Details

analyze5.0ms (0.2%)

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
74.9%	25%	0.1%	3
87.4%	12.5%	0.1%	4
93.7%	6.2%	0.1%	5
96.8%	3.1%	0.1%	6
98.3%	1.6%	0.1%	7
99.1%	0.8%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.1s (35.3%)

Symmetry

(sort re im)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`hypot-def_binary64`
2×	`fma-def_binary64`
1×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	11
1	14	11
2	16	11
3	16	11

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.6b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))

Compiler

Compiled 39 to 29 computations (25.6% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.6b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))

series28.0ms (0.9%)

Counts

1 → 24

Calls

1 calls:

28.0ms

(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))

rewrite69.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

703×	`log1p-expm1-u_binary64`
703×	`expm1-log1p-u_binary64`
142×	`expm1-udef_binary64`
141×	`log1p-udef_binary64`
82×	`fma-udef_binary64`

Counts

1 → 34

Calls

1 calls:

68.0ms

(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	158	11
2	1843	11
3	4992	11
4	4911	11
0	0	0
1	0	0

simplify76.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

428×	`associate-/l/_binary64`
348×	`associate-/r/_binary64`
292×	`times-frac_binary64`
224×	`fma-def_binary64`
223×	`sub-neg_binary64`

Counts

58 → 73

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	936
1	247	924
2	685	880
3	2534	860
4	4655	860
5	4995	860
6	4963	860

prune55.0ms (1.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	65	8	73
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	65	9	74

Error

0.0b

Counts

74 → 9

Alt Table

Status	Error	Program
	1.3b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) 2) (sqrt.f64 (log.f64 10))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (sqrt.f64 (log.f64 10))))
✓	0.6b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
	19.0b	(exp.f64 (log.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	0.7b	(cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (pow.f64 (log.f64 10) 3)))
	0.7b	(neg.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 1/10)))
	0.6b	(pow.f64 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))) -1)
	18.8b	(pow.f64 (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))) 2)
	1.3b	(pow.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))) 3)
▶	0.6b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))

Compiler

Compiled 1662 to 1184 computations (28.8% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))
✓	0.4b	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))

series55.0ms (1.7%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))
26.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))

rewrite59.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

541×	`log-prod_binary64`
195×	`expm1-udef_binary64`
194×	`log1p-udef_binary64`
186×	`log-pow_binary64`
178×	`pow3_binary64`

Counts

2 → 102

Calls

2 calls:

57.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))
56.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	238	24
2	2726	24
3	4980	24
0	0	0
1	0	0

simplify75.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

587×	`fma-def_binary64`
422×	`times-frac_binary64`
352×	`sub-neg_binary64`
304×	`associate-/r*_binary64`
284×	`associate-/l*_binary64`

Counts

150 → 180

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	142	2156
1	452	2108
2	1234	1872
3	4550	1868
4	5028	1868

prune134.0ms (4.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	176	4	180
Fresh	5	2	7
Picked	1	0	1
Done	1	0	1
Total	183	6	189

Error

Counts

189 → 6

Alt Table

Status	Error	Program
	0.5b	(/.f64 (/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))) (cbrt.f64 (log.f64 10))) (cbrt.f64 (sqrt.f64 (log.f64 10))))
	1.3b	(pow.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))) 3)
	0.5b	(/.f64 (/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))) (pow.f64 (log.f64 10) 1/4)) (pow.f64 (log.f64 10) 1/4))
▶	0.4b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (log.f64 (hypot.f64 re im)) (pow.f64 (log.f64 10) -1/2)))
	0.7b	(neg.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 1/10)))
	0.6b	(pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 1)

Compiler

Compiled 4375 to 3380 computations (22.7% saved)

localize11.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (log.f64 (hypot.f64 re im)) (pow.f64 (log.f64 10) -1/2)))
✓	0.3b	(*.f64 (log.f64 (hypot.f64 re im)) (pow.f64 (log.f64 10) -1/2))

series55.0ms (1.7%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (pow.f64 (log.f64 10) -1/2))
26.0ms	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (log.f64 (hypot.f64 re im)) (pow.f64 (log.f64 10) -1/2)))

rewrite83.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

546×	`log-prod_binary64`
287×	`prod-diff_binary64`
210×	`expm1-udef_binary64`
209×	`log1p-udef_binary64`
196×	`log-pow_binary64`

Counts

2 → 53

Calls

2 calls:

82.0ms	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (log.f64 (hypot.f64 re im)) (pow.f64 (log.f64 10) -1/2)))
82.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (pow.f64 (log.f64 10) -1/2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	35
1	280	27
2	2768	27
3	4980	27
4	5313	27
0	0	0
1	0	0

simplify81.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

587×	`fma-def_binary64`
422×	`times-frac_binary64`
352×	`sub-neg_binary64`
304×	`associate-/r*_binary64`
284×	`associate-/l*_binary64`

