Details

analyze8.0ms (0.1%)

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)

sample2.1s (32.4%)

Symmetry

(sort re im)

Results

2.0s

8256×

body

128

valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify14.0ms (0.2%)

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

prune6.0ms (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)

localize13.0ms (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))

series56.0ms (0.9%)

Counts

1 → 24

Calls

1 calls:

56.0ms

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

rewrite98.0ms (1.5%)

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 → 33

Calls

1 calls:

96.0ms

(/.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

simplify113.0ms (1.8%)

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

57 → 72

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

prune125.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	64	8	72
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	64	9	73

Error

0.0b

Counts

73 → 9

Alt Table

Status	Error	Program
✓	0.6b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
	17.4b	(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)))
	0.6b	(neg.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 1/10)))
	1.4b	(*.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 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))
	0.7b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3))
	0.6b	(pow.f64 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))) -1)
	17.1b	(*.f64 (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) 1) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (log.f64 10)))

Compiler

Compiled 1667 to 1183 computations (29% saved)

localize19.0ms (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))))
✓	0.5b	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))

series118.0ms (1.8%)

Counts

2 → 48

Calls

2 calls:

63.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))
55.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))

rewrite99.0ms (1.5%)

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 → 101

Calls

2 calls:

95.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))
95.0ms	(/.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

simplify128.0ms (2%)

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

149 → 179

Iterations

Useful iterations: 3 (0.0ms)

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

prune284.0ms (4.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	174	5	179
Fresh	6	1	7
Picked	1	0	1
Done	1	0	1
Total	182	6	188

Error

Counts

188 → 6

Alt Table

Status	Error	Program
	0.6b	(/.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	(/.f64 (cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 2) (log.f64 10))) (/.f64 (sqrt.f64 (log.f64 10)) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))))
	0.6b	(/.f64 (pow.f64 (log.f64 10) -1/2) (/.f64 (sqrt.f64 (log.f64 10)) (log.f64 (hypot.f64 re im))))
	0.6b	(neg.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 1/10)))
	0.6b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) 1) (log.f64 10))

Compiler

Compiled 4381 to 3382 computations (22.8% saved)

localize23.0ms (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))

series119.0ms (1.8%)

Counts

2 → 48

Calls

2 calls:

63.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (pow.f64 (log.f64 10) -1/2))
55.0ms	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (log.f64 (hypot.f64 re im)) (pow.f64 (log.f64 10) -1/2)))

rewrite114.0ms (1.8%)

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 → 52

Calls

2 calls:

112.0ms	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (log.f64 (hypot.f64 re im)) (pow.f64 (log.f64 10) -1/2)))
112.0ms	(*.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

simplify129.0ms (2%)

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

100 → 130

Iterations

Useful iterations: 3 (0.0ms)

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

prune304.0ms (4.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	130	6	136

Error

Counts

136 → 6

Alt Table

Status	Error	Program
	0.6b	(/.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	(/.f64 (cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 2) (log.f64 10))) (/.f64 (sqrt.f64 (log.f64 10)) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))))
▶	0.6b	(/.f64 (pow.f64 (log.f64 10) -1/2) (/.f64 (sqrt.f64 (log.f64 10)) (log.f64 (hypot.f64 re im))))
	0.6b	(neg.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 1/10)))
	0.6b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) 1) (log.f64 10))

Compiler

Compiled 3525 to 2814 computations (20.2% saved)

localize21.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (pow.f64 (log.f64 10) -1/2) (/.f64 (sqrt.f64 (log.f64 10)) (log.f64 (hypot.f64 re im))))
✓	0.5b	(/.f64 (sqrt.f64 (log.f64 10)) (log.f64 (hypot.f64 re im)))

series219.0ms (3.4%)

Counts

2 → 48

Calls

2 calls:

164.0ms	(/.f64 (sqrt.f64 (log.f64 10)) (log.f64 (hypot.f64 re im)))
54.0ms	(/.f64 (pow.f64 (log.f64 10) -1/2) (/.f64 (sqrt.f64 (log.f64 10)) (log.f64 (hypot.f64 re im))))

rewrite99.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

593×	`log-prod_binary64`
214×	`expm1-udef_binary64`
213×	`log1p-udef_binary64`
200×	`log-pow_binary64`
125×	`prod-diff_binary64`

Counts

2 → 82

Calls

2 calls:

96.0ms	(/.f64 (pow.f64 (log.f64 10) -1/2) (/.f64 (sqrt.f64 (log.f64 10)) (log.f64 (hypot.f64 re im))))
95.0ms	(/.f64 (sqrt.f64 (log.f64 10)) (log.f64 (hypot.f64 re im)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	34
1	252	27
2	3008	27
3	5310	27
0	0	0
1	0	0

simplify144.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

520×	`fma-neg_binary64`
422×	`unswap-sqr_binary64`
302×	`fma-def_binary64`
281×	`sub-neg_binary64`
252×	`associate-/r*_binary64`

Counts

130 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	336	3108
1	1075	2919
2	4062	2889
3	5559	2889

prune296.0ms (4.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	2	2	4
Picked	1	0	1
Done	1	0	1
Total	172	3	175

Error

Counts

175 → 3

Alt Table

Status	Error	Program
	0.3b	(*.f64 (/.f64 (pow.f64 (log.f64 10) -1/2) (neg.f64 (sqrt.f64 (log.f64 10)))) (neg.f64 (log.f64 (hypot.f64 re im))))
	0.6b	(neg.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 1/10)))
	0.6b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) 1) (log.f64 10))

Compiler

Compiled 5494 to 4255 computations (22.6% saved)

regimes1.6s (25.7%)

Accuracy

Total 0.3b remaining (98.4%)

Threshold costs 0.3b (98.4%)

Counts

86 → 1

Compiler

Compiled 11356 to 9449 computations (16.8% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	23	25
2	32	25
3	41	25
4	46	25
5	49	25
6	50	25
7	50	25

end146.0ms (2.3%)

Remove: (sort re im)
Compiler: Compiled 106 to 92 computations (13.2% saved)

Details

analyze8.0ms (0.1%)

sample2.1s (32.4%)

simplify14.0ms (0.2%)

prune6.0ms (0.1%)

localize13.0ms (0.2%)

series56.0ms (0.9%)

rewrite98.0ms (1.5%)

simplify113.0ms (1.8%)

prune125.0ms (1.9%)

localize19.0ms (0.3%)

series118.0ms (1.8%)

rewrite99.0ms (1.5%)

simplify128.0ms (2%)

prune284.0ms (4.4%)

localize23.0ms (0.4%)

series119.0ms (1.8%)

rewrite114.0ms (1.8%)

simplify129.0ms (2%)

prune304.0ms (4.7%)

localize21.0ms (0.3%)

series219.0ms (3.4%)

rewrite99.0ms (1.5%)

simplify144.0ms (2.2%)

prune296.0ms (4.6%)

regimes1.6s (25.7%)

simplify6.0ms (0.1%)

end146.0ms (2.3%)

Profiling