Details

analyze573.0ms (8%)

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)

sample1.8s (25.2%)

Results

1.6s	8256×	body	128	valid
194.0ms	1033×	body	128	invalid

Compiler

Compiled 64 to 42 computations (34.4% saved)

preprocess46.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

628×	`fma-def_binary64`
405×	`associate-/l/_binary64`
300×	`distribute-rgt-in_binary64`
288×	`cube-prod_binary64`
262×	`associate-*l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	88
1	91	84
2	108	84
3	141	56
4	196	44
5	221	44
6	648	44
7	2437	44
8	4041	44
9	4419	44
0	3	3
1	3	3

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort re im)

Compiler

Compiled 31 to 20 computations (35.5% saved)

simplify41.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

567×	`associate-/l/_binary64`
526×	`cube-prod_binary64`
434×	`times-frac_binary64`
365×	`sqr-pow_binary64`
291×	`pow-sqr_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	22
1	31	21
2	38	21
3	49	14
4	66	11
5	75	11
6	218	11
7	1196	11
8	1804	11
9	2015	11
10	2509	11
11	2992	11
12	3869	11

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0.1%)

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
▶	0.4b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
	32.1b	(/.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

▶

0.4b

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

32.1b

(/.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)
✓	0.4b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

series584.0ms (8.1%)

Counts

2 → 60

Calls

15 calls:

214.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))	base	-inf
167.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))	base	0
157.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))	base	inf
10.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))	re	-inf
5.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))	re	0

rewrite45.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

713×	`log1p-expm1-u_binary64`
713×	`expm1-log1p-u_binary64`
145×	`expm1-udef_binary64`
145×	`log1p-udef_binary64`
81×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	158	15
2	1965	15

Stop Event

1×	node limit

Counts

2 → 54

simplify42.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

762×	`times-frac_binary64`
406×	`associate-/r*_binary64`
360×	`associate-/l*_binary64`
332×	`fma-def_binary64`
209×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	133	1684
1	394	1570
2	1188	1490

Stop Event

1×	node limit

Counts

114 → 129

prune103.0ms (1.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	116	13	129
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	118	13	131

Error

0.0b

Counts

131 → 13

Alt Table

Status	Error	Program
	31.6b	(pow.f64 (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) 2)
	15.1b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))) 1)
	0.7b	(cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (pow.f64 (log.f64 base) 3)))
	15.7b	(*.f64 (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) 1) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (log.f64 base)))
	1.3b	(*.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (pow.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) 2))
	0.5b	(pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) -1)
▶	0.4b	(/.f64 (log.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2))) (log.f64 base))
	33.8b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 base))))
	1.2b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	31.5b	(exp.f64 (log.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	14.8b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	0.6b	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base))))
	1.2b	(.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) 2) (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 1 (log.f64 base))))

Compiler

Compiled 2718 to 1459 computations (46.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2))
✓	0.4b	(/.f64 (log.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2))) (log.f64 base))
✓	0.5b	(pow.f64 (cbrt.f64 (hypot.f64 re im)) 2)
✓	0.5b	(cbrt.f64 (hypot.f64 re im))

series616.0ms (8.6%)

Counts

4 → 76

Calls

27 calls:

180.0ms	(/.f64 (log.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2))) (log.f64 base))	base	0
163.0ms	(/.f64 (log.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2))) (log.f64 base))	base	-inf
161.0ms	(/.f64 (log.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2))) (log.f64 base))	base	inf
10.0ms	(pow.f64 (cbrt.f64 (hypot.f64 re im)) 2)	re	0
8.0ms	(cbrt.f64 (hypot.f64 re im))	re	0

rewrite55.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

479×	`log-prod_binary64`
262×	`pow2_binary64`
184×	`pow1/3_binary64`
183×	`expm1-udef_binary64`
183×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	30
1	241	30
2	2622	30

Stop Event

1×	node limit

Counts

4 → 106

simplify54.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

762×	`times-frac_binary64`
677×	`fma-def_binary64`
296×	`cancel-sign-sub-inv_binary64`
208×	`fma-neg_binary64`
136×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	221	2206
1	671	2090
2	2069	1994

Stop Event

1×	node limit

Counts

182 → 213

prune230.0ms (3.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	253	2	255
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	255	13	268

Error

Counts

268 → 13

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 (log.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (pow.f64 (hypot.f64 re im) 1/3) 2))) (log.f64 base))
	14.8b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	0.7b	(cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (pow.f64 (log.f64 base) 3)))
	15.7b	(*.f64 (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) 1) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (log.f64 base)))
	1.3b	(*.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (pow.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) 2))
	0.5b	(pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) -1)
	31.6b	(pow.f64 (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) 2)
	0.5b	(*.f64 (/.f64 1 (log.f64 base)) (log.f64 (hypot.f64 re im)))
✓	0.4b	(/.f64 (log.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2))) (log.f64 base))
	1.2b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	31.5b	(exp.f64 (log.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	0.6b	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base))))
	1.2b	(.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) 2) (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 1 (log.f64 base))))

Compiler

Compiled 5790 to 3113 computations (46.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (log.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (pow.f64 (hypot.f64 re im) 1/3) 2))) (log.f64 base))
✓	0.5b	(pow.f64 (pow.f64 (hypot.f64 re im) 1/3) 2)
	0.5b	(cbrt.f64 (hypot.f64 re im))
✓	5.1b	(pow.f64 (hypot.f64 re im) 1/3)

series601.0ms (8.4%)

