Details

analyze47.0ms (1.8%)

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
50%	50%	0.1%	4
50%	50%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
87.4%	12.5%	0.1%	8
87.4%	12.5%	0.1%	9
93.7%	6.2%	0.1%	10
93.7%	6.2%	0.1%	11
96.8%	3.1%	0.1%	12
96.8%	3.1%	0.1%	13
98.3%	1.6%	0.1%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample808.0ms (30%)

Results

621.0ms	7647×	body	128	valid
50.0ms	212×	body	1024	valid
45.0ms	152×	body	2048	valid
27.0ms	145×	body	512	valid
13.0ms	100×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify22.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

254×	`fma-neg_binary64`
112×	`fma-def_binary64`
90×	`cancel-sign-sub-inv_binary64`
48×	`sub-neg_binary64`
40×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	43	10
4	79	10
5	146	10
6	244	10
7	348	8
8	442	8
9	595	8
10	650	8
11	590	8

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 (-.f64 x y) 1/2 x)

Compiler

Compiled 31 to 18 computations (41.9% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (-.f64 x y) 1/2 x)

series4.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

4.0ms

(fma.f64 (-.f64 x y) 1/2 x)

rewrite38.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

666×	`log1p-expm1-u_binary64`
666×	`expm1-log1p-u_binary64`
408×	`prod-diff_binary64`
123×	`log1p-udef_binary64`
68×	`add-sqr-sqrt_binary64`

Counts

1 → 24

Calls

1 calls:

37.0ms

(fma.f64 (-.f64 x y) 1/2 x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	132	8
2	1638	8
3	5022	8
0	0	0
1	0	0

simplify23.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

120×	`fma-def_binary64`
71×	`fma-neg_binary64`
31×	`cancel-sign-sub-inv_binary64`
17×	`distribute-rgt-neg-in_binary64`
16×	`sub-neg_binary64`

Counts

48 → 28

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	204
1	18	168
2	26	168
3	40	168
4	61	168
5	87	168
6	137	168
7	177	168
8	215	168
9	234	168
10	250	168
11	254	168
12	212	168

prune19.0ms (0.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	24	4	28
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	24	5	29

Error

0.0b

Counts

29 → 5

Alt Table

Status	Error	Program
	39.6b	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 x y) 1/2 x) 3))
	32.8b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 2)
▶	1.3b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 3)
	27.9b	(/.f64 (-.f64 (.f64 (.f64 (-.f64 x y) 1/2) (.f64 (-.f64 x y) 1/2)) (.f64 x x)) (-.f64 (*.f64 (-.f64 x y) 1/2) x))
✓	0.1b	(fma.f64 (-.f64 x y) 1/2 x)

Compiler

Compiled 413 to 236 computations (42.9% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (-.f64 x y) 1/2 x)
✓	0.6b	(cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 3)

series603.0ms (22.4%)

Counts

2 → 48

Calls

2 calls:

586.0ms	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 3)
17.0ms	(cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))

rewrite51.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

823×	`log1p-expm1-u_binary64`
823×	`expm1-log1p-u_binary64`
408×	`prod-diff_binary64`
86×	`add-sqr-sqrt_binary64`
82×	`add-cbrt-cube_binary64`

Counts

2 → 50

Calls

2 calls:

50.0ms	(cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))
50.0ms	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	179	18
2	2058	18
3	5680	18
0	0	0
1	0	0

simplify75.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

710×	`times-frac_binary64`
398×	`fma-def_binary64`
312×	`fma-neg_binary64`
263×	`cancel-sign-sub-inv_binary64`
183×	`distribute-rgt-neg-in_binary64`

