Details

analyze573.0ms (11.4%)

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 (35.3%)

Results

1.6s	8256×	body	128	valid
190.0ms	1033×	body	128	invalid

Compiler

Compiled 64 to 42 computations (34.4% saved)

preprocess55.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

752×	`fma-neg_binary64`
403×	`fma-def_binary64`
349×	`associate-/l*_binary64`
278×	`distribute-rgt-in_binary64`
264×	`div-sub_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	80
1	137	76
2	227	48
3	329	36
4	407	36
5	993	36
6	2449	36
7	3517	36
8	4122	36
9	4229	36
10	4431	36
11	4946	36
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 31 to 20 computations (35.5% saved)

simplify22.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

877×	`fma-def_binary64`
692×	`fma-neg_binary64`
407×	`associate-/l*_binary64`
380×	`div-sub_binary64`
313×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	20
1	41	19
2	68	12
3	94	9
4	115	9
5	273	9
6	1005	9
7	2320	9
8	3369	9

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
▶	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	32.0b	(/.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))

32.0b

(/.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))

series360.0ms (7.1%)

Counts

1 → 8

Calls

9 calls:

71.0ms	(/.f64 (atan2.f64 im re) (log.f64 base))	re	inf
58.0ms	(/.f64 (atan2.f64 im re) (log.f64 base))	im	0
50.0ms	(/.f64 (atan2.f64 im re) (log.f64 base))	re	-inf
49.0ms	(/.f64 (atan2.f64 im re) (log.f64 base))	im	inf
49.0ms	(/.f64 (atan2.f64 im re) (log.f64 base))	re	0

rewrite40.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

702×	`pow1_binary64`
643×	`add-log-exp_binary64`
643×	`log1p-expm1-u_binary64`
643×	`expm1-log1p-u_binary64`
72×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	139	9
2	1734	9

Stop Event

1×	node limit

Counts

1 → 32

simplify30.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

762×	`div-sub_binary64`
628×	`fma-neg_binary64`
494×	`fma-def_binary64`
292×	`distribute-rgt-in_binary64`
231×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	16	104
1	29	104
2	43	96
3	92	72
4	189	72
5	583	72
6	2308	72
7	4815	72

Stop Event

1×	node limit

Counts

40 → 35

prune39.0ms (0.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	23	12	35
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	24	13	37

Error

0.0b

Counts

37 → 13

Alt Table

Status	Error	Program
	34.3b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (atan2.f64 im re)) 2) (sqrt.f64 (log.f64 base))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (sqrt.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))))
	30.8b	(exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	33.8b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))))
	7.0b	(cbrt.f64 (/.f64 (pow.f64 (atan2.f64 im re) 3) (pow.f64 (log.f64 base) 3)))
	30.3b	(pow.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 2)
▶	0.3b	(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
	1.0b	(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)
	31.1b	(*.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))))
	32.0b	(/.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)))
	1.5b	(pow.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 3)
	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	30.9b	(.f64 (sqrt.f64 (atan2.f64 im re)) (.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 1 (log.f64 base))))

Compiler

Compiled 822 to 412 computations (49.9% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (/.f64 1 base))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base)))

series409.0ms (8.1%)

Counts

2 → 16

Calls

12 calls:

62.0ms	(/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base)))	im	-inf
60.0ms	(/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base)))	re	inf
59.0ms	(/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base)))	im	inf
58.0ms	(/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base)))	re	-inf
58.0ms	(/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base)))	im	0

rewrite46.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

845×	`pow1_binary64`
775×	`log1p-expm1-u_binary64`
775×	`expm1-log1p-u_binary64`
89×	`add-sqr-sqrt_binary64`
87×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	180	16
2	2180	16

Stop Event

1×	node limit

Counts

2 → 58

simplify44.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

901×	`fma-neg_binary64`
549×	`div-sub_binary64`
510×	`fma-def_binary64`
352×	`times-frac_binary64`
216×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	176
1	23	176
2	36	176
3	54	176
4	80	176
5	147	176
6	266	176
7	404	176
8	501	176
9	635	176
10	750	176
11	1004	176
12	1406	176
13	2527	176
14	4213	176

Stop Event

1×	node limit

Counts

74 → 63

prune65.0ms (1.3%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	56	7	63
Fresh	4	8	12
Picked	0	1	1
Done	0	0	0
Total	60	16	76

