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 (37.6%)

Symmetry

(sort re im)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 2

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)

localize20.0ms (0.7%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 re im)
✓	0.6b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))

series33.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

24.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
8.0ms	(hypot.f64 re im)

rewrite37.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

703×	`log1p-expm1-u_binary64`
703×	`expm1-log1p-u_binary64`
142×	`expm1-udef_binary64`
141×	`log1p-udef_binary64`
78×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	160	15
2	1927	15

Stop Event

1×	node limit

Counts

2 → 54

Calls

2 calls:

36.0ms	(hypot.f64 re im)
36.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))

simplify33.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

760×	`times-frac_binary64`
404×	`associate-/r*_binary64`
356×	`associate-/l*_binary64`
339×	`fma-def_binary64`
209×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	1424
1	378	1394
2	1183	1334

Stop Event

1×	node limit

Counts

102 → 123

prune89.0ms (3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	115	8	123
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	115	9	124

Error

Counts

124 → 9

Alt Table

Status	Error	Program
	0.7b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3))
	0.6b	(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)
	16.3b	(pow.f64 (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))) 2)
✓	0.6b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
▶	0.5b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))
	1.1b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) 2) (pow.f64 (cbrt.f64 (log.f64 10)) 2)) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	16.3b	(*.f64 (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) 1) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (log.f64 10)))
	1.2b	(*.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))) (pow.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))) 2))

Compiler

Compiled 2504 to 1799 computations (28.2% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	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)))

series53.0ms (1.8%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))
24.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))

rewrite50.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

541×	`log-prod_binary64`
195×	`expm1-udef_binary64`
194×	`log1p-udef_binary64`
186×	`log-pow_binary64`
115×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	242	24
2	2947	24

Stop Event

1×	node limit

Counts

2 → 96

Calls

2 calls:

48.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))
48.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))

simplify42.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

577×	`fma-def_binary64`
422×	`times-frac_binary64`
304×	`associate-/r*_binary64`
280×	`associate-/l*_binary64`
214×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	142	2156
1	452	2108
2	1394	1872

Stop Event

1×	node limit

Counts

144 → 174

prune167.0ms (5.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	222	3	225
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	227	7	234

Error

Counts

234 → 7

Alt Table

Status	Error	Program
	16.3b	(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 10) (sqrt.f64 (log.f64 (hypot.f64 re im)))))
	16.3b	(*.f64 (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) 1) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (log.f64 10)))
	0.6b	(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)
✓	0.6b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
	0.5b	(/.f64 (pow.f64 (log.f64 10) -1/2) (/.f64 (sqrt.f64 (log.f64 10)) (log.f64 (hypot.f64 re im))))
▶	0.4b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (log.f64 (hypot.f64 re im)) (pow.f64 (log.f64 10) -1/2)))

Compiler

Compiled 5465 to 4223 computations (22.7% saved)

localize12.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	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 (1.9%)

Counts

2 → 48

Calls

2 calls:

30.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (pow.f64 (log.f64 10) -1/2))
25.0ms	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (log.f64 (hypot.f64 re im)) (pow.f64 (log.f64 10) -1/2)))

rewrite56.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

546×	`log-prod_binary64`
210×	`expm1-udef_binary64`
209×	`log1p-udef_binary64`
196×	`log-pow_binary64`
125×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	35
1	283	27
2	3139	27

Stop Event

1×	node limit

Counts

2 → 51

Calls

2 calls:

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

simplify41.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

577×	`fma-def_binary64`
422×	`times-frac_binary64`
304×	`associate-/r*_binary64`
280×	`associate-/l*_binary64`
214×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	142	2156
1	452	2108
2	1394	1872

Stop Event

1×	node limit

Counts

99 → 129

prune135.0ms (4.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	180	7	187

Error

Counts

187 → 7

Alt Table

Status	Error	Program
	16.3b	(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 10) (sqrt.f64 (log.f64 (hypot.f64 re im)))))
	16.3b	(*.f64 (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) 1) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (log.f64 10)))
	0.6b	(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)
✓	0.6b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
▶	0.5b	(/.f64 (pow.f64 (log.f64 10) -1/2) (/.f64 (sqrt.f64 (log.f64 10)) (log.f64 (hypot.f64 re im))))
✓	0.4b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (log.f64 (hypot.f64 re im)) (pow.f64 (log.f64 10) -1/2)))