Counts

98 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	1921
1	524	1828
2	1671	1631
3	4882	1631
4	5089	1631

prune88.0ms (3.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	147	8	155

Error

0.0b

Counts

155 → 8

Alt Table

Status	Error	Program
	39.6b	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 x y) 1/2 x) 3))
	32.8b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 2)
✓	1.3b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 3)
	27.9b	(/.f64 (-.f64 (.f64 (.f64 (-.f64 x y) 1/2) (.f64 (-.f64 x y) 1/2)) (.f64 x x)) (-.f64 (*.f64 (-.f64 x y) 1/2) x))
✓	0.1b	(fma.f64 (-.f64 x y) 1/2 x)
	1.8b	(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) 2) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 2)))
	26.7b	(*.f64 x (cbrt.f64 27/8))
▶	1.0b	(.f64 (cbrt.f64 -1/8) (-.f64 y (.f64 3 x)))

Compiler

Compiled 3169 to 2300 computations (27.4% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 y (*.f64 3 x))
✓	1.0b	(cbrt.f64 -1/8)

series4.0ms (0.1%)

Counts

2 → 6

Calls

2 calls:

4.0ms	(-.f64 y (*.f64 3 x))
0.0ms	(cbrt.f64 -1/8)

rewrite53.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

789×	`log1p-expm1-u_binary64`
789×	`expm1-log1p-u_binary64`
599×	`prod-diff_binary64`
95×	`egg-rr`
85×	`add-sqr-sqrt_binary64`

Counts

2 → 95

Calls

2 calls:

51.0ms	(-.f64 y (*.f64 3 x))
51.0ms	(cbrt.f64 -1/8)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	172	10
2	1995	10
3	5851	10
0	0	0
1	0	0

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Counts

101 → 97

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
1	6	15
2	6	15

prune52.0ms (1.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	96	9	105

Error

0.0b

Counts

105 → 9

Alt Table

Status	Error	Program
▶	1.4b	(.f64 (cbrt.f64 -1/8) (.f64 (cbrt.f64 (-.f64 y (.f64 3 x))) (pow.f64 (cbrt.f64 (-.f64 y (.f64 3 x))) 2)))
	39.6b	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 x y) 1/2 x) 3))
	32.8b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 2)
✓	1.3b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 3)
	27.9b	(/.f64 (-.f64 (.f64 (.f64 (-.f64 x y) 1/2) (.f64 (-.f64 x y) 1/2)) (.f64 x x)) (-.f64 (*.f64 (-.f64 x y) 1/2) x))
✓	0.1b	(fma.f64 (-.f64 x y) 1/2 x)
	1.8b	(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) 2) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 2)))
	26.7b	(*.f64 x (cbrt.f64 27/8))
✓	1.0b	(.f64 (cbrt.f64 -1/8) (-.f64 y (.f64 3 x)))

Compiler

Compiled 2121 to 1349 computations (36.4% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (cbrt.f64 (-.f64 y (.f64 3 x))) (pow.f64 (cbrt.f64 (-.f64 y (*.f64 3 x))) 2))
✓	0.5b	(cbrt.f64 (-.f64 y (*.f64 3 x)))
✓	0.5b	(pow.f64 (cbrt.f64 (-.f64 y (*.f64 3 x))) 2)
	1.0b	(cbrt.f64 -1/8)

series104.0ms (3.9%)

Counts

3 → 72

Calls

3 calls:

50.0ms	(cbrt.f64 (-.f64 y (*.f64 3 x)))
41.0ms	(pow.f64 (cbrt.f64 (-.f64 y (*.f64 3 x))) 2)
13.0ms	(.f64 (cbrt.f64 (-.f64 y (.f64 3 x))) (pow.f64 (cbrt.f64 (-.f64 y (*.f64 3 x))) 2))

rewrite129.0ms (4.8%)

Algorithm

2×	batch-egg-rewrite

Rules

835×	`log1p-expm1-u_binary64`
835×	`expm1-log1p-u_binary64`
599×	`prod-diff_binary64`
116×	`egg-rr`
93×	`add-sqr-sqrt_binary64`

Counts

3 → 116

Calls

3 calls:

