Details

analyze737.0ms (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)

sample54.0ms (0.4%)

Algorithm

1×

intervals

Results

32.0ms	256×	body	128	valid
3.0ms	25×	body	128	nan

Compiler

Compiled 66 to 44 computations (33.3% saved)

simplify95.0ms (0.7%)

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
▶	0.4b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
	29.7b	(/.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

▶

0.4b

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

29.7b

(/.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 1 expressions with local error:

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

series662.0ms (4.8%)

Counts

1 → 36

Calls

1 calls:

662.0ms

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

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`times-frac_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
11×	`pow1_binary64`

Counts

1 → 38

Calls

1 calls:

3.0ms

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

simplify83.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

890×	`fma-neg_binary64`
369×	`div-sub_binary64`
319×	`times-frac_binary64`
242×	`associate-/l*_binary64`
231×	`associate-/r*_binary64`

Counts

74 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	1913
1	345	1739
2	855	1699
3	2882	1699
4	4710	1699
5	5508	1699

prune97.0ms (0.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	81	12	93
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	82	13	95

Error

0.0b

Counts

95 → 13

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
	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))))
	1.3b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base)))
	17.4b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	16.0b	(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 base) (sqrt.f64 (log.f64 (hypot.f64 re im)))))
	30.7b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	0.6b	(log.f64 (exp.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	16.0b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	0.7b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)) 3))
	29.7b	(/.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)))
	31.1b	(exp.f64 (log.f64 (/.f64 (log.f64 (hypot.f64 im re)) (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))))
	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)))

Compiler

Compiled 2308 to 1026 computations (55.5% saved)

localize15.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series2.2s (16%)

Counts

2 → 72

Calls

2 calls:

1.2s	(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))
1.0s	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))

rewrite36.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`times-frac_binary64`
69×	`*-un-lft-identity_binary64`
69×	`add-sqr-sqrt_binary64`
69×	`add-cube-cbrt_binary64`
45×	`pow1_binary64`

Counts

2 → 144

Calls

2 calls:

9.0ms	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
5.0ms	(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))

simplify258.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

432×	`fma-neg_binary64`
429×	`times-frac_binary64`
347×	`associate-/r*_binary64`
294×	`associate-/l*_binary64`
190×	`fma-def_binary64`

Counts

216 → 240

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	394	6731
1	1231	5978
2	4749	5978
3	5095	5978

prune394.0ms (2.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	233	7	240
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	239	14	253

Error

0.0b

Counts

253 → 14

Alt Table

Status	Error	Program
▶	0.5b	(*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (/.f64 1 (log.f64 (hypot.f64 re im)))))
	0.6b	(log.f64 (exp.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	31.3b	(/.f64 1 (*.f64 (sqrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) (sqrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))))
	0.7b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)) 3))
	1.3b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base)))
	1.3b	(/.f64 1 (.f64 (.f64 (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))) (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))))
	17.4b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	30.7b	(/.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (sqrt.f64 (log.f64 base)) (log.f64 (hypot.f64 re im))))
	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)))
	16.1b	(/.f64 1 (/.f64 (/.f64 (log.f64 base) (sqrt.f64 (log.f64 (hypot.f64 re im)))) (sqrt.f64 (log.f64 (hypot.f64 re im)))))
	16.0b	(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 base) (sqrt.f64 (log.f64 (hypot.f64 re im)))))
	1.3b	(.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (/.f64 1 (/.f64 (log.f64 base) (cbrt.f64 (log.f64 (hypot.f64 re im))))))
	16.0b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	0.5b	(pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) -1)

Compiler

Compiled 7144 to 3472 computations (51.4% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series1.3s (9.6%)

Counts

4 → 92

Calls

4 calls:

1.1s	(*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (/.f64 1 (log.f64 (hypot.f64 re im)))))
98.0ms	(/.f64 1 (log.f64 (hypot.f64 re im)))
59.0ms	(/.f64 1 (log.f64 base))
37.0ms	(/.f64 1 (/.f64 1 (log.f64 (hypot.f64 re im))))

rewrite115.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

260×	`times-frac_binary64`
184×	`add-sqr-sqrt_binary64`
176×	`add-exp-log_binary64`
142×	`*-un-lft-identity_binary64`
120×	`add-cube-cbrt_binary64`

Counts

4 → 338

Calls

4 calls:

39.0ms	(*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (/.f64 1 (log.f64 (hypot.f64 re im)))))
8.0ms	(/.f64 1 (/.f64 1 (log.f64 (hypot.f64 re im))))
4.0ms	(/.f64 1 (log.f64 (hypot.f64 re im)))
4.0ms	(/.f64 1 (log.f64 base))

simplify341.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

429×	`fma-neg_binary64`
348×	`sub-neg_binary64`
270×	`associate-/r*_binary64`
244×	`times-frac_binary64`
213×	`fma-def_binary64`