Compiler

Compiled 4713 to 3743 computations (20.6% saved)

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.3b	(/.f64 (pow.f64 (log.f64 10) -1/2) (/.f64 (sqrt.f64 (log.f64 10)) (log.f64 (hypot.f64 re im))))
✓	0.4b	(/.f64 (sqrt.f64 (log.f64 10)) (log.f64 (hypot.f64 re im)))

series81.0ms (2.8%)

Counts

2 → 48

Calls

2 calls:

56.0ms	(/.f64 (sqrt.f64 (log.f64 10)) (log.f64 (hypot.f64 re im)))
25.0ms	(/.f64 (pow.f64 (log.f64 10) -1/2) (/.f64 (sqrt.f64 (log.f64 10)) (log.f64 (hypot.f64 re im))))

rewrite50.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	34
1	255	27
2	3212	27

Stop Event

1×	node limit

Counts

2 → 82

Calls

2 calls:

48.0ms	(/.f64 (pow.f64 (log.f64 10) -1/2) (/.f64 (sqrt.f64 (log.f64 10)) (log.f64 (hypot.f64 re im))))
48.0ms	(/.f64 (sqrt.f64 (log.f64 10)) (log.f64 (hypot.f64 re im)))

simplify66.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

520×	`fma-neg_binary64`
302×	`fma-def_binary64`
250×	`associate-/r*_binary64`
220×	`times-frac_binary64`
215×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	336	3108
1	1115	2917
2	4699	2913

Stop Event

1×	node limit

Counts

130 → 176

prune183.0ms (6.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	3	1	4
Picked	0	1	1
Done	1	1	2
Total	230	4	234

Error

Counts

234 → 4

Alt Table

Status	Error	Program
	0.6b	(neg.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 1/10)))
✓	0.6b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
✓	0.5b	(/.f64 (pow.f64 (log.f64 10) -1/2) (/.f64 (sqrt.f64 (log.f64 10)) (log.f64 (hypot.f64 re im))))
	0.3b	(*.f64 (/.f64 (pow.f64 (log1p.f64 9) -1/2) (neg.f64 (sqrt.f64 (log1p.f64 9)))) (neg.f64 (log.f64 (hypot.f64 re im))))

Compiler

Compiled 6813 to 5257 computations (22.8% saved)

regimes506.0ms (17.2%)

Accuracy

Total 0.3b remaining (98.4%)

Threshold costs 0.3b (98.4%)

Counts

63 → 1

Compiler

Compiled 7963 to 6515 computations (18.2% saved)

simplify3.0ms (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	33	25
3	42	25
4	47	25
5	50	25
6	51	25

Stop Event

1×

saturated

end86.0ms (2.9%)

Remove: (sort re im)
Compiler: Compiled 119 to 103 computations (13.4% saved)

Details

analyze5.0ms (0.2%)

sample1.1s (37.6%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize20.0ms (0.7%)

series33.0ms (1.1%)

rewrite37.0ms (1.3%)

simplify33.0ms (1.1%)

prune89.0ms (3%)

localize9.0ms (0.3%)

series53.0ms (1.8%)

rewrite50.0ms (1.7%)

simplify42.0ms (1.4%)

prune167.0ms (5.7%)

localize12.0ms (0.4%)

series55.0ms (1.9%)

rewrite56.0ms (1.9%)

simplify41.0ms (1.4%)

prune135.0ms (4.6%)

localize10.0ms (0.4%)

series81.0ms (2.8%)

rewrite50.0ms (1.7%)

simplify66.0ms (2.3%)

prune183.0ms (6.2%)

regimes506.0ms (17.2%)

simplify3.0ms (0.1%)

end86.0ms (2.9%)

Profiling