Details

analyze627.0ms (8.6%)

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)

sample2.3s (31.2%)

Results

2.0s	8256×	body	128	valid
221.0ms	1035×	body	128	invalid

Compiler

Compiled 95 to 62 computations (34.7% saved)

simplify125.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1042×	`fma-def_binary64`
693×	`fma-neg_binary64`
662×	`cube-prod_binary64`
522×	`pow-sqr_binary64`
453×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	20
1	35	19
2	57	12
3	80	9
4	89	9
5	216	9
6	486	9
7	978	9
8	1296	9
9	1996	9
10	2287	9
11	3311	9
12	4367	9
13	4644	9
14	4721	9
15	4986	9
16	4826	9

prune5.0ms (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
▶	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	34.7b	(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))

Status

Error

Program

▶

0.3b

(/.f64 (atan2.f64 im re) (log.f64 base))

34.7b

(/.f64 (-.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) 0)) (+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 0 0)))

Compiler

Compiled 117 to 73 computations (37.6% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))

series417.0ms (5.7%)

Counts

1 → 8

Calls

1 calls:

417.0ms

(/.f64 (atan2.f64 im re) (log.f64 base))

rewrite43.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

643×	`log1p-expm1-u_binary64`
643×	`expm1-log1p-u_binary64`
351×	`log-prod_binary64`
131×	`expm1-udef_binary64`
131×	`log1p-udef_binary64`

Counts

1 → 36

Calls

1 calls:

42.0ms

(/.f64 (atan2.f64 im re) (log.f64 base))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	138	9
2	1687	9
3	5224	9
0	0	0
1	0	0

simplify246.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

1250×	`distribute-rgt-in_binary64`
882×	`div-sub_binary64`
628×	`fma-neg_binary64`
606×	`associate--r-_binary64`
502×	`fma-def_binary64`

Counts

44 → 39

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	16	104
1	29	104
2	42	96
3	90	72
4	154	72
5	462	72
6	987	72
7	1899	72
8	2363	72
9	2430	72
10	2491	72
11	2599	72
12	4628	72
13	3636	72
14	4106	72
15	4340	72
16	4364	72
17	4364	72
18	4313	72
19	4363	72
20	4469	72
21	4475	72
22	5538	72

prune35.0ms (0.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	29	10	39
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	29	12	41

Error

0.1b

Counts

41 → 12

Alt Table

Status	Error	Program
	31.6b	(exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
▶	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	31.0b	(pow.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 2)
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	32.8b	(*.f64 (/.f64 (sqrt.f64 (atan2.f64 im re)) (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (cbrt.f64 (log.f64 base))))
	1.7b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (atan2.f64 im re)) 2) (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	1.1b	(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
	32.7b	(.f64 (sqrt.f64 (atan2.f64 im re)) (.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 1 (log.f64 base))))
	5.4b	(cbrt.f64 (/.f64 (pow.f64 (atan2.f64 im re) 3) (pow.f64 (log.f64 base) 3)))
	5.4b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3))
	0.7b	(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)
	34.7b	(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))

Compiler

Compiled 838 to 397 computations (52.6% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (log.f64 base))
✓	0.3b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))

series464.0ms (6.3%)

Counts

2 → 44

Calls

2 calls:

432.0ms	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
32.0ms	(/.f64 1 (log.f64 base))

rewrite105.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

712×	`log1p-expm1-u_binary64`
712×	`expm1-log1p-u_binary64`
149×	`expm1-udef_binary64`
149×	`log1p-udef_binary64`
92×	`fma-neg_binary64`

Counts

2 → 49

Calls

2 calls:

104.0ms	(/.f64 1 (log.f64 base))
104.0ms	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	174	15
2	1909	15
3	4988	15
4	5000	15
5	5007	15
0	0	0
1	0	0

simplify279.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

1250×	`distribute-rgt-in_binary64`
882×	`div-sub_binary64`
628×	`fma-neg_binary64`
606×	`associate--r-_binary64`
502×	`fma-def_binary64`

