Details

analyze557.0ms (5.6%)

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)

sample2.3s (23.2%)

Symmetry

(sort re im)

Results

2.0s	8256×	body	128	valid
197.0ms	1001×	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

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
▶	0.3b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
	32.7b	(/.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

▶

0.3b

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

32.7b

(/.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 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))

series699.0ms (7%)

Counts

2 → 60

Calls

2 calls:

686.0ms	(/.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)

simplify85.0ms (0.9%)

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

prune103.0ms (1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	131	11	142
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	132	12	144

Error

0.0b

Counts

144 → 12

Alt Table

Status	Error	Program
	33.5b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	18.1b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (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)))
	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))))
	0.4b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
	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))))
	1.2b	(.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)))
	32.7b	(/.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)))
▶	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
	0.6b	(log.f64 (exp.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	0.6b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)) 3))
	17.2b	(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 base) (sqrt.f64 (log.f64 (hypot.f64 re im)))))

Compiler

Compiled 3078 to 1435 computations (53.4% 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)))

series701.0ms (7%)

Counts

2 → 44

Calls

2 calls:

667.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
34.0ms	(/.f64 1 (log.f64 base))

rewrite14.0ms (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:

7.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
2.0ms	(/.f64 1 (log.f64 base))

simplify105.0ms (1.1%)

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

prune134.0ms (1.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	186	3	189
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	188	13	201

Error

0.0b

Counts

201 → 13

Alt Table

Status	Error	Program
	33.5b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (sqrt.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)))
	33.6b	(.f64 (log.f64 (hypot.f64 re im)) (.f64 (sqrt.f64 (/.f64 1 (log.f64 base))) (sqrt.f64 (/.f64 1 (log.f64 base)))))
	0.6b	(log.f64 (exp.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	0.8b	(*.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
	0.6b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)) 3))
▶	0.4b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
	18.1b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (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))))
	32.7b	(/.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)))
✓	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
	17.2b	(/.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 (log.f64 (hypot.f64 re im)) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base)))

Compiler

Compiled 3898 to 2004 computations (48.6% 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 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
✓	0.4b	(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))

series2.0s (20%)

Counts

2 → 72

Calls

2 calls:

1.3s	(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))
646.0ms	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))

rewrite24.0ms (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)))

simplify151.0ms (1.5%)

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

prune222.0ms (2.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	284	4	288
Fresh	4	7	11
Picked	1	0	1
Done	0	1	1
Total	289	12	301

Error

Counts

301 → 12

Alt Table

Status	Error	Program
✓	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
	0.7b	(/.f64 1 (cbrt.f64 (.f64 (.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))))
	33.6b	(.f64 (log.f64 (hypot.f64 re im)) (.f64 (sqrt.f64 (/.f64 1 (log.f64 base))) (sqrt.f64 (/.f64 1 (log.f64 base)))))
	0.6b	(log.f64 (exp.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	0.6b	(/.f64 1 (log.f64 (exp.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))))
	0.8b	(*.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
	0.6b	(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)))
	15.7b	(/.f64 1 (expm1.f64 (log1p.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))))
	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))))
	17.2b	(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 base) (sqrt.f64 (log.f64 (hypot.f64 re im)))))
▶	0.5b	(/.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 (hypot.f64 re im))))

Compiler

Compiled 7905 to 3945 computations (50.1% 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 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 (hypot.f64 re im))))
	0.3b	(/.f64 1 (log.f64 base))

series698.0ms (7%)

Counts

2 → 60

Calls

2 calls:

635.0ms	(/.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 (hypot.f64 re im))))
63.0ms	(/.f64 1 (log.f64 (hypot.f64 re im)))

rewrite66.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

676×	`times-frac_binary64`
283×	`*-un-lft-identity_binary64`
283×	`add-sqr-sqrt_binary64`
283×	`add-cube-cbrt_binary64`
109×	`pow1_binary64`

Counts

2 → 359

Calls

2 calls:

12.0ms	(/.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 (hypot.f64 re im))))
2.0ms	(/.f64 1 (log.f64 (hypot.f64 re im)))

simplify282.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

424×	`unswap-sqr_binary64`
336×	`fma-neg_binary64`
290×	`associate-/r*_binary64`
284×	`sub-neg_binary64`
225×	`times-frac_binary64`

Counts

419 → 375

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	422	12745
1	1197	11157
2	3981	10961
3	5226	10961

prune482.0ms (4.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	460	2	462
Fresh	2	8	10
Picked	1	0	1
Done	1	0	1
Total	464	10	474

Error

Counts

474 → 10

Alt Table

Status	Error	Program
	0.8b	(*.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
	0.6b	(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)))
	15.7b	(/.f64 1 (expm1.f64 (log1p.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))))
	0.7b	(/.f64 (/.f64 1 (log.f64 base)) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 (hypot.f64 re im))) 3)))
	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))))
	0.3b	(neg.f64 (/.f64 (log.f64 (hypot.f64 re im)) (neg.f64 (log.f64 base))))
	0.7b	(/.f64 1 (cbrt.f64 (.f64 (.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))))
	0.6b	(/.f64 1 (log.f64 (exp.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))))
	17.2b	(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 base) (sqrt.f64 (log.f64 (hypot.f64 re im)))))

Compiler

Compiled 12309 to 6794 computations (44.8% saved)

regimes1.0s (10.5%)

Accuracy

Total 0.3b remaining (88.8%)

Threshold costs 0.3b (88.8%)

Counts

183 → 1

Compiler

Compiled 16556 to 11541 computations (30.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	18	15
2	24	15
3	28	15
4	29	15
5	29	15

end154.0ms (1.5%)

Remove: (sort re im)
Compiler: Compiled 227 to 144 computations (36.6% saved)

Details

analyze557.0ms (5.6%)

sample2.3s (23.2%)

simplify93.0ms (0.9%)

prune5.0ms (0%)

localize7.0ms (0.1%)

series699.0ms (7%)

rewrite5.0ms (0.1%)

simplify85.0ms (0.9%)

prune103.0ms (1%)

localize8.0ms (0.1%)

series701.0ms (7%)

rewrite14.0ms (0.1%)

simplify105.0ms (1.1%)

prune134.0ms (1.3%)

localize8.0ms (0.1%)

series2.0s (20%)

rewrite24.0ms (0.2%)

simplify151.0ms (1.5%)

prune222.0ms (2.2%)

localize9.0ms (0.1%)

series698.0ms (7%)

rewrite66.0ms (0.7%)

simplify282.0ms (2.8%)

prune482.0ms (4.8%)

regimes1.0s (10.5%)

simplify2.0ms (0%)

end154.0ms (1.5%)

Profiling