Counts

3 → 52

Calls

21 calls:

168.0ms	(/.f64 (log.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (pow.f64 (hypot.f64 re im) 1/3) 2))) (log.f64 base))	base	0
165.0ms	(/.f64 (log.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (pow.f64 (hypot.f64 re im) 1/3) 2))) (log.f64 base))	base	-inf
162.0ms	(/.f64 (log.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (pow.f64 (hypot.f64 re im) 1/3) 2))) (log.f64 base))	base	inf
9.0ms	(pow.f64 (pow.f64 (hypot.f64 re im) 1/3) 2)	im	0
8.0ms	(pow.f64 (pow.f64 (hypot.f64 re im) 1/3) 2)	re	0

rewrite49.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

512×	`log-prod_binary64`
199×	`expm1-udef_binary64`
199×	`log1p-udef_binary64`
187×	`log-pow_binary64`
118×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	26
1	276	26
2	2908	26

Stop Event

1×	node limit

Counts

3 → 83

simplify45.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

616×	`associate-r_binary64`
552×	`fma-def_binary64`
548×	`associate-l_binary64`
294×	`times-frac_binary64`
240×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	187	1718
1	549	1620
2	1629	1540

Stop Event

1×	node limit

Counts

135 → 160

prune153.0ms (2.1%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	202	13	215

Error

Counts

215 → 13

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 (log.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (pow.f64 (hypot.f64 re im) 1/3) 2))) (log.f64 base))
	14.8b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	0.7b	(cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (pow.f64 (log.f64 base) 3)))
	15.7b	(*.f64 (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) 1) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (log.f64 base)))
	1.3b	(*.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (pow.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) 2))
▶	0.5b	(pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) -1)
	31.6b	(pow.f64 (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) 2)
	0.5b	(*.f64 (/.f64 1 (log.f64 base)) (log.f64 (hypot.f64 re im)))
✓	0.4b	(/.f64 (log.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2))) (log.f64 base))
	1.2b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	31.5b	(exp.f64 (log.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	0.6b	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base))))
	1.2b	(.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) 2) (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 1 (log.f64 base))))

Compiler

Compiled 5024 to 2735 computations (45.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series1.2s (16%)

Counts

2 → 72

Calls

18 calls:

182.0ms	(pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) -1)	base	0
177.0ms	(pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) -1)	base	-inf
176.0ms	(pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) -1)	base	inf
166.0ms	(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))	base	inf
165.0ms	(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))	base	-inf

rewrite49.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

861×	`log1p-expm1-u_binary64`
861×	`expm1-log1p-u_binary64`
100×	`add-sqr-sqrt_binary64`
93×	`add-log-exp_binary64`
92×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	200	22
2	2429	22

Stop Event

1×	node limit

Counts

2 → 76

simplify55.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

465×	`times-frac_binary64`
386×	`associate-/r*_binary64`
283×	`associate-/l*_binary64`
248×	`fma-def_binary64`
193×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	352	3790
1	1280	3520

Stop Event

1×	node limit

Counts

148 → 179

prune187.0ms (2.6%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	229	1	230
Fresh	2	8	10
Picked	0	1	1
Done	0	2	2
Total	231	12	243

Error

Counts

243 → 12

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 (log.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (pow.f64 (hypot.f64 re im) 1/3) 2))) (log.f64 base))
	14.8b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	1.3b	(*.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (pow.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) 2))
✓	0.5b	(pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) -1)
	31.6b	(pow.f64 (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) 2)
✓	0.4b	(/.f64 (log.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2))) (log.f64 base))
	0.5b	(/.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 (hypot.f64 re im))))
	1.2b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	31.5b	(exp.f64 (log.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	15.7b	(*.f64 (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) 1) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (log.f64 base)))
	0.6b	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base))))
	1.2b	(.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) 2) (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 1 (log.f64 base))))

Compiler

Compiled 6627 to 3767 computations (43.2% saved)

regimes485.0ms (6.8%)

Accuracy

Total 0.3b remaining (89.5%)

Threshold costs 0.3b (89.5%)

Counts

99 → 1

Compiler

Compiled 7581 to 5476 computations (27.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15

Stop Event

1×

saturated

end155.0ms (2.2%)

Stop Event

1×

fuel

Remove

(sort re im)

Compiler

Compiled 234 to 161 computations (31.2% saved)

Details

analyze573.0ms (8%)

sample1.8s (25.2%)

preprocess46.0ms (0.6%)

simplify41.0ms (0.6%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series584.0ms (8.1%)

rewrite45.0ms (0.6%)

simplify42.0ms (0.6%)

prune103.0ms (1.4%)

localize10.0ms (0.1%)

series616.0ms (8.6%)

rewrite55.0ms (0.8%)

simplify54.0ms (0.8%)

prune230.0ms (3.2%)

localize14.0ms (0.2%)

series601.0ms (8.4%)

rewrite49.0ms (0.7%)

simplify45.0ms (0.6%)

prune153.0ms (2.1%)

localize8.0ms (0.1%)

series1.2s (16%)

rewrite49.0ms (0.7%)

simplify55.0ms (0.8%)

prune187.0ms (2.6%)

regimes485.0ms (6.8%)

simplify2.0ms (0%)

end155.0ms (2.2%)

Profiling