Details

analyze86.0ms (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
25%	74.9%	0.1%	5
37.5%	50%	12.6%	6
50%	37.5%	12.6%	7
56.2%	25%	18.8%	8
62.4%	18.7%	18.8%	9
65.6%	12.5%	22%	10
68.7%	9.4%	22%	11
70.2%	6.2%	23.5%	12
71.8%	4.7%	23.5%	13
72.6%	3.1%	24.3%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample725.0ms (33.8%)

Results

706.0ms	8256×	body	128	valid
8.0ms	97×	body	128	invalid

Compiler

Compiled 20 to 14 computations (30% saved)

preprocess22.0ms (1%)

Algorithm

2×	egg-herbie

Rules

24×	`associate-l_binary64`
21×	`associate-r_binary64`
8×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	22	20
2	50	20
3	73	20
4	74	20
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

15×	`associate-l_binary64`
13×	`associate-r_binary64`
8×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	13	10
2	27	10
3	45	10
4	48	10

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.3b	(.f64 x (.f64 x (*.f64 3 y)))
	8.4b	(.f64 (.f64 (*.f64 x 3) x) y)

Compiler

Compiled 52 to 34 computations (34.6% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 x (.f64 x (*.f64 3 y)))
✓	0.2b	(.f64 x (.f64 3 y))

series15.0ms (0.7%)

Counts

2 → 48

Calls

12 calls:

2.0ms	(.f64 x (.f64 3 y))	x	0
2.0ms	(.f64 x (.f64 x (*.f64 3 y)))	y	0
2.0ms	(.f64 x (.f64 x (*.f64 3 y)))	y	-inf
2.0ms	(.f64 x (.f64 x (*.f64 3 y)))	y	inf
1.0ms	(.f64 x (.f64 x (*.f64 3 y)))	x	-inf

rewrite38.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

609×	`log1p-expm1-u_binary64`
609×	`expm1-log1p-u_binary64`
379×	`log-prod_binary64`
126×	`expm1-udef_binary64`
126×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	142	17
2	1686	17

Stop Event

1×	node limit

Counts

2 → 36

simplify84.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

775×	`sqr-pow_binary64`
404×	`fabs-mul_binary64`
386×	`cube-prod_binary64`
381×	`pow-sqr_binary64`
294×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	408
1	22	408
2	45	408
3	87	408
4	235	408
5	779	408
6	1012	408
7	1426	408
8	1526	408
9	1661	408
10	1830	408
11	2075	408
12	2390	408
13	2762	408
14	3219	408
15	3802	408
16	4508	408

Stop Event

1×	node limit

Counts

84 → 40

prune34.0ms (1.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	32	8	40
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	32	10	42

Error

0.0b

Counts

42 → 10

Alt Table

Status	Error	Program
	8.4b	(.f64 3 (.f64 y (pow.f64 x 2)))
✓	0.3b	(.f64 x (.f64 x (*.f64 3 y)))
	25.0b	(cbrt.f64 (pow.f64 (.f64 x (.f64 y (*.f64 x 3))) 3))
	0.9b	(pow.f64 (cbrt.f64 (.f64 x (.f64 y (*.f64 x 3)))) 3)
	25.7b	(.f64 x (pow.f64 (sqrt.f64 (.f64 y (*.f64 x 3))) 2))
	0.9b	(.f64 x (pow.f64 (cbrt.f64 (.f64 y (*.f64 x 3))) 3))
	0.3b	(.f64 x (+.f64 0 (.f64 y (*.f64 x 3))))
	8.4b	(.f64 y (.f64 3 (*.f64 x x)))
▶	0.2b	(.f64 x (.f64 3 (*.f64 y x)))
	8.4b	(.f64 (.f64 (*.f64 x 3) x) y)

Compiler

Compiled 649 to 461 computations (29% saved)

localize8.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 x (.f64 3 (*.f64 y x)))
✓	0.2b	(.f64 3 (.f64 y x))

series13.0ms (0.6%)

Counts

2 → 24

Calls

12 calls:

2.0ms	(.f64 x (.f64 3 (*.f64 y x)))	y	0
2.0ms	(.f64 x (.f64 3 (*.f64 y x)))	y	-inf
2.0ms	(.f64 x (.f64 3 (*.f64 y x)))	y	inf
1.0ms	(.f64 x (.f64 3 (*.f64 y x)))	x	inf
1.0ms	(.f64 x (.f64 3 (*.f64 y x)))	x	-inf

rewrite40.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

620×	`log1p-expm1-u_binary64`
620×	`expm1-log1p-u_binary64`
387×	`log-prod_binary64`
128×	`expm1-udef_binary64`
128×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	143	17
2	1715	17

Stop Event

1×	node limit

Counts

2 → 34

simplify69.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

775×	`sqr-pow_binary64`
404×	`fabs-mul_binary64`
386×	`cube-prod_binary64`
381×	`pow-sqr_binary64`
269×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	240
1	17	240
2	37	240
3	79	240
4	208	240
5	713	240
6	971	240
7	1385	240
8	1485	240
9	1618	240
10	1790	240
11	2033	240
12	2348	240
13	2718	240
14	3174	240
15	3757	240
16	4465	240