Counts

93 → 54

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	388
1	32	388
2	45	372
3	92	372
4	154	372
5	462	372
6	987	372
7	1899	372
8	2365	372
9	2430	372
10	2491	372
11	2599	372
12	4628	372
13	3636	372
14	4106	372
15	4340	372
16	4364	372
17	4364	372
18	4313	372
19	4363	372
20	4469	372
21	4475	372
22	5538	372

prune45.0ms (0.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	49	5	54
Fresh	6	4	10
Picked	0	1	1
Done	0	1	1
Total	55	11	66

Error

0.0b

Counts

66 → 11

Alt Table

Status	Error	Program
	31.0b	(pow.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 2)
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	32.8b	(*.f64 (/.f64 (sqrt.f64 (atan2.f64 im re)) (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (cbrt.f64 (log.f64 base))))
	0.9b	(.f64 (atan2.f64 im re) (.f64 (/.f64 1 (cbrt.f64 (log.f64 base))) (cbrt.f64 (pow.f64 (log.f64 base) -2))))
	1.1b	(/.f64 (/.f64 (atan2.f64 im re) (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (cbrt.f64 (log.f64 base)))
✓	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	34.5b	(*.f64 (atan2.f64 im re) (exp.f64 (neg.f64 (log.f64 (log.f64 base)))))
	0.8b	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
	5.4b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3))
▶	0.7b	(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)
	1.2b	(*.f64 (atan2.f64 im re) (pow.f64 (/.f64 1 (cbrt.f64 (log.f64 base))) 3))

Compiler

Compiled 849 to 448 computations (47.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (log.f64 base) (atan2.f64 im re))
✓	0.5b	(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)

series860.0ms (11.8%)

Counts

2 → 44

Calls

2 calls:

436.0ms	(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)
424.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))

rewrite51.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

791×	`log1p-expm1-u_binary64`
791×	`expm1-log1p-u_binary64`
158×	`log1p-udef_binary64`
91×	`add-sqr-sqrt_binary64`
84×	`add-log-exp_binary64`

Counts

2 → 76

Calls

2 calls:

49.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))
49.0ms	(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	180	18
2	2075	18
3	5147	18
0	0	0
1	0	0

simplify218.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1461×	`associate-+l+_binary64`
799×	`distribute-rgt-in_binary64`
752×	`unsub-neg_binary64`
736×	`sub-neg_binary64`
662×	`div-sub_binary64`

Counts

120 → 81

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	428
1	40	428
2	63	396
3	122	396
4	307	396
5	758	396
6	1494	396
7	1867	396
8	2145	396
9	2393	396
10	2795	396
11	2863	396
12	2728	396
13	3858	396
14	3444	396
15	3670	396
16	3982	396
17	3982	396
18	4094	396
19	5463	396

prune65.0ms (0.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	2	6	8
Picked	0	1	1
Done	1	1	2
Total	80	12	92

Error

0.0b

Counts

92 → 12

Alt Table

Status	Error	Program
	0.9b	(.f64 (atan2.f64 im re) (.f64 (/.f64 1 (cbrt.f64 (log.f64 base))) (cbrt.f64 (pow.f64 (log.f64 base) -2))))
	33.9b	(pow.f64 (pow.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) 3) 1/3) -1)
	34.5b	(*.f64 (atan2.f64 im re) (exp.f64 (neg.f64 (log.f64 (log.f64 base)))))
	33.4b	(/.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))
	32.8b	(*.f64 (/.f64 (sqrt.f64 (atan2.f64 im re)) (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (cbrt.f64 (log.f64 base))))
	1.4b	(pow.f64 (.f64 (pow.f64 (cbrt.f64 (log.f64 base)) 2) (.f64 (cbrt.f64 (log.f64 base)) (/.f64 1 (atan2.f64 im re)))) -1)
	1.5b	(/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) 2)) (cbrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))
▶	0.8b	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
	5.4b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3))
✓	0.7b	(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	1.2b	(*.f64 (atan2.f64 im re) (pow.f64 (/.f64 1 (cbrt.f64 (log.f64 base))) 3))