125.0ms	(.f64 (cbrt.f64 (-.f64 y (.f64 3 x))) (pow.f64 (cbrt.f64 (-.f64 y (*.f64 3 x))) 2))
125.0ms	(cbrt.f64 (-.f64 y (*.f64 3 x)))
125.0ms	(pow.f64 (cbrt.f64 (-.f64 y (*.f64 3 x))) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	197	28
2	2130	28
3	6130	28
0	0	0
1	0	0

simplify64.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

798×	`fma-def_binary64`
738×	`times-frac_binary64`
251×	`unswap-sqr_binary64`
206×	`fma-neg_binary64`
190×	`associate-r_binary64`

Counts

188 → 200

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	218	2180
1	684	2138
2	2321	2046
3	4963	2046

prune254.0ms (9.4%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	285	0	285
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	285	9	294

Error

0.0b

Counts

294 → 9

Alt Table

Status	Error	Program
✓	1.4b	(.f64 (cbrt.f64 -1/8) (.f64 (cbrt.f64 (-.f64 y (.f64 3 x))) (pow.f64 (cbrt.f64 (-.f64 y (.f64 3 x))) 2)))
	39.6b	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 x y) 1/2 x) 3))
	32.8b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 2)
✓	1.3b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 3)
	27.9b	(/.f64 (-.f64 (.f64 (.f64 (-.f64 x y) 1/2) (.f64 (-.f64 x y) 1/2)) (.f64 x x)) (-.f64 (*.f64 (-.f64 x y) 1/2) x))
✓	0.1b	(fma.f64 (-.f64 x y) 1/2 x)
	1.8b	(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) 2) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 2)))
	26.7b	(*.f64 x (cbrt.f64 27/8))
✓	1.0b	(.f64 (cbrt.f64 -1/8) (-.f64 y (.f64 3 x)))

Compiler

Compiled 8649 to 6635 computations (23.3% saved)

regimes76.0ms (2.8%)

Accuracy

Total 0.1b remaining (84.6%)

Threshold costs 0.1b (84.6%)

Counts

25 → 1

Compiler

Compiled 927 to 680 computations (26.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	8	8
2	13	8
3	15	8
4	16	8
5	16	8

end142.0ms (5.3%)

Compiler: Compiled 149 to 102 computations (31.5% saved)

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	43	10
4	79	10
5	146	10
6	244	10
7	348	8
8	442	8
9	595	8
10	650	8
11	590	8

Iter	Nodes	Cost
0	10	204
1	18	168
2	26	168
3	40	168
4	61	168
5	87	168
6	137	168
7	177	168
8	215	168
9	234	168
10	250	168
11	254	168
12	212	168

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	43	10
4	79	10
5	146	10
6	244	10
7	348	8
8	442	8
9	595	8
10	650	8
11	590	8

Iter	Nodes	Cost
0	10	204
1	18	168
2	26	168
3	40	168
4	61	168
5	87	168
6	137	168
7	177	168
8	215	168
9	234	168
10	250	168
11	254	168
12	212	168

Details

analyze47.0ms (1.8%)

sample808.0ms (30%)

simplify22.0ms (0.8%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series4.0ms (0.1%)

rewrite38.0ms (1.4%)

simplify23.0ms (0.8%)

prune19.0ms (0.7%)

localize6.0ms (0.2%)

series603.0ms (22.4%)

rewrite51.0ms (1.9%)

simplify75.0ms (2.8%)

prune88.0ms (3.3%)

localize6.0ms (0.2%)

series4.0ms (0.1%)

rewrite53.0ms (2%)

simplify7.0ms (0.3%)

prune52.0ms (1.9%)

localize9.0ms (0.3%)

series104.0ms (3.9%)

rewrite129.0ms (4.8%)

simplify64.0ms (2.4%)

prune254.0ms (9.4%)

regimes76.0ms (2.8%)

simplify3.0ms (0.1%)

end142.0ms (5.3%)

Profiling

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	43	10
4	79	10
5	146	10
6	244	10
7	348	8
8	442	8
9	595	8
10	650	8
11	590	8

Iter	Nodes	Cost
0	10	204
1	18	168
2	26	168
3	40	168
4	61	168
5	87	168
6	137	168
7	177	168
8	215	168
9	234	168
10	250	168
11	254	168
12	212	168