1) (pow.f64 (sqrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) -1))
	19.1b	(pow.f64 (-.f64 (exp.f64 (log1p.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))) 1) -1)
	0.7b	(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (log.f64 base) 3) (pow.f64 (log.f64 (hypot.f64 re im)) 3))) -1)
	14.5b	(*.f64 (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) 1) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (log.f64 base)))
	34.2b	(/.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)))
	14.5b	(/.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))
▶	0.3b	(*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 1)
	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))))
	0.6b	(pow.f64 (log.f64 (pow.f64 base (/.f64 1 (log.f64 (hypot.f64 re im))))) -1)
	0.7b	(cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (pow.f64 (log.f64 base) 3)))

Compiler

Compiled 6873 to 3938 computations (42.7% 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 (log.f64 (hypot.f64 re im)) (log.f64 base))

prune101.0ms (1.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	129	12	141

Error

Counts

141 → 12

Alt Table

Status	Error	Program
	0.6b	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base))))
▶	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
	35.3b	(*.f64 (pow.f64 (sqrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) -1) (pow.f64 (sqrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) -1))
	19.1b	(pow.f64 (-.f64 (exp.f64 (log1p.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))) 1) -1)
	0.7b	(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (log.f64 base) 3) (pow.f64 (log.f64 (hypot.f64 re im)) 3))) -1)
	14.5b	(*.f64 (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) 1) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (log.f64 base)))
	14.5b	(/.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))
✓	0.3b	(*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 1)
	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))))
	0.7b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 3)) 1)
	0.6b	(pow.f64 (log.f64 (pow.f64 base (/.f64 1 (log.f64 (hypot.f64 re im))))) -1)
	0.7b	(cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (pow.f64 (log.f64 base) 3)))

Compiler

Compiled 2966 to 1718 computations (42.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.3b	(/.f64 1 (log.f64 base))
✓	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))

series519.0ms (8.1%)

Counts

2 → 44

Calls

2 calls:

487.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
31.0ms	(/.f64 1 (log.f64 base))

rewrite40.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	194	17
2	2236	17

Stop Event

1×	node limit

Counts

2 → 49

Calls

2 calls:

39.0ms	(/.f64 1 (log.f64 base))
39.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))

simplify42.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

890×	`fma-neg_binary64`
294×	`times-frac_binary64`
219×	`sub-neg_binary64`
214×	`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	3020	1040

Stop Event

1×	node limit

Counts

93 → 95

prune113.0ms (1.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	147	11	158

Error

Counts

158 → 11

Alt Table

Status	Error	Program
	0.7b	(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (log.f64 base) 3) (pow.f64 (log.f64 (hypot.f64 re im)) 3))) -1)
	14.5b	(*.f64 (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) 1) (/.f64 (sqrt.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))))
	14.5b	(/.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))
	35.3b	(*.f64 (pow.f64 (sqrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) -1) (pow.f64 (sqrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) -1))
✓	0.3b	(*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 1)
	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))))
	0.7b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 3)) 1)
	0.6b	(pow.f64 (log.f64 (pow.f64 base (/.f64 1 (log.f64 (hypot.f64 re im))))) -1)
	0.7b	(cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (pow.f64 (log.f64 base) 3)))
	0.7b	(*.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))

Compiler

Compiled 2753 to 1531 computations (44.4% saved)

regimes650.0ms (10.2%)

Accuracy

Total 0.3b remaining (93%)

Threshold costs 0.3b (93%)

Counts

118 → 1

Compiler

Compiled 8846 to 6486 computations (26.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16

Stop Event

1×

saturated

end169.0ms (2.6%)

Remove: (sort re im)
Compiler: Compiled 239 to 170 computations (28.9% saved)

Details

analyze607.0ms (9.5%)

sample2.0s (30.7%)

simplify39.0ms (0.6%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series522.0ms (8.2%)

rewrite45.0ms (0.7%)

simplify37.0ms (0.6%)

prune95.0ms (1.5%)

localize11.0ms (0.2%)

series1.1s (17.7%)

rewrite48.0ms (0.8%)

simplify49.0ms (0.8%)

prune188.0ms (2.9%)

localize8.0ms (0.1%)

prune101.0ms (1.6%)

localize8.0ms (0.1%)

series519.0ms (8.1%)

rewrite40.0ms (0.6%)

simplify42.0ms (0.7%)

prune113.0ms (1.8%)

regimes650.0ms (10.2%)

simplify2.0ms (0%)

end169.0ms (2.6%)

Profiling