Details

analyze5.0ms (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)

sample1.1s (31.6%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

preprocess24.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

2×	`hypot-def_binary64`
2×	`fma-def_binary64`
1×	`swap-re-im`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	22
1	19	22
0	2	2
1	2	2

Stop Event

1×	unsound
1×	saturated

Symmetry

(sort re im)

Compiler

Compiled 14 to 10 computations (28.6% 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)

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))

series31.0ms (0.9%)

Counts

1 → 24

Calls

6 calls:

9.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))	re	-inf
4.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))	re	0
4.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))	im	0
4.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))	im	-inf
4.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))	im	inf

rewrite37.0ms (1%)

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	11
1	160	11
2	1927	11

Stop Event

1×	node limit

Counts

1 → 33

simplify40.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

428×	`associate-/l/_binary64`
349×	`associate-/r/_binary64`
292×	`times-frac_binary64`
222×	`sub-neg_binary64`
220×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	936
1	247	924
2	725	880
3	2992	860

Stop Event

1×	node limit

Counts

57 → 72

prune56.0ms (1.5%)

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
	12.8b	(*.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	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
	13.2b	(exp.f64 (log.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	1.3b	(*.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))
	13.1b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	0.8b	(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)
▶	0.5b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))

Compiler

Compiled 1661 to 1187 computations (28.5% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.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)))

series59.0ms (1.6%)

Counts

2 → 48

Calls

12 calls:

8.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))	im	inf
5.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))	re	0
5.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))	im	-inf
5.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))	im	0
5.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))	re	-inf

rewrite56.0ms (1.6%)

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

simplify51.0ms (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

prune152.0ms (4.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	170	4	174
Fresh	5	2	7
Picked	0	1	1
Done	1	0	1
Total	176	7	183

Error

Counts

183 → 7

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (pow.f64 (log.f64 10) -1/2))))
	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))
	13.2b	(exp.f64 (log.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	0.5b	(/.f64 (*.f64 (neg.f64 (log.f64 (hypot.f64 re im))) (pow.f64 (log.f64 10) -1/2)) (neg.f64 (sqrt.f64 (log.f64 10))))
	0.7b	(neg.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 1/10)))
	0.6b	(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)))) (cbrt.f64 (exp.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)))))) (log.f64 (cbrt.f64 (exp.f64 (/.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))))

Compiler

Compiled 4350 to 3366 computations (22.6% saved)

localize13.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (pow.f64 (log.f64 10) -1/2))))
✓	3.9b	(pow.f64 (hypot.f64 re im) (pow.f64 (log.f64 10) -1/2))

series156.0ms (4.3%)

Counts

2 → 48

Calls

12 calls:

20.0ms	(pow.f64 (hypot.f64 re im) (pow.f64 (log.f64 10) -1/2))	re	-inf
16.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (pow.f64 (log.f64 10) -1/2))))	re	inf
15.0ms	(pow.f64 (hypot.f64 re im) (pow.f64 (log.f64 10) -1/2))	im	-inf
15.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (pow.f64 (log.f64 10) -1/2))))	im	0
13.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (pow.f64 (log.f64 10) -1/2))))	re	0

rewrite45.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

544×	`log-prod_binary64`
212×	`expm1-udef_binary64`
211×	`log1p-udef_binary64`
208×	`log-pow_binary64`
128×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	33
1	286	26
2	3201	26

Stop Event

1×	node limit

Counts

2 → 49

simplify80.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

517×	`cancel-sign-sub-inv_binary64`
279×	`fma-neg_binary64`
256×	`fma-def_binary64`
200×	`associate-*r/_binary64`
199×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	273	3924
1	973	3843
2	3931	3503

Stop Event

1×	node limit

Counts

97 → 143

prune165.0ms (4.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	141	2	143
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	143	7	150

Error

Counts

150 → 7

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (pow.f64 (log.f64 10) -1/2))))
▶	0.5b	(/.f64 (*.f64 (pow.f64 (log1p.f64 9) -1/2) (log.f64 (hypot.f64 re im))) (sqrt.f64 (log1p.f64 9)))
	0.6b	(cbrt.f64 (/.f64 (pow.f64 (*.f64 (pow.f64 (log1p.f64 9) -1/2) (log.f64 (hypot.f64 re im))) 3) (pow.f64 (log1p.f64 9) 3/2)))
	13.2b	(exp.f64 (log.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	0.7b	(neg.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 1/10)))
	0.6b	(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)))) (cbrt.f64 (exp.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)))))) (log.f64 (cbrt.f64 (exp.f64 (/.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))))

