Details

analyze575.0ms (6.5%)

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)

sample2.1s (23.6%)

Symmetry

(sort re im)

Results

1.8s	8256×	body	128	valid
201.0ms	1011×	body	128	invalid

Compiler

Compiled 95 to 62 computations (34.7% saved)

simplify678.0ms (7.6%)

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 (0.1%)

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))
	32.2b	(/.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)))

Status

Error

Program

▶

0.3b

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

32.2b

(/.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)))

Compiler

Compiled 120 to 77 computations (35.8% saved)

localize9.0ms (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))

series665.0ms (7.5%)

Counts

2 → 60

Calls

2 calls:

652.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
12.0ms	(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)

simplify92.0ms (1%)

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

prune99.0ms (1.1%)

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
	28.1b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	30.1b	(*.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))))
▶	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
	0.7b	(log.f64 (exp.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	1.2b	(.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))))
	0.7b	(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))))
	0.7b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)) 3))
	0.5b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
	1.1b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	1.5b	(.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	(.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)))
	18.1b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))

Compiler

Compiled 3104 to 1441 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)
✓	0.3b	(/.f64 1 (log.f64 base))
✓	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))

series700.0ms (7.9%)

Counts

2 → 44

Calls

2 calls:

653.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
46.0ms	(/.f64 1 (log.f64 base))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
26×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
16×	`associate-r_binary64`

Counts

2 → 79

Calls

2 calls:

6.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
2.0ms	(/.f64 1 (log.f64 base))

simplify103.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

453×	`div-sub_binary64`
341×	`times-frac_binary64`
295×	`associate-/l*_binary64`
248×	`fma-def_binary64`
229×	`sub-neg_binary64`

Counts

123 → 141

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	2246
1	382	1983
2	984	1943
3	3458	1943
4	4757	1943
5	5751	1943

prune137.0ms (1.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	185	4	189
Fresh	6	6	12
Picked	0	1	1
Done	0	0	0
Total	191	11	202

Error

0.0b

Counts

202 → 11

Alt Table

Status	Error	Program
	1.6b	(.f64 (.f64 (log.f64 (hypot.f64 re im)) (*.f64 (cbrt.f64 (/.f64 1 (log.f64 base))) (cbrt.f64 (/.f64 1 (log.f64 base))))) (cbrt.f64 (/.f64 1 (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))))
	30.0b	(exp.f64 (log.f64 (*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))))
✓	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
	1.2b	(.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))))
	30.1b	(*.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))))
▶	0.7b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)) 3))
	0.7b	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
	1.1b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	0.8b	(.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))
	1.2b	(.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 3844 to 1966 computations (48.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 im re)
✓	0.3b	(/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))
✓	0.5b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)) 3))
✓	0.7b	(pow.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)) 3)

series2.1s (23.4%)

Counts

4 → 132

Calls

4 calls:

776.0ms	(pow.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)) 3)
658.0ms	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)) 3))
643.0ms	(/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))
11.0ms	(hypot.f64 im re)

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
47×	`pow1_binary64`

Counts

4 → 168

Calls

4 calls:

4.0ms	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)) 3))
4.0ms	(/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))
4.0ms	(pow.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)) 3)
0.0ms	(hypot.f64 im re)

simplify189.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

701×	`fma-def_binary64`
540×	`times-frac_binary64`
410×	`associate-/r*_binary64`
314×	`associate-/l*_binary64`
204×	`associate-*r/_binary64`

Counts

300 → 292

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	456	9124
1	1415	8205
2	4735	8199
3	5275	8199

prune356.0ms (4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	288	4	292
Fresh	4	5	9
Picked	0	1	1
Done	0	1	1
Total	292	11	303

Error

Counts

303 → 11

Alt Table

Status	Error	Program
	0.7b	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
	0.6b	(cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 im re)) 3) (pow.f64 (log.f64 base) 3)))
▶	0.3b	(*.f64 1 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))
	0.9b	(.f64 (cbrt.f64 (/.f64 1 (.f64 (log.f64 base) (log.f64 base)))) (/.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (log.f64 base))))
	1.2b	(.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))))
	30.1b	(*.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))))
✓	0.7b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)) 3))
✓	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
	1.3b	(cbrt.f64 (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (cbrt.f64 (log.f64 (hypot.f64 im re)))) 1) 3) (pow.f64 (/.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)) 3)))
	0.8b	(.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))
	1.2b	(.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 8123 to 4350 computations (46.4% 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))

prune99.0ms (1.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	2	6	8
Picked	0	1	1
Done	0	2	2
Total	142	11	153

Error

Counts

153 → 11

Alt Table

Status	Error	Program
	0.7b	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
	28.1b	(.f64 1 (.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (log.f64 (hypot.f64 im re)) (sqrt.f64 (log.f64 base)))))
	0.6b	(cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 im re)) 3) (pow.f64 (log.f64 base) 3)))
	0.8b	(.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))
	0.5b	(*.f64 1 (/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))))
✓	0.3b	(*.f64 1 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))
	0.9b	(.f64 (cbrt.f64 (/.f64 1 (.f64 (log.f64 base) (log.f64 base)))) (/.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (log.f64 base))))
	1.2b	(.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))))
✓	0.7b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)) 3))
✓	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
	1.3b	(cbrt.f64 (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (cbrt.f64 (log.f64 (hypot.f64 im re)))) 1) 3) (pow.f64 (/.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)) 3)))

Compiler

Compiled 3099 to 1596 computations (48.5% saved)

regimes785.0ms (8.8%)

Accuracy

Total 0.3b remaining (89.7%)

Threshold costs 0.3b (89.7%)

Counts

139 → 1

Compiler

Compiled 12386 to 8291 computations (33.1% saved)

simplify2.0ms (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	10	11
1	13	11
2	12	11

end161.0ms (1.8%)

Remove: (sort re im)
Compiler: Compiled 231 to 159 computations (31.2% saved)

Details

analyze575.0ms (6.5%)

sample2.1s (23.6%)

simplify678.0ms (7.6%)

prune5.0ms (0.1%)

localize9.0ms (0.1%)

series665.0ms (7.5%)

rewrite5.0ms (0.1%)

simplify92.0ms (1%)

prune99.0ms (1.1%)

localize8.0ms (0.1%)

series700.0ms (7.9%)

rewrite12.0ms (0.1%)

simplify103.0ms (1.2%)

prune137.0ms (1.5%)

localize14.0ms (0.2%)

series2.1s (23.4%)

rewrite25.0ms (0.3%)

simplify189.0ms (2.1%)

prune356.0ms (4%)

localize8.0ms (0.1%)

prune99.0ms (1.1%)

regimes785.0ms (8.8%)

simplify2.0ms (0%)

end161.0ms (1.8%)

Profiling