Details

analyze4.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	50%	25%	3
37.5%	25%	37.5%	4
43.7%	12.5%	43.8%	5
46.9%	6.2%	46.9%	6
48.4%	3.1%	48.5%	7
49.2%	1.6%	49.2%	8
49.6%	0.8%	49.6%	9
49.6%	0.4%	50%	10
49.7%	0.2%	50.1%	11
49.7%	0.1%	50.2%	12
49.7%	0%	50.2%	13
49.7%	0%	50.2%	14

Compiler

Compiled 6 to 4 computations (33.3% saved)

sample742.0ms (37%)

Results

730.0ms	8256×	body	128	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 12 to 8 computations (33.3% saved)

preprocess16.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	5	6
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 5 to 3 computations (40% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	5	6

Stop Event

1×

saturated

Counts

1 → 1

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.3b	(*.f64 x (log.f64 x))

Compiler

Compiled 15 to 9 computations (40% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 x (log.f64 x))

series32.0ms (1.6%)

Counts

1 → 12

Calls

3 calls:

15.0ms	(*.f64 x (log.f64 x))	x	0
7.0ms	(*.f64 x (log.f64 x))	x	-inf
7.0ms	(*.f64 x (log.f64 x))	x	inf

rewrite30.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

319×	`log1p-expm1-u_binary64`
319×	`expm1-log1p-u_binary64`
286×	`add-log-exp_binary64`
285×	`add-exp-log_binary64`
266×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	76	6
2	895	6

Stop Event

1×	node limit

Counts

1 → 21

simplify44.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1161×	`fma-neg_binary64`
786×	`fma-def_binary64`
322×	`unsub-neg_binary64`
233×	`distribute-rgt-in_binary64`
168×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	72
1	30	72
2	57	72
3	131	72
4	357	72
5	1022	72
6	2544	72
7	3677	72
8	4075	72
9	4166	72
10	4176	72
11	4339	72

Stop Event

1×	node limit

Counts

33 → 25

prune10.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	22	4	26

Error

0.2b

Counts

26 → 4

Alt Table

Status	Error	Program
▶	1.3b	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 3)
✓	0.3b	(*.f64 x (log.f64 x))
	41.6b	(cbrt.f64 (pow.f64 (*.f64 x (log.f64 x)) 3))
	32.0b	(pow.f64 (sqrt.f64 (*.f64 x (log.f64 x))) 2)

Compiler

Compiled 254 to 125 computations (50.8% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.3b	(*.f64 x (log.f64 x))
✓	0.5b	(cbrt.f64 (*.f64 x (log.f64 x)))
✓	0.7b	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 3)

series38.0ms (1.9%)

Counts

2 → 0

Calls

6 calls:

17.0ms	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 3)	x	-inf
11.0ms	(cbrt.f64 (*.f64 x (log.f64 x)))	x	-inf
3.0ms	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 3)	x	0
3.0ms	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 3)	x	inf
2.0ms	(cbrt.f64 (*.f64 x (log.f64 x)))	x	0

rewrite46.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

493×	`log1p-expm1-u_binary64`
493×	`expm1-log1p-u_binary64`
485×	`unpow-prod-down_binary64`
269×	`log-prod_binary64`
140×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	138	14
2	1413	14

Stop Event

1×	node limit

Counts

2 → 110

simplify10.0ms (0.5%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

110 → 110

prune66.0ms (3.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	125	10	135
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	127	12	139

Error

0.0b

Counts

139 → 12

Alt Table

Status	Error	Program
✓	1.3b	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 3)
✓	0.3b	(*.f64 x (log.f64 x))
	1.8b	(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (log.f64 x)))) 2) (.f64 (cbrt.f64 (cbrt.f64 (.f64 x (log.f64 x)))) (pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 2)))
	1.4b	(.f64 (cbrt.f64 (.f64 x (log.f64 x))) (pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 2))
	2.5b	(pow.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 x (log.f64 x)))) (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 x (log.f64 x)))) 2)) 3)
	1.6b	(pow.f64 (*.f64 (cbrt.f64 (log.f64 x)) (cbrt.f64 x)) 3)
	1.3b	(.f64 (.f64 (pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 2) (cbrt.f64 x)) (cbrt.f64 (log.f64 x)))
	1.2b	(.f64 (.f64 x (pow.f64 (cbrt.f64 (log.f64 x)) 2)) (cbrt.f64 (log.f64 x)))
▶	0.6b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 x)))
	32.1b	(.f64 (sqrt.f64 (log.f64 x)) (.f64 (sqrt.f64 (log.f64 x)) x))
	1.3b	(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (log.f64 x)))
	1.3b	(.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (log.f64 x)) (pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 2)))

