Details

analyze4.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
62.5%	12.5%	25%	5
62.5%	6.2%	31.3%	6
65.6%	3.1%	31.3%	7
65.6%	1.6%	32.8%	8
66.4%	0.8%	32.8%	9
66.4%	0.4%	33.2%	10
66.6%	0.2%	33.2%	11
66.6%	0.1%	33.3%	12
66.6%	0%	33.4%	13
66.6%	0%	33.4%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample827.0ms (38.2%)

Results

646.0ms

8256×

body

128

valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify165.0ms (7.6%)

Algorithm

1×	egg-herbie

Rules

1514×	`fma-def_binary64`
1229×	`fma-neg_binary64`
587×	`distribute-rgt-neg-in_binary64`
552×	`cancel-sign-sub-inv_binary64`
522×	`sqr-pow_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	42	11
3	96	11
4	169	11
5	224	11
6	343	11
7	549	11
8	728	11
9	1208	11
10	1666	11
11	2306	11
12	2905	11
13	3028	11
14	3233	11
15	3418	11
16	4282	11
17	3230	11
18	3595	11
19	4713	11
20	4755	11

prune2.0ms (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

0.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.2b	(.f64 (.f64 x x) (fma.f64 x -2 3))

Compiler

Compiled 36 to 23 computations (36.1% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 x x) (fma.f64 x -2 3))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(*.f64 (*.f64 x x) (fma.f64 x -2 3))

rewrite70.0ms (3.2%)

Algorithm

2×	batch-egg-rewrite

Rules

588×	`log1p-expm1-u_binary64`
588×	`expm1-log1p-u_binary64`
296×	`log-prod_binary64`
171×	`pow2_binary64`
120×	`pow1/3_binary64`

Counts

1 → 24

Calls

1 calls:

69.0ms

(*.f64 (*.f64 x x) (fma.f64 x -2 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	144	11
2	1532	11
3	4967	11
4	4888	11
0	0	0
1	0	0

simplify88.0ms (4%)

Algorithm

1×	egg-herbie

Rules

906×	`fma-neg_binary64`
851×	`fma-def_binary64`
771×	`distribute-rgt-neg-in_binary64`
628×	`distribute-lft-neg-in_binary64`
439×	`neg-mul-1_binary64`

Counts

36 → 30

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	165
1	30	147
2	77	138
3	219	120
4	616	120
5	1129	120
6	2106	120
7	3386	120
8	4690	120
9	4971	120
10	4943	120

prune22.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	26	4	30
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	5	31

Error

0.0b

Counts

31 → 5

Alt Table

Status	Error	Program
✓	0.2b	(.f64 (.f64 x x) (fma.f64 x -2 3))
	0.2b	(.f64 x (.f64 x (fma.f64 x -2 3)))
	25.0b	(cbrt.f64 (pow.f64 (.f64 (.f64 x x) (fma.f64 x -2 3)) 3))
	8.2b	(pow.f64 (*.f64 x (sqrt.f64 (fma.f64 x -2 3))) 2)
▶	0.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))

Compiler

Compiled 437 to 287 computations (34.3% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (pow.f64 x 3))
✓	0.0b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
✓	0.2b	(*.f64 3 (pow.f64 x 2))

series9.0ms (0.4%)

Counts

3 → 3

Calls

3 calls:

4.0ms	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
3.0ms	(*.f64 2 (pow.f64 x 3))
2.0ms	(*.f64 3 (pow.f64 x 2))

rewrite63.0ms (2.9%)

Algorithm

2×	batch-egg-rewrite

Rules

888×	`log1p-expm1-u_binary64`
888×	`expm1-log1p-u_binary64`
94×	`add-sqr-sqrt_binary64`
90×	`add-cube-cbrt_binary64`
90×	`add-cbrt-cube_binary64`

Counts

3 → 76

Calls

3 calls:

61.0ms	(*.f64 2 (pow.f64 x 3))
61.0ms	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
61.0ms	(*.f64 3 (pow.f64 x 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	206	28
2	2266	28
3	5276	28
0	0	0
1	0	0

simplify156.0ms (7.2%)

