Details

analyze681.0ms (10.5%)

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)

sample1.9s (29.9%)

Results

1.7s	8256×	body	128	valid
178.0ms	1004×	body	128	invalid

Compiler

Compiled 95 to 62 computations (34.7% saved)

simplify125.0ms (1.9%)

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))
	33.2b	(/.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))

33.2b

(/.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)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series356.0ms (5.5%)

Counts

1 → 8

Calls

1 calls:

356.0ms

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

rewrite44.0ms (0.7%)

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 → 37

Calls

1 calls:

43.0ms

(/.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 (3.8%)

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

45 → 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

prune34.0ms (0.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	30	9	39
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	30	11	41

Error

0.1b

Counts

41 → 11

Alt Table

Status	Error	Program
	7.1b	(cbrt.f64 (/.f64 (pow.f64 (atan2.f64 im re) 3) (pow.f64 (log.f64 base) 3)))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	29.4b	(*.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))))
	33.2b	(/.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)))
	35.8b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))))
	1.2b	(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
	1.7b	(.f64 (pow.f64 (cbrt.f64 (atan2.f64 im re)) 2) (.f64 (cbrt.f64 (atan2.f64 im re)) (/.f64 1 (log.f64 base))))
▶	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	31.2b	(exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	0.6b	(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)
	30.5b	(pow.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 2)

Compiler

Compiled 804 to 373 computations (53.6% saved)

localize6.0ms (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)))

series362.0ms (5.6%)

Counts

2 → 44

Calls

2 calls:

329.0ms	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
33.0ms	(/.f64 1 (log.f64 base))

rewrite105.0ms (1.6%)

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 → 50

Calls

2 calls:

103.0ms	(/.f64 1 (log.f64 base))
103.0ms	(*.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

simplify273.0ms (4.2%)

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

94 → 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

prune46.0ms (0.7%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	47	7	54
Fresh	3	6	9
Picked	0	1	1
Done	0	1	1
Total	50	15	65

Error

0.0b

Counts

65 → 15

Alt Table

Status	Error	Program
✓	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	7.2b	(cbrt.f64 (*.f64 (pow.f64 (atan2.f64 im re) 3) (pow.f64 (/.f64 1 (log.f64 base)) 3)))
	31.2b	(exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	1.2b	(/.f64 (/.f64 (atan2.f64 im re) (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (cbrt.f64 (log.f64 base)))
	7.1b	(cbrt.f64 (/.f64 (pow.f64 (atan2.f64 im re) 3) (pow.f64 (log.f64 base) 3)))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
▶	0.6b	(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)
	1.7b	(/.f64 (pow.f64 (cbrt.f64 (atan2.f64 im re)) 2) (/.f64 (log.f64 base) (cbrt.f64 (atan2.f64 im re))))
	0.7b	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
	1.2b	(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
	35.7b	(*.f64 (atan2.f64 im re) (pow.f64 (pow.f64 (log.f64 base) -1/2) 2))
	1.2b	(*.f64 (atan2.f64 im re) (pow.f64 (/.f64 1 (cbrt.f64 (log.f64 base))) 3))
	0.9b	(.f64 (atan2.f64 im re) (.f64 (/.f64 1 (cbrt.f64 (log.f64 base))) (cbrt.f64 (pow.f64 (log.f64 base) -2))))
	30.5b	(pow.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 2)
	33.2b	(/.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 997 to 556 computations (44.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (log.f64 base) (atan2.f64 im re))
✓	0.4b	(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)

series693.0ms (10.7%)

Counts

2 → 44

Calls

2 calls:

361.0ms	(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)
332.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))

rewrite47.0ms (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 → 77

Calls

2 calls:

45.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))
45.0ms	(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

simplify214.0ms (3.3%)

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

121 → 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 (1%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	1	11	12
Picked	1	0	1
Done	0	2	2
Total	79	17	96