Error

0.0b

Counts

76 → 16

Alt Table

Status	Error	Program
	31.0b	(*.f64 -1 (/.f64 (atan2.f64 im re) (-.f64 (exp.f64 (log1p.f64 (neg.f64 (log.f64 base)))) 1)))
	30.8b	(exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	33.8b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))))
	30.7b	(*.f64 -1 (/.f64 (atan2.f64 im re) (+.f64 (log.f64 (cbrt.f64 (pow.f64 base -2))) (log.f64 (/.f64 1 (cbrt.f64 base))))))
	1.0b	(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)
	7.0b	(cbrt.f64 (/.f64 (pow.f64 (atan2.f64 im re) 3) (pow.f64 (log.f64 base) 3)))
	30.3b	(pow.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 2)
	31.3b	(*.f64 -1 (pow.f64 (sqrt.f64 (/.f64 (neg.f64 (atan2.f64 im re)) (log.f64 base))) 2))
	1.5b	(pow.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 3)
	0.5b	(.f64 -1 (/.f64 (atan2.f64 im re) (/.f64 (-.f64 0 (pow.f64 (log.f64 base) 3)) (+.f64 0 (+.f64 (.f64 (log.f64 base) (log.f64 base)) (*.f64 0 (log.f64 base)))))))
✓	0.3b	(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
	34.3b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (atan2.f64 im re)) 2) (sqrt.f64 (log.f64 base))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (sqrt.f64 (log.f64 base))))
▶	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	30.9b	(.f64 -1 (.f64 (/.f64 1 (sqrt.f64 (neg.f64 (log.f64 base)))) (/.f64 (atan2.f64 im re) (sqrt.f64 (neg.f64 (log.f64 base))))))
	31.1b	(*.f64 -1 (/.f64 (atan2.f64 im re) (exp.f64 (log.f64 (neg.f64 (log.f64 base))))))
	1.2b	(*.f64 -1 (/.f64 (atan2.f64 im re) (pow.f64 (cbrt.f64 (neg.f64 (log.f64 base))) 3)))

Compiler

Compiled 1355 to 733 computations (45.9% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series371.0ms (7.3%)

Counts

2 → 44

Calls

12 calls:

58.0ms	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))	im	0
51.0ms	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))	re	inf
51.0ms	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))	re	0
50.0ms	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))	im	inf
50.0ms	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))	im	-inf

rewrite39.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

779×	`pow1_binary64`
712×	`log1p-expm1-u_binary64`
712×	`expm1-log1p-u_binary64`
86×	`add-sqr-sqrt_binary64`
84×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	175	15
2	2031	15

Stop Event

1×	node limit

Counts

2 → 49

simplify42.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

741×	`div-sub_binary64`
628×	`fma-neg_binary64`
498×	`fma-def_binary64`
292×	`distribute-rgt-in_binary64`
231×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	388
1	32	388
2	46	372
3	94	372
4	190	372
5	584	372
6	2294	372
7	4775	372

Stop Event

1×	node limit

Counts

93 → 54

prune51.0ms (1%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	50	4	54
Fresh	3	11	14
Picked	1	0	1
Done	0	1	1
Total	54	16	70

Error

0.0b

Counts

70 → 16

Alt Table

Status	Error	Program
	31.0b	(*.f64 -1 (/.f64 (atan2.f64 im re) (-.f64 (exp.f64 (log1p.f64 (neg.f64 (log.f64 base)))) 1)))
	30.8b	(exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	30.7b	(*.f64 -1 (/.f64 (atan2.f64 im re) (+.f64 (log.f64 (cbrt.f64 (pow.f64 base -2))) (log.f64 (/.f64 1 (cbrt.f64 base))))))
	1.0b	(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)
	7.0b	(cbrt.f64 (/.f64 (pow.f64 (atan2.f64 im re) 3) (pow.f64 (log.f64 base) 3)))
	30.3b	(pow.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 2)
	34.0b	(*.f64 (atan2.f64 im re) (exp.f64 (neg.f64 (log.f64 (log.f64 base)))))
	31.3b	(*.f64 -1 (pow.f64 (sqrt.f64 (/.f64 (neg.f64 (atan2.f64 im re)) (log.f64 base))) 2))
	1.5b	(pow.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 3)
	33.8b	(*.f64 (atan2.f64 im re) (pow.f64 (pow.f64 (log.f64 base) -1/2) 2))
▶	0.4b	(*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) -1))
	31.1b	(*.f64 -1 (/.f64 (atan2.f64 im re) (exp.f64 (log.f64 (neg.f64 (log.f64 base))))))
	0.5b	(.f64 -1 (/.f64 (atan2.f64 im re) (/.f64 (-.f64 0 (pow.f64 (log.f64 base) 3)) (+.f64 0 (+.f64 (.f64 (log.f64 base) (log.f64 base)) (*.f64 0 (log.f64 base)))))))
✓	0.3b	(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
	0.8b	(.f64 (atan2.f64 im re) (.f64 (pow.f64 (cbrt.f64 (pow.f64 (log.f64 base) 2)) -1) (pow.f64 (cbrt.f64 (log.f64 base)) -1)))
	1.2b	(*.f64 -1 (/.f64 (atan2.f64 im re) (pow.f64 (cbrt.f64 (neg.f64 (log.f64 base))) 3)))

