Details

analyze585.0ms (5.8%)

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 (19.1%)

Symmetry

(sort re im)

Results

1.6s	8256×	body	128	valid
182.0ms	1012×	body	128	invalid

Compiler

Compiled 95 to 62 computations (34.7% saved)

simplify93.0ms (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

prune4.0ms (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
	30.7b	(/.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

30.7b

(/.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))

series534.0ms (5.3%)

Counts

2 → 60

Calls

2 calls:

525.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
9.0ms	(hypot.f64 re im)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 48

Calls

2 calls:

3.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
0.0ms	(hypot.f64 re im)

simplify81.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

787×	`times-frac_binary64`
599×	`fma-neg_binary64`
441×	`associate-/r*_binary64`
410×	`associate-/l*_binary64`
341×	`fma-def_binary64`

Counts

108 → 142

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	194	2481
1	484	2312
2	1291	2236
3	4583	2236
4	4984	2236

prune97.0ms (1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	129	13	142
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	131	13	144

Error

0.0b

Counts

144 → 13

Alt Table

Status	Error	Program
	1.6b	(.f64 (/.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 base))))
	1.2b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	41.7b	(/.f64 (log.f64 (cbrt.f64 (pow.f64 (hypot.f64 im re) 3))) (log.f64 base))
	15.7b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	31.8b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	17.1b	(/.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 (log.f64 base) (cbrt.f64 (log.f64 (hypot.f64 re im)))))
	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
▶	0.4b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
	34.0b	(*.f64 (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	0.6b	(cbrt.f64 (/.f64 (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (.f64 (.f64 (log.f64 base) (log.f64 base)) (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))))
	0.6b	(log.f64 (exp.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))

Compiler

Compiled 3096 to 1435 computations (53.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.2b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
✓	0.3b	(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))

series1.1s (10.9%)

Counts

2 → 72

Calls

2 calls:

572.0ms	(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))
533.0ms	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))

rewrite21.0ms (0.2%)

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:

5.0ms	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
3.0ms	(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))

simplify147.0ms (1.4%)

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

prune225.0ms (2.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	282	6	288
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	289	12	301

Error

0.0b

Counts

301 → 12

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 (hypot.f64 re im))))
	1.4b	(.f64 (/.f64 1 (.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)))))) (/.f64 1 (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))))
	1.6b	(.f64 (/.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 base))))
	1.2b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	31.8b	(/.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (sqrt.f64 (log.f64 base)) (log.f64 (hypot.f64 re im))))
	15.7b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	0.7b	(/.f64 1 (cbrt.f64 (/.f64 (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base)) (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))))))
	17.1b	(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 base) (sqrt.f64 (log.f64 (hypot.f64 re im)))))
	0.6b	(/.f64 1 (log.f64 (exp.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))))
	0.6b	(cbrt.f64 (/.f64 (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
	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))))))
	0.6b	(log.f64 (exp.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))

Compiler

Compiled 7991 to 3966 computations (50.4% 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 1 (log.f64 (hypot.f64 re im)))
✓	0.3b	(/.f64 1 (log.f64 base))
✓	0.3b	(/.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 (hypot.f64 re im))))

series772.0ms (7.6%)

Counts

3 → 68

Calls

3 calls:

660.0ms	(/.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 (hypot.f64 re im))))
68.0ms	(/.f64 1 (log.f64 base))
43.0ms	(/.f64 1 (log.f64 (hypot.f64 re im)))

rewrite79.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

688×	`times-frac_binary64`
293×	`*-un-lft-identity_binary64`
293×	`add-sqr-sqrt_binary64`
293×	`add-cube-cbrt_binary64`
115×	`pow1_binary64`

Counts

3 → 396

Calls

3 calls:

15.0ms	(/.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 (hypot.f64 re im))))
2.0ms	(/.f64 1 (log.f64 (hypot.f64 re im)))
2.0ms	(/.f64 1 (log.f64 base))

simplify266.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

424×	`unswap-sqr_binary64`
338×	`fma-neg_binary64`
295×	`associate-/r*_binary64`
284×	`sub-neg_binary64`
226×	`times-frac_binary64`

Counts

464 → 414

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	429	13196
1	1204	11542
2	4025	11326
3	5281	11326

prune355.0ms (3.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	457	5	462
Fresh	6	5	11
Picked	0	1	1
Done	0	0	0
Total	463	11	474