Counts

101 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	142	2156
1	452	2108
2	1234	1872
3	4550	1868
4	5028	1868

prune94.0ms (2.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	131	6	137

Error

Counts

137 → 6

Alt Table

Status	Error	Program
	0.5b	(/.f64 (/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))) (pow.f64 (log.f64 10) 1/4)) (pow.f64 (log.f64 10) 1/4))
✓	0.4b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (log.f64 (hypot.f64 re im)) (pow.f64 (log.f64 10) -1/2)))
	0.8b	(cbrt.f64 (pow.f64 (*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 10))) 3))
	0.7b	(neg.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 1/10)))
	0.6b	(pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 1)
▶	0.5b	(/.f64 (/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))) (cbrt.f64 (log.f64 10))) (cbrt.f64 (sqrt.f64 (log.f64 10))))

Compiler

Compiled 3518 to 2811 computations (20.1% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))) (cbrt.f64 (log.f64 10)))
✓	0.5b	(/.f64 (/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))) (cbrt.f64 (log.f64 10))) (cbrt.f64 (sqrt.f64 (log.f64 10))))
✓	1.0b	(cbrt.f64 (log.f64 10))
✓	1.0b	(cbrt.f64 (sqrt.f64 (log.f64 10)))

series84.0ms (2.6%)

Counts

4 → 48

Calls

4 calls:

59.0ms	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))) (cbrt.f64 (log.f64 10)))
24.0ms	(/.f64 (/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))) (cbrt.f64 (log.f64 10))) (cbrt.f64 (sqrt.f64 (log.f64 10))))
0.0ms	(cbrt.f64 (sqrt.f64 (log.f64 10)))
0.0ms	(cbrt.f64 (log.f64 10))

rewrite74.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

230×	`expm1-udef_binary64`
229×	`log1p-udef_binary64`
222×	`log-pow_binary64`
208×	`log-div_binary64`
135×	`prod-diff_binary64`

Counts

4 → 133

Calls

4 calls:

72.0ms	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))) (cbrt.f64 (log.f64 10)))
72.0ms	(/.f64 (/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))) (cbrt.f64 (log.f64 10))) (cbrt.f64 (sqrt.f64 (log.f64 10))))
72.0ms	(cbrt.f64 (log.f64 10))
72.0ms	(cbrt.f64 (sqrt.f64 (log.f64 10)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	61
1	266	36
2	3428	36
3	5141	36
0	0	0
1	0	0

simplify77.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

793×	`fma-neg_binary64`
640×	`fma-def_binary64`
478×	`times-frac_binary64`
320×	`associate-/l*_binary64`
307×	`associate-/r*_binary64`

Counts

181 → 212

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	143	2396
1	461	2356
2	1354	2016
3	4478	1988
4	5008	1988

prune179.0ms (5.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	212	0	212
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	212	6	218

Error

Counts

218 → 6

Alt Table

Status	Error	Program
	0.5b	(/.f64 (/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))) (pow.f64 (log.f64 10) 1/4)) (pow.f64 (log.f64 10) 1/4))
✓	0.4b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (log.f64 (hypot.f64 re im)) (pow.f64 (log.f64 10) -1/2)))
	0.8b	(cbrt.f64 (pow.f64 (*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 10))) 3))
	0.7b	(neg.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 1/10)))
	0.6b	(pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 1)
✓	0.5b	(/.f64 (/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))) (cbrt.f64 (log.f64 10))) (cbrt.f64 (sqrt.f64 (log.f64 10))))

Compiler

Compiled 5461 to 4368 computations (20% saved)

regimes646.0ms (19.9%)

Accuracy

Total 0.3b remaining (97.5%)

Threshold costs 0.3b (97.5%)

Counts

79 → 1

Compiler

Compiled 11056 to 9162 computations (17.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	24
1	17	24
2	16	24

end111.0ms (3.4%)

Remove: (sort re im)
Compiler: Compiled 159 to 139 computations (12.6% saved)

Details

analyze5.0ms (0.2%)

sample1.1s (35.3%)

simplify9.0ms (0.3%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series28.0ms (0.9%)

rewrite69.0ms (2.1%)

simplify76.0ms (2.4%)

prune55.0ms (1.7%)

localize9.0ms (0.3%)

series55.0ms (1.7%)

rewrite59.0ms (1.8%)

simplify75.0ms (2.3%)

prune134.0ms (4.1%)

localize11.0ms (0.4%)

series55.0ms (1.7%)

rewrite83.0ms (2.6%)

simplify81.0ms (2.5%)

prune94.0ms (2.9%)

localize13.0ms (0.4%)

series84.0ms (2.6%)

rewrite74.0ms (2.3%)

simplify77.0ms (2.4%)

prune179.0ms (5.5%)

regimes646.0ms (19.9%)

simplify2.0ms (0.1%)

end111.0ms (3.4%)

Profiling