Compiler

Compiled 2067 to 927 computations (55.2% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (sqrt.f64 x) (log.f64 x))
✓	0.4b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 x)))

series28.0ms (1.4%)

Counts

2 → 8

Calls

6 calls:

8.0ms	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 x)))	x	0
7.0ms	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 x)))	x	inf
6.0ms	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 x)))	x	-inf
3.0ms	(*.f64 (sqrt.f64 x) (log.f64 x))	x	-inf
2.0ms	(*.f64 (sqrt.f64 x) (log.f64 x))	x	inf

rewrite34.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

485×	`log1p-expm1-u_binary64`
485×	`expm1-log1p-u_binary64`
457×	`unpow-prod-down_binary64`
305×	`log-prod_binary64`
143×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	14
1	117	14
2	1389	14

Stop Event

1×	node limit

Counts

2 → 34

simplify52.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1640×	`fma-neg_binary64`
564×	`fma-def_binary64`
213×	`distribute-rgt-in_binary64`
196×	`unsub-neg_binary64`
175×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	48
1	21	48
2	36	48
3	75	48
4	140	48
5	199	48
6	224	48
7	290	48
8	676	48
9	1176	48
10	2498	48
11	3219	48
12	3492	48
13	3558	48
14	3580	48
15	3585	48

Stop Event

1×	node limit

Counts

42 → 37

prune25.0ms (1.3%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	1	8	9
Picked	0	1	1
Done	0	2	2
Total	36	13	49

Error

0.0b

Counts

49 → 13

Alt Table

Status	Error	Program
	20.7b	(.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 x) (log.f64 x)) 3)))
	1.4b	(.f64 (cbrt.f64 (.f64 x (log.f64 x))) (pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 2))
✓	1.3b	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 3)
✓	0.3b	(*.f64 x (log.f64 x))
	1.8b	(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (log.f64 x)))) 2) (.f64 (cbrt.f64 (cbrt.f64 (.f64 x (log.f64 x)))) (pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 2)))
	1.4b	(.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (.f64 (sqrt.f64 x) (log.f64 x))) 3))
	1.6b	(pow.f64 (*.f64 (cbrt.f64 (log.f64 x)) (cbrt.f64 x)) 3)
	1.3b	(.f64 (.f64 (pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 2) (cbrt.f64 x)) (cbrt.f64 (log.f64 x)))
▶	1.2b	(.f64 (.f64 x (pow.f64 (cbrt.f64 (log.f64 x)) 2)) (cbrt.f64 (log.f64 x)))
✓	0.6b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 x)))
	32.1b	(.f64 (sqrt.f64 (log.f64 x)) (.f64 (sqrt.f64 (log.f64 x)) x))
	1.3b	(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (log.f64 x)))
	1.3b	(.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (log.f64 x)) (pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 2)))

Compiler

Compiled 637 to 309 computations (51.5% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 x (pow.f64 (cbrt.f64 (log.f64 x)) 2))
✓	0.3b	(.f64 (.f64 x (pow.f64 (cbrt.f64 (log.f64 x)) 2)) (cbrt.f64 (log.f64 x)))
✓	0.4b	(pow.f64 (cbrt.f64 (log.f64 x)) 2)
✓	0.5b	(cbrt.f64 (log.f64 x))

series427.0ms (21.3%)

Counts

4 → 48

Calls

12 calls:

94.0ms	(cbrt.f64 (log.f64 x))	x	inf
94.0ms	(pow.f64 (cbrt.f64 (log.f64 x)) 2)	x	inf
38.0ms	(*.f64 x (pow.f64 (cbrt.f64 (log.f64 x)) 2))	x	-inf
36.0ms	(*.f64 x (pow.f64 (cbrt.f64 (log.f64 x)) 2))	x	inf
36.0ms	(*.f64 x (pow.f64 (cbrt.f64 (log.f64 x)) 2))	x	0

rewrite48.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

602×	`log1p-expm1-u_binary64`
602×	`expm1-log1p-u_binary64`
355×	`log-prod_binary64`
125×	`expm1-udef_binary64`
125×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	30
1	158	30
2	1774	30