Compiler

Compiled 1375 to 610 computations (55.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f64 1 (log.f64 base))
✓	0.3b	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
✓	0.6b	(cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3))
✓	0.8b	(pow.f64 (/.f64 1 (log.f64 base)) 3)

series495.0ms (6.8%)

Counts

3 → 60

Calls

3 calls:

422.0ms	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
41.0ms	(pow.f64 (/.f64 1 (log.f64 base)) 3)
32.0ms	(cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3))

rewrite55.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

868×	`log1p-expm1-u_binary64`
868×	`expm1-log1p-u_binary64`
104×	`add-sqr-sqrt_binary64`
97×	`add-log-exp_binary64`
96×	`add-cbrt-cube_binary64`

Counts

3 → 79

Calls

3 calls:

53.0ms	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
53.0ms	(cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3))
53.0ms	(pow.f64 (/.f64 1 (log.f64 base)) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	27
1	221	21
2	2337	21
3	5244	21
0	0	0
1	0	0

simplify102.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

681×	`fma-neg_binary64`
634×	`unsub-neg_binary64`
624×	`div-sub_binary64`
491×	`fma-def_binary64`
456×	`distribute-rgt-in_binary64`

Counts

139 → 85

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	504
1	58	504
2	112	504
3	301	504
4	691	504
5	2735	504
6	4412	504
7	4991	504
8	4995	504
9	4876	504

prune90.0ms (1.2%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	111	12	123

Error

0.0b

Counts

123 → 12

Alt Table

Status	Error	Program
	0.9b	(.f64 (atan2.f64 im re) (.f64 (/.f64 1 (cbrt.f64 (log.f64 base))) (cbrt.f64 (pow.f64 (log.f64 base) -2))))
	33.9b	(pow.f64 (pow.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) 3) 1/3) -1)
	34.5b	(*.f64 (atan2.f64 im re) (exp.f64 (neg.f64 (log.f64 (log.f64 base)))))
	33.4b	(/.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))
	32.8b	(*.f64 (/.f64 (sqrt.f64 (atan2.f64 im re)) (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (cbrt.f64 (log.f64 base))))
	1.4b	(pow.f64 (.f64 (pow.f64 (cbrt.f64 (log.f64 base)) 2) (.f64 (cbrt.f64 (log.f64 base)) (/.f64 1 (atan2.f64 im re)))) -1)
	1.5b	(/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) 2)) (cbrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))
✓	0.8b	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
	5.4b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3))
✓	0.7b	(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	1.2b	(*.f64 (atan2.f64 im re) (pow.f64 (/.f64 1 (cbrt.f64 (log.f64 base))) 3))

Compiler

Compiled 1576 to 853 computations (45.9% saved)

regimes513.0ms (7%)

Accuracy

Total 0.2b remaining (81.2%)

Threshold costs 0.2b (81.2%)

Counts

96 → 1

Compiler

Compiled 7366 to 5351 computations (27.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

end153.0ms (2.1%)

Compiler: Compiled 205 to 139 computations (32.2% saved)

Details

analyze627.0ms (8.6%)

sample2.3s (31.2%)

simplify125.0ms (1.7%)

prune5.0ms (0.1%)

localize6.0ms (0.1%)

series417.0ms (5.7%)

rewrite43.0ms (0.6%)

simplify246.0ms (3.4%)

prune35.0ms (0.5%)

localize7.0ms (0.1%)

series464.0ms (6.3%)

rewrite105.0ms (1.4%)

simplify279.0ms (3.8%)

prune45.0ms (0.6%)

localize7.0ms (0.1%)

series860.0ms (11.8%)

rewrite51.0ms (0.7%)

simplify218.0ms (3%)

prune65.0ms (0.9%)

localize10.0ms (0.1%)

series495.0ms (6.8%)

rewrite55.0ms (0.8%)

simplify102.0ms (1.4%)

prune90.0ms (1.2%)

regimes513.0ms (7%)

simplify2.0ms (0%)

end153.0ms (2.1%)

Profiling