Error

0.0b

Counts

96 → 17

Alt Table

Status	Error	Program
✓	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	7.2b	(cbrt.f64 (*.f64 (pow.f64 (atan2.f64 im re) 3) (pow.f64 (/.f64 1 (log.f64 base)) 3)))
	31.3b	(sqrt.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -2))
	31.2b	(exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	1.2b	(/.f64 (/.f64 (atan2.f64 im re) (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (cbrt.f64 (log.f64 base)))
	7.1b	(cbrt.f64 (/.f64 (pow.f64 (atan2.f64 im re) 3) (pow.f64 (log.f64 base) 3)))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	30.5b	(pow.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 2)
	7.2b	(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (log.f64 base) 3) (pow.f64 (atan2.f64 im re) 3))) -1)
▶	0.7b	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
	1.2b	(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
	35.7b	(*.f64 (atan2.f64 im re) (pow.f64 (pow.f64 (log.f64 base) -1/2) 2))
	1.2b	(*.f64 (atan2.f64 im re) (pow.f64 (/.f64 1 (cbrt.f64 (log.f64 base))) 3))
	0.9b	(.f64 (atan2.f64 im re) (.f64 (/.f64 1 (cbrt.f64 (log.f64 base))) (cbrt.f64 (pow.f64 (log.f64 base) -2))))
	11.2b	(pow.f64 (log.f64 (pow.f64 base (/.f64 1 (atan2.f64 im re)))) -1)
	32.3b	(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) 2) -1)
	33.2b	(/.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 1505 to 726 computations (51.8% saved)

localize11.0ms (0.2%)

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))
✓	0.7b	(pow.f64 (/.f64 1 (log.f64 base)) 3)

series404.0ms (6.2%)

Counts

3 → 60

Calls

3 calls:

335.0ms	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
37.0ms	(pow.f64 (/.f64 1 (log.f64 base)) 3)
32.0ms	(cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3))

rewrite49.0ms (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 → 80

Calls

3 calls:

48.0ms	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
48.0ms	(cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3))
48.0ms	(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

simplify98.0ms (1.5%)

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

140 → 86

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

prune82.0ms (1.3%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	108	4	112
Fresh	4	10	14
Picked	1	0	1
Done	0	2	2
Total	113	16	129

Error

Counts

129 → 16

Alt Table

Status	Error	Program
	1.2b	(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
	7.1b	(cbrt.f64 (*.f64 (pow.f64 (log.f64 base) -3) (pow.f64 (atan2.f64 im re) 3)))
✓	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	7.2b	(cbrt.f64 (*.f64 (pow.f64 (atan2.f64 im re) 3) (pow.f64 (/.f64 1 (log.f64 base)) 3)))
	31.3b	(sqrt.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -2))
	30.5b	(pow.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 2)
	0.7b	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (log.f64 base) -3)))
	7.2b	(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (log.f64 base) 3) (pow.f64 (atan2.f64 im re) 3))) -1)
	1.1b	(.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (.f64 (cbrt.f64 (pow.f64 (log.f64 base) -2)) (/.f64 1 (cbrt.f64 (log.f64 base)))) 3)))
	35.7b	(*.f64 (atan2.f64 im re) (pow.f64 (pow.f64 (log.f64 base) -1/2) 2))
	1.2b	(*.f64 (atan2.f64 im re) (pow.f64 (/.f64 1 (cbrt.f64 (log.f64 base))) 3))
	1.2b	(/.f64 (/.f64 (atan2.f64 im re) (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (cbrt.f64 (log.f64 base)))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	0.8b	(.f64 (atan2.f64 im re) (cbrt.f64 (.f64 (cbrt.f64 (pow.f64 (log.f64 base) -2)) (*.f64 (/.f64 1 (cbrt.f64 (log.f64 base))) (pow.f64 (log.f64 base) -2)))))
	11.2b	(pow.f64 (log.f64 (pow.f64 base (/.f64 1 (atan2.f64 im re)))) -1)
	33.2b	(/.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 1650 to 914 computations (44.6% saved)

regimes371.0ms (5.7%)

Accuracy

Total 0.3b remaining (88.4%)

Threshold costs 0.3b (88.4%)

Counts

58 → 1

Compiler

Compiled 4636 to 3256 computations (29.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

end203.0ms (3.1%)

Compiler: Compiled 270 to 196 computations (27.4% saved)

Details

analyze681.0ms (10.5%)

sample1.9s (29.9%)

simplify125.0ms (1.9%)

prune5.0ms (0.1%)

localize5.0ms (0.1%)

series356.0ms (5.5%)

rewrite44.0ms (0.7%)

simplify246.0ms (3.8%)

prune34.0ms (0.5%)

localize6.0ms (0.1%)

series362.0ms (5.6%)

rewrite105.0ms (1.6%)

simplify273.0ms (4.2%)

prune46.0ms (0.7%)

localize6.0ms (0.1%)

series693.0ms (10.7%)

rewrite47.0ms (0.7%)

simplify214.0ms (3.3%)

prune65.0ms (1%)

localize11.0ms (0.2%)

series404.0ms (6.2%)

rewrite49.0ms (0.8%)

simplify98.0ms (1.5%)

prune82.0ms (1.3%)

regimes371.0ms (5.7%)

simplify2.0ms (0%)

end203.0ms (3.1%)

Profiling