Error

Counts

474 → 11

Alt Table

Status	Error	Program
	0.7b	(/.f64 1 (cbrt.f64 (/.f64 (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base)) (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))))))
	0.7b	(/.f64 (/.f64 1 (log.f64 base)) (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))))))
	0.6b	(/.f64 1 (log.f64 (exp.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))))
	0.8b	(/.f64 (cbrt.f64 (.f64 (.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base)))) (/.f64 1 (log.f64 (hypot.f64 re im))))
▶	0.4b	(/.f64 (/.f64 (sqrt.f64 1) 1) (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
	0.6b	(cbrt.f64 (/.f64 (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
	0.6b	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base))))
	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))))))
✓	0.5b	(/.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 (hypot.f64 re im))))
	17.2b	(*.f64 (/.f64 1 (sqrt.f64 (/.f64 1 (log.f64 (hypot.f64 re im))))) (/.f64 (/.f64 1 (log.f64 base)) (sqrt.f64 (/.f64 1 (log.f64 (hypot.f64 re im))))))
	15.7b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))

Compiler

Compiled 12574 to 6968 computations (44.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.2b	(/.f64 (/.f64 (sqrt.f64 1) 1) (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
	0.3b	(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))

series555.0ms (5.5%)

Counts

1 → 36

Calls

1 calls:

555.0ms

(/.f64 (/.f64 (sqrt.f64 1) 1) (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))

rewrite138.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

1186×	`times-frac_binary64`
481×	`*-un-lft-identity_binary64`
481×	`add-sqr-sqrt_binary64`
481×	`add-cube-cbrt_binary64`
189×	`sqrt-prod_binary64`

Counts

1 → 506

Calls

1 calls:

14.0ms

(/.f64 (/.f64 (sqrt.f64 1) 1) (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))

simplify478.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

918×	`fma-neg_binary64`
665×	`times-frac_binary64`
364×	`associate-/r*_binary64`
327×	`associate-/l*_binary64`
225×	`sub-neg_binary64`

Counts

542 → 397

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	180	15300
1	412	13314
2	1064	12989
3	3736	12989
4	4981	12989
5	4999	12989
6	4964	12989

prune489.0ms (4.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	529	1	530
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	531	10	541

Error

Counts

541 → 10

Alt Table

Status	Error	Program
	0.7b	(/.f64 1 (cbrt.f64 (/.f64 (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base)) (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))))))
	0.7b	(/.f64 (/.f64 1 (log.f64 base)) (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))))))
	0.6b	(/.f64 1 (log.f64 (exp.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))))
	0.8b	(/.f64 (cbrt.f64 (.f64 (.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base)))) (/.f64 1 (log.f64 (hypot.f64 re im))))
	0.3b	(/.f64 (log.f64 (hypot.f64 re im)) (+.f64 (log.f64 base) 0))
	0.6b	(cbrt.f64 (/.f64 (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
	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))))))
✓	0.5b	(/.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 (hypot.f64 re im))))
	17.2b	(*.f64 (/.f64 1 (sqrt.f64 (/.f64 1 (log.f64 (hypot.f64 re im))))) (/.f64 (/.f64 1 (log.f64 base)) (sqrt.f64 (/.f64 1 (log.f64 (hypot.f64 re im))))))
	15.7b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))

Compiler

Compiled 15868 to 8366 computations (47.3% saved)

regimes2.0s (19.3%)

Accuracy

Total 0.3b remaining (88.9%)

Threshold costs 0.3b (88.9%)

Counts

316 → 1

Compiler

Compiled 32251 to 22851 computations (29.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	12	29
2	12	29

end190.0ms (1.9%)

Remove: (sort re im)
Compiler: Compiled 296 to 172 computations (41.9% saved)

Details

analyze585.0ms (5.8%)

sample1.9s (19.1%)

simplify93.0ms (0.9%)

prune4.0ms (0%)

localize7.0ms (0.1%)

series534.0ms (5.3%)

rewrite5.0ms (0.1%)

simplify81.0ms (0.8%)

prune97.0ms (1%)

localize8.0ms (0.1%)

series1.1s (10.9%)

rewrite21.0ms (0.2%)

simplify147.0ms (1.4%)

prune225.0ms (2.2%)

localize9.0ms (0.1%)

series772.0ms (7.6%)

rewrite79.0ms (0.8%)

simplify266.0ms (2.6%)

prune355.0ms (3.5%)

localize9.0ms (0.1%)

series555.0ms (5.5%)

rewrite138.0ms (1.4%)

simplify478.0ms (4.7%)

prune489.0ms (4.8%)

regimes2.0s (19.3%)

simplify2.0ms (0%)

end190.0ms (1.9%)

Profiling