Compiler

Compiled 6246 to 5193 computations (16.9% saved)

localize11.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (pow.f64 (log1p.f64 9) -1/2) (log.f64 (hypot.f64 re im)))
✓	0.4b	(/.f64 (*.f64 (pow.f64 (log1p.f64 9) -1/2) (log.f64 (hypot.f64 re im))) (sqrt.f64 (log1p.f64 9)))

series64.0ms (1.8%)

Counts

2 → 48

Calls

12 calls:

10.0ms	(/.f64 (*.f64 (pow.f64 (log1p.f64 9) -1/2) (log.f64 (hypot.f64 re im))) (sqrt.f64 (log1p.f64 9)))	im	0
7.0ms	(*.f64 (pow.f64 (log1p.f64 9) -1/2) (log.f64 (hypot.f64 re im)))	re	inf
5.0ms	(*.f64 (pow.f64 (log1p.f64 9) -1/2) (log.f64 (hypot.f64 re im)))	re	0
5.0ms	(*.f64 (pow.f64 (log1p.f64 9) -1/2) (log.f64 (hypot.f64 re im)))	im	0
5.0ms	(*.f64 (pow.f64 (log1p.f64 9) -1/2) (log.f64 (hypot.f64 re im)))	im	inf

rewrite51.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

562×	`log-prod_binary64`
207×	`expm1-udef_binary64`
207×	`log1p-udef_binary64`
193×	`log-pow_binary64`
117×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	252	28
2	3025	28

Stop Event

1×	node limit

Counts

2 → 63

simplify47.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

581×	`fma-def_binary64`
422×	`times-frac_binary64`
304×	`associate-/r*_binary64`
281×	`associate-/l*_binary64`
215×	`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

111 → 142

prune113.0ms (3.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	3	1	4
Picked	0	1	1
Done	1	1	2
Total	145	4	149

Error

Counts

149 → 4

Alt Table

Status	Error	Program
	0.3b	(*.f64 (/.f64 (pow.f64 (log.f64 10) -1/2) (sqrt.f64 (log.f64 10))) (log.f64 (hypot.f64 re im)))
	0.7b	(neg.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 1/10)))
✓	0.2b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (pow.f64 (log.f64 10) -1/2))))
✓	0.5b	(/.f64 (*.f64 (pow.f64 (log1p.f64 9) -1/2) (log.f64 (hypot.f64 re im))) (sqrt.f64 (log1p.f64 9)))

Compiler

Compiled 3581 to 2822 computations (21.2% saved)

regimes1.1s (30.3%)

Accuracy

Total 0.3b remaining (99.4%)

Threshold costs 0.3b (99.4%)

Counts

120 → 1

Compiler

Compiled 16339 to 13579 computations (16.9% saved)

simplify3.0ms (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

Stop Event

1×

saturated

end93.0ms (2.6%)

Stop Event

1×

fuel

Remove

(sort re im)

Compiler

Compiled 125 to 109 computations (12.8% saved)

Details

analyze5.0ms (0.1%)

sample1.1s (31.6%)

preprocess24.0ms (0.7%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series31.0ms (0.9%)

rewrite37.0ms (1%)

simplify40.0ms (1.1%)

prune56.0ms (1.5%)

localize9.0ms (0.3%)

series59.0ms (1.6%)

rewrite56.0ms (1.6%)

simplify51.0ms (1.4%)

prune152.0ms (4.2%)

localize13.0ms (0.4%)

series156.0ms (4.3%)

rewrite45.0ms (1.2%)

simplify80.0ms (2.2%)

prune165.0ms (4.6%)

localize11.0ms (0.3%)

series64.0ms (1.8%)

rewrite51.0ms (1.4%)

simplify47.0ms (1.3%)

prune113.0ms (3.1%)

regimes1.1s (30.3%)

simplify3.0ms (0.1%)

end93.0ms (2.6%)

Profiling