Stop Event

1×	node limit

Counts

58 → 36

prune35.0ms (1.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	35	1	36
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	35	11	46

Error

0.0b

Counts

46 → 11

Alt Table

Status	Error	Program
	8.4b	(.f64 3 (.f64 y (pow.f64 x 2)))
✓	0.3b	(.f64 x (.f64 x (*.f64 3 y)))
	25.0b	(cbrt.f64 (pow.f64 (.f64 x (.f64 y (*.f64 x 3))) 3))
	0.9b	(pow.f64 (cbrt.f64 (.f64 x (.f64 y (*.f64 x 3)))) 3)
	25.7b	(.f64 x (pow.f64 (sqrt.f64 (.f64 y (*.f64 x 3))) 2))
	0.9b	(.f64 x (pow.f64 (cbrt.f64 (.f64 y (*.f64 x 3))) 3))
▶	0.3b	(.f64 x (+.f64 0 (.f64 y (*.f64 x 3))))
	8.4b	(.f64 y (.f64 3 (*.f64 x x)))
✓	0.2b	(.f64 x (.f64 3 (*.f64 y x)))
	8.4b	(.f64 (.f64 (*.f64 x 3) x) y)
	25.4b	(.f64 x (sqrt.f64 (.f64 (pow.f64 (*.f64 y x) 2) 9)))

Compiler

Compiled 628 to 426 computations (32.2% saved)

localize8.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 x (+.f64 0 (.f64 y (*.f64 x 3))))
✓	0.2b	(.f64 y (.f64 x 3))

series13.0ms (0.6%)

Counts

2 → 48

Calls

12 calls:

2.0ms	(.f64 x (+.f64 0 (.f64 y (*.f64 x 3))))	y	0
2.0ms	(.f64 x (+.f64 0 (.f64 y (*.f64 x 3))))	y	inf
2.0ms	(.f64 x (+.f64 0 (.f64 y (*.f64 x 3))))	y	-inf
1.0ms	(.f64 x (+.f64 0 (.f64 y (*.f64 x 3))))	x	-inf
1.0ms	(.f64 x (+.f64 0 (.f64 y (*.f64 x 3))))	x	inf

rewrite46.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

729×	`log1p-expm1-u_binary64`
729×	`expm1-log1p-u_binary64`
133×	`log1p-udef_binary64`
82×	`add-sqr-sqrt_binary64`
79×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	195	17
2	2215	17

Stop Event

1×	node limit

Counts

2 → 54

simplify80.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

775×	`sqr-pow_binary64`
404×	`fabs-mul_binary64`
386×	`cube-prod_binary64`
381×	`pow-sqr_binary64`
294×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	408
1	22	408
2	45	408
3	87	408
4	235	408
5	779	408
6	1012	408
7	1426	408
8	1526	408
9	1661	408
10	1830	408
11	2075	408
12	2390	408
13	2762	408
14	3219	408
15	3802	408
16	4508	408

Stop Event

1×	node limit

Counts

102 → 58

prune57.0ms (2.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	55	3	58
Fresh	2	6	8
Picked	0	1	1
Done	1	1	2
Total	58	11	69

Error

0.0b

Counts

69 → 11

Alt Table

Status	Error	Program
▶	0.9b	(.f64 x (pow.f64 (cbrt.f64 (.f64 y (*.f64 x 3))) 3))
	27.8b	(/.f64 (.f64 (neg.f64 (pow.f64 (.f64 3 (.f64 y x)) 2)) x) (neg.f64 (.f64 3 (*.f64 y x))))
	8.4b	(.f64 y (.f64 3 (*.f64 x x)))
	48.0b	(/.f64 (+.f64 0 (pow.f64 (.f64 y (.f64 (.f64 x 3) x)) 3)) (+.f64 0 (-.f64 (pow.f64 (.f64 y (.f64 (.f64 x 3) x)) 2) (.f64 0 (.f64 y (.f64 (.f64 x 3) x))))))
	8.4b	(.f64 3 (.f64 y (pow.f64 x 2)))
✓	0.3b	(.f64 x (.f64 x (*.f64 3 y)))
	25.0b	(cbrt.f64 (pow.f64 (.f64 x (.f64 y (*.f64 x 3))) 3))
	0.9b	(pow.f64 (cbrt.f64 (.f64 x (.f64 y (*.f64 x 3)))) 3)
✓	0.3b	(.f64 x (+.f64 0 (.f64 y (*.f64 x 3))))
	8.4b	(.f64 (.f64 (*.f64 x 3) x) y)
	22.5b	(.f64 x (+.f64 0 (/.f64 1 (/.f64 (neg.f64 (.f64 3 (.f64 y x))) (neg.f64 (pow.f64 (.f64 3 (*.f64 y x)) 2))))))