Stop Event

1×	node limit

Counts

4 → 83

simplify35.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

895×	`fma-def_binary64`
486×	`unswap-sqr_binary64`
339×	`distribute-rgt-in_binary64`
312×	`associate-l_binary64`
288×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	428
1	86	420
2	171	420
3	559	420
4	2071	420

Stop Event

1×	node limit

Counts

131 → 99

prune67.0ms (3.3%)

Pruning

14 alts after pruning (10 fresh and 4 done)

	Pruned	Kept	Total
New	124	5	129
Fresh	4	5	9
Picked	0	1	1
Done	0	3	3
Total	128	14	142

Error

0.0b

Counts

142 → 14

Alt Table

Status	Error	Program
✓	1.3b	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 3)
✓	0.3b	(*.f64 x (log.f64 x))
	1.5b	(.f64 (.f64 x (.f64 (.f64 (cbrt.f64 (log.f64 x)) (pow.f64 (cbrt.f64 (cbrt.f64 (log.f64 x))) 2)) (cbrt.f64 (cbrt.f64 (log.f64 x))))) (cbrt.f64 (log.f64 x)))
	1.3b	(.f64 (.f64 (pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 2) (cbrt.f64 x)) (cbrt.f64 (log.f64 x)))
	1.1b	(.f64 (.f64 x (pow.f64 (pow.f64 (log.f64 x) 2) 1/3)) (cbrt.f64 (log.f64 x)))
✓	1.2b	(.f64 (.f64 x (pow.f64 (cbrt.f64 (log.f64 x)) 2)) (cbrt.f64 (log.f64 x)))
	32.7b	(.f64 (.f64 x (pow.f64 (cbrt.f64 (log.f64 x)) 2)) (*.f64 (pow.f64 (log.f64 (/.f64 1 x)) 1/3) (cbrt.f64 -1)))
	1.4b	(.f64 (cbrt.f64 (.f64 x (log.f64 x))) (pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 2))
	2.7b	(.f64 (.f64 x (pow.f64 (cbrt.f64 (log.f64 x)) 2)) (log1p.f64 (expm1.f64 (cbrt.f64 (log.f64 x)))))
	0.8b	(.f64 (.f64 x (cbrt.f64 (pow.f64 (log.f64 x) 2))) (cbrt.f64 (log.f64 x)))
✓	0.6b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 x)))
	32.1b	(.f64 (sqrt.f64 (log.f64 x)) (.f64 (sqrt.f64 (log.f64 x)) x))
	1.3b	(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (log.f64 x)))
	1.3b	(.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (log.f64 x)) (pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 2)))

Compiler

Compiled 2017 to 963 computations (52.3% saved)

regimes66.0ms (3.3%)

Accuracy

Total 0.2b remaining (88%)

Threshold costs 0.2b (88%)

Counts

32 → 1

Compiler

Compiled 848 to 556 computations (34.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	5	6

Stop Event

1×

saturated

end151.0ms (7.5%)

Stop Event

1×

fuel

Compiler

Compiled 188 to 117 computations (37.8% saved)

Details

analyze4.0ms (0.2%)

sample742.0ms (37%)

preprocess16.0ms (0.8%)

simplify6.0ms (0.3%)

prune1.0ms (0.1%)

localize3.0ms (0.2%)

series32.0ms (1.6%)

rewrite30.0ms (1.5%)

simplify44.0ms (2.2%)

prune10.0ms (0.5%)

localize8.0ms (0.4%)

series38.0ms (1.9%)

rewrite46.0ms (2.3%)

simplify10.0ms (0.5%)

prune66.0ms (3.3%)

localize5.0ms (0.3%)

series28.0ms (1.4%)

rewrite34.0ms (1.7%)

simplify52.0ms (2.6%)

prune25.0ms (1.3%)

localize7.0ms (0.3%)

series427.0ms (21.3%)

rewrite48.0ms (2.4%)

simplify35.0ms (1.8%)

prune67.0ms (3.3%)

regimes66.0ms (3.3%)

simplify2.0ms (0.1%)

end151.0ms (7.5%)

Profiling