Compiler

Compiled 1028 to 602 computations (41.4% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series379.0ms (7.5%)

Counts

2 → 48

Calls

12 calls:

61.0ms	(*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) -1))	im	0
56.0ms	(*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) -1))	re	inf
52.0ms	(*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) -1))	im	inf
49.0ms	(*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) -1))	im	-inf
49.0ms	(*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) -1))	re	0

rewrite37.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

769×	`pow1_binary64`
705×	`log1p-expm1-u_binary64`
705×	`expm1-log1p-u_binary64`
87×	`add-sqr-sqrt_binary64`
84×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	175	15
2	1965	15

Stop Event

1×	node limit

Counts

2 → 37

simplify36.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

796×	`div-sub_binary64`
628×	`fma-neg_binary64`
494×	`fma-def_binary64`
292×	`distribute-rgt-in_binary64`
231×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	396
1	33	396
2	47	396
3	94	396
4	190	396
5	585	396
6	2311	396
7	4812	396

Stop Event

1×	node limit

Counts

85 → 41

prune30.0ms (0.6%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	14	14
Picked	0	1	1
Done	0	1	1
Total	41	16	57

Error

0.0b

Counts

57 → 16

Alt Table

Status	Error	Program
	31.0b	(*.f64 -1 (/.f64 (atan2.f64 im re) (-.f64 (exp.f64 (log1p.f64 (neg.f64 (log.f64 base)))) 1)))
	30.8b	(exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	30.7b	(*.f64 -1 (/.f64 (atan2.f64 im re) (+.f64 (log.f64 (cbrt.f64 (pow.f64 base -2))) (log.f64 (/.f64 1 (cbrt.f64 base))))))
	1.0b	(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)
	7.0b	(cbrt.f64 (/.f64 (pow.f64 (atan2.f64 im re) 3) (pow.f64 (log.f64 base) 3)))
	30.3b	(pow.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 2)
	34.0b	(*.f64 (atan2.f64 im re) (exp.f64 (neg.f64 (log.f64 (log.f64 base)))))
	31.3b	(*.f64 -1 (pow.f64 (sqrt.f64 (/.f64 (neg.f64 (atan2.f64 im re)) (log.f64 base))) 2))
	1.5b	(pow.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 3)
	33.8b	(*.f64 (atan2.f64 im re) (pow.f64 (pow.f64 (log.f64 base) -1/2) 2))
✓	0.4b	(*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) -1))
	31.1b	(*.f64 -1 (/.f64 (atan2.f64 im re) (exp.f64 (log.f64 (neg.f64 (log.f64 base))))))
	0.5b	(.f64 -1 (/.f64 (atan2.f64 im re) (/.f64 (-.f64 0 (pow.f64 (log.f64 base) 3)) (+.f64 0 (+.f64 (.f64 (log.f64 base) (log.f64 base)) (*.f64 0 (log.f64 base)))))))
✓	0.3b	(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
	0.8b	(.f64 (atan2.f64 im re) (.f64 (pow.f64 (cbrt.f64 (pow.f64 (log.f64 base) 2)) -1) (pow.f64 (cbrt.f64 (log.f64 base)) -1)))
	1.2b	(*.f64 -1 (/.f64 (atan2.f64 im re) (pow.f64 (cbrt.f64 (neg.f64 (log.f64 base))) 3)))

Compiler

Compiled 675 to 380 computations (43.7% saved)

regimes347.0ms (6.9%)

Accuracy

Total 0.3b remaining (91.1%)

Threshold costs 0.3b (91.1%)

Counts

66 → 1

Compiler

Compiled 5186 to 3616 computations (30.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	17
1	19	17
2	24	17
3	28	17
4	30	17

Stop Event

1×

saturated

end217.0ms (4.3%)

Stop Event

1×

fuel

Compiler

Compiled 263 to 200 computations (24% saved)

Details

analyze573.0ms (11.4%)

sample1.8s (35.3%)

preprocess55.0ms (1.1%)

simplify22.0ms (0.4%)

prune4.0ms (0.1%)

localize5.0ms (0.1%)

series360.0ms (7.1%)

rewrite40.0ms (0.8%)

simplify30.0ms (0.6%)

prune39.0ms (0.8%)

localize7.0ms (0.1%)

series409.0ms (8.1%)

rewrite46.0ms (0.9%)

simplify44.0ms (0.9%)

prune65.0ms (1.3%)

localize8.0ms (0.2%)

series371.0ms (7.3%)

rewrite39.0ms (0.8%)

simplify42.0ms (0.8%)

prune51.0ms (1%)

localize6.0ms (0.1%)

series379.0ms (7.5%)

rewrite37.0ms (0.7%)

simplify36.0ms (0.7%)

prune30.0ms (0.6%)

regimes347.0ms (6.9%)

simplify2.0ms (0%)

end217.0ms (4.3%)

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