Compiler

Compiled 1072 to 728 computations (32.1% saved)

localize6.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 x (pow.f64 (cbrt.f64 (.f64 y (*.f64 x 3))) 3))
	0.2b	(.f64 y (.f64 x 3))
✓	0.6b	(pow.f64 (cbrt.f64 (.f64 y (.f64 x 3))) 3)
✓	11.3b	(cbrt.f64 (.f64 y (.f64 x 3)))

series257.0ms (12%)

Counts

3 → 24

Calls

18 calls:

57.0ms	(.f64 x (pow.f64 (cbrt.f64 (.f64 y (*.f64 x 3))) 3))	y	-inf
53.0ms	(.f64 x (pow.f64 (cbrt.f64 (.f64 y (*.f64 x 3))) 3))	x	-inf
20.0ms	(pow.f64 (cbrt.f64 (.f64 y (.f64 x 3))) 3)	x	-inf
19.0ms	(pow.f64 (cbrt.f64 (.f64 y (.f64 x 3))) 3)	y	-inf
13.0ms	(.f64 x (pow.f64 (cbrt.f64 (.f64 y (*.f64 x 3))) 3))	y	0

rewrite48.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

717×	`log1p-expm1-u_binary64`
717×	`expm1-log1p-u_binary64`
141×	`expm1-udef_binary64`
141×	`log1p-udef_binary64`
83×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	183	26
2	2028	26

Stop Event

1×	node limit

Counts

3 → 80

simplify73.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

775×	`sqr-pow_binary64`
404×	`fabs-mul_binary64`
386×	`cube-prod_binary64`
381×	`pow-sqr_binary64`
269×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	240
1	17	240
2	37	240
3	79	240
4	208	240
5	713	240
6	971	240
7	1385	240
8	1485	240
9	1618	240
10	1790	240
11	2033	240
12	2348	240
13	2718	240
14	3174	240
15	3757	240
16	4465	240

Stop Event

1×	node limit

Counts

104 → 82

prune108.0ms (5.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	110	3	113
Fresh	2	6	8
Picked	1	0	1
Done	0	2	2
Total	113	11	124

Error

0.0b

Counts

124 → 11

Alt Table

Status	Error	Program
✓	0.3b	(.f64 x (+.f64 0 (.f64 y (*.f64 x 3))))
	8.7b	(.f64 x (.f64 (cbrt.f64 (.f64 (.f64 x x) 9)) (.f64 (cbrt.f64 (.f64 x 3)) y)))
	8.4b	(.f64 y (.f64 3 (*.f64 x x)))
	48.0b	(/.f64 (+.f64 0 (pow.f64 (.f64 y (.f64 (.f64 x 3) x)) 3)) (+.f64 0 (-.f64 (pow.f64 (.f64 y (.f64 (.f64 x 3) x)) 2) (.f64 0 (.f64 y (.f64 (.f64 x 3) x))))))
	8.4b	(.f64 3 (.f64 y (pow.f64 x 2)))
✓	0.3b	(.f64 x (.f64 x (*.f64 3 y)))
	1.2b	(.f64 x (pow.f64 (.f64 (cbrt.f64 (*.f64 x 3)) (cbrt.f64 y)) 3))
	8.4b	(.f64 (.f64 (*.f64 x 3) x) y)
	25.0b	(cbrt.f64 (pow.f64 (.f64 x (.f64 y (*.f64 x 3))) 3))
	27.8b	(/.f64 (.f64 (neg.f64 (pow.f64 (.f64 3 (.f64 y x)) 2)) x) (neg.f64 (.f64 3 (*.f64 y x))))
	1.1b	(.f64 x (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 3 (*.f64 y x))) 3)) 3))

Compiler

Compiled 1705 to 1194 computations (30% saved)

regimes150.0ms (7%)

Accuracy

Total 0.2b remaining (87.8%)

Threshold costs 0.2b (87.8%)

Counts

43 → 1

Compiler

Compiled 2522 to 1872 computations (25.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	10	10

Stop Event

1×

saturated

end113.0ms (5.3%)

Stop Event

1×

fuel

Compiler

Compiled 176 to 127 computations (27.8% saved)

Details

analyze86.0ms (4%)

sample725.0ms (33.8%)

preprocess22.0ms (1%)

simplify7.0ms (0.3%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series15.0ms (0.7%)

rewrite38.0ms (1.8%)

simplify84.0ms (3.9%)

prune34.0ms (1.6%)

localize8.0ms (0.4%)

series13.0ms (0.6%)

rewrite40.0ms (1.9%)

simplify69.0ms (3.2%)

prune35.0ms (1.6%)

localize8.0ms (0.4%)

series13.0ms (0.6%)

rewrite46.0ms (2.1%)

simplify80.0ms (3.7%)

prune57.0ms (2.6%)

localize6.0ms (0.3%)

series257.0ms (12%)

rewrite48.0ms (2.2%)

simplify73.0ms (3.4%)

prune108.0ms (5.1%)

regimes150.0ms (7%)

simplify2.0ms (0.1%)

end113.0ms (5.3%)

Profiling