Counts

430 → 512

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	476	8403
1	1274	7741
2	4157	7725
3	4984	7725

prune824.0ms (6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	505	7	512
Fresh	9	4	13
Picked	1	0	1
Done	0	0	0
Total	515	11	526

Error

Counts

526 → 11

Alt Table

Status	Error	Program
	16.1b	(*.f64 (/.f64 (/.f64 1 (log.f64 base)) (sqrt.f64 (/.f64 1 (log.f64 (hypot.f64 re im))))) (/.f64 1 (sqrt.f64 (/.f64 1 (log.f64 (hypot.f64 re im))))))
	16.4b	(*.f64 (/.f64 1 (log.f64 base)) (expm1.f64 (log1p.f64 (log.f64 (hypot.f64 re im)))))
	0.5b	(pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) -1)
	0.8b	(.f64 (cbrt.f64 (.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base)))) (/.f64 1 (/.f64 1 (log.f64 (hypot.f64 re im)))))
▶	0.4b	(*.f64 (/.f64 1 1) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))
	0.7b	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 1 (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)))
	16.1b	(/.f64 1 (/.f64 (/.f64 (log.f64 base) (sqrt.f64 (log.f64 (hypot.f64 re im)))) (sqrt.f64 (log.f64 (hypot.f64 re im)))))
	0.7b	(*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (cbrt.f64 (/.f64 1 (pow.f64 (log.f64 (hypot.f64 re im)) 3)))))
	1.5b	(.f64 (.f64 (cbrt.f64 (/.f64 1 (log.f64 base))) (cbrt.f64 (/.f64 1 (log.f64 base)))) (*.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (/.f64 1 (log.f64 base)))))
	1.3b	(/.f64 1 (.f64 (.f64 (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))) (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))))

Compiler

Compiled 13038 to 7599 computations (41.7% saved)

localize18.0ms (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))

prune152.0ms (1.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	93	11	104

Error

Counts

104 → 11

Alt Table

Status	Error	Program
	0.5b	(pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) -1)
	0.8b	(.f64 (cbrt.f64 (.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base)))) (/.f64 1 (/.f64 1 (log.f64 (hypot.f64 re im)))))
✓	0.4b	(*.f64 (/.f64 1 1) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))
	0.7b	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base))))
	16.0b	(.f64 (/.f64 1 1) (.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base))))
	0.7b	(*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (cbrt.f64 (/.f64 1 (pow.f64 (log.f64 (hypot.f64 re im)) 3)))))
	1.5b	(.f64 (.f64 (cbrt.f64 (/.f64 1 (log.f64 base))) (cbrt.f64 (/.f64 1 (log.f64 base)))) (*.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (/.f64 1 (log.f64 base)))))
	17.4b	(*.f64 (/.f64 1 1) (expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)))))
	16.4b	(*.f64 (/.f64 1 (log.f64 base)) (expm1.f64 (log1p.f64 (log.f64 (hypot.f64 re im)))))
	1.3b	(/.f64 1 (.f64 (.f64 (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))) (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))))
	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)))

Compiler

Compiled 2428 to 1270 computations (47.7% saved)

regimes3.1s (23%)

Accuracy

Total 0.3b remaining (90.2%)

Threshold costs 0.3b (90.2%)

Counts

292 → 1

Compiler

Compiled 28081 to 21016 computations (25.2% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	11
1	15	11
2	12	11

end12.0ms (0.1%)

Remove: (sort re im)
Compiler: Compiled 30 to 21 computations (30% saved)

sample3.1s (22.7%)

Algorithm

1×

intervals

Results

2.0s	8000×	body	128	valid
225.0ms	999×	body	128	nan

Compiler

Compiled 259 to 173 computations (33.2% saved)

Details

analyze737.0ms (5.4%)

sample54.0ms (0.4%)

simplify95.0ms (0.7%)

prune5.0ms (0%)

localize7.0ms (0.1%)

series662.0ms (4.8%)

rewrite5.0ms (0%)

simplify83.0ms (0.6%)

prune97.0ms (0.7%)

localize15.0ms (0.1%)

series2.2s (16%)

rewrite36.0ms (0.3%)

simplify258.0ms (1.9%)

prune394.0ms (2.9%)

localize20.0ms (0.1%)

series1.3s (9.6%)

rewrite115.0ms (0.8%)

simplify341.0ms (2.5%)

prune824.0ms (6%)

localize18.0ms (0.1%)

prune152.0ms (1.1%)

regimes3.1s (23%)

simplify4.0ms (0%)

end12.0ms (0.1%)

sample3.1s (22.7%)

Profiling