Algorithm

1×	egg-herbie

Rules

968×	`sqr-pow_binary64`
623×	`cube-prod_binary64`
608×	`fabs-mul_binary64`
562×	`pow-sqr_binary64`
538×	`unswap-sqr_binary64`

Counts

79 → 79

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	22	21
2	50	21
3	104	21
4	245	21
5	923	21
6	1516	21
7	1655	21
8	1879	21
9	2106	21
10	2437	21
11	2516	21
12	2827	21
13	3296	21
14	3593	21
15	3806	21
16	3930	21
17	3976	21
18	4003	21
19	4658	21
20	4764	21
21	4855	21

prune65.0ms (3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	1	2	3
Picked	0	1	1
Done	1	0	1
Total	79	5	84

Error

0.0b

Counts

84 → 5

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 3 (.f64 x x) (.f64 (pow.f64 x 3) -2))
	12.2b	(-.f64 (sqrt.f64 (.f64 9 (pow.f64 x 4))) (.f64 2 (pow.f64 x 3)))
	25.0b	(cbrt.f64 (pow.f64 (.f64 (.f64 x x) (fma.f64 x -2 3)) 3))
	0.2b	(.f64 x (.f64 x (fma.f64 x -2 3)))
✓	0.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))

Compiler

Compiled 1622 to 1218 computations (24.9% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (pow.f64 x 3) -2)
✓	0.1b	(fma.f64 3 (.f64 x x) (.f64 (pow.f64 x 3) -2))

series6.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(fma.f64 3 (.f64 x x) (.f64 (pow.f64 x 3) -2))
3.0ms	(*.f64 (pow.f64 x 3) -2)

rewrite48.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

629×	`log1p-expm1-u_binary64`
629×	`expm1-log1p-u_binary64`
316×	`log-prod_binary64`
129×	`expm1-udef_binary64`
129×	`log1p-udef_binary64`

Counts

2 → 45

Calls

2 calls:

47.0ms	(*.f64 (pow.f64 x 3) -2)
47.0ms	(fma.f64 3 (.f64 x x) (.f64 (pow.f64 x 3) -2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	165	21
2	1656	21
3	5039	21
0	0	0
1	0	0

simplify115.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

906×	`fma-neg_binary64`
851×	`fma-def_binary64`
771×	`distribute-rgt-neg-in_binary64`
628×	`distribute-lft-neg-in_binary64`
439×	`neg-mul-1_binary64`

Counts

69 → 51

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	249
1	30	231
2	77	222
3	219	204
4	616	204
5	1129	204
6	2106	204
7	3386	204
8	4690	204
9	4971	204
10	4943	204

prune37.0ms (1.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	51	5	56

Error

0.0b

Counts

56 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 3 (.f64 x x) (.f64 (pow.f64 x 3) -2))
	12.2b	(-.f64 (sqrt.f64 (.f64 9 (pow.f64 x 4))) (.f64 2 (pow.f64 x 3)))
	25.0b	(cbrt.f64 (pow.f64 (.f64 (.f64 x x) (fma.f64 x -2 3)) 3))
▶	0.2b	(.f64 x (.f64 x (fma.f64 x -2 3)))
✓	0.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))

Compiler

Compiled 857 to 601 computations (29.9% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (fma.f64 x -2 3))
✓	0.2b	(.f64 x (.f64 x (fma.f64 x -2 3)))

series6.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(.f64 x (.f64 x (fma.f64 x -2 3)))
2.0ms	(*.f64 x (fma.f64 x -2 3))

rewrite82.0ms (3.8%)

Algorithm

2×	batch-egg-rewrite

Rules

600×	`log1p-expm1-u_binary64`
600×	`expm1-log1p-u_binary64`
319×	`log-prod_binary64`
124×	`pow1/3_binary64`
123×	`expm1-udef_binary64`

Counts

2 → 48

Calls

2 calls:

81.0ms	(*.f64 x (fma.f64 x -2 3))
81.0ms	(.f64 x (.f64 x (fma.f64 x -2 3)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	143	19
2	1570	19
3	4969	19
4	4912	19
0	0	0
1	0	0

simplify96.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

807×	`fma-neg_binary64`
685×	`fma-def_binary64`
500×	`distribute-rgt-neg-in_binary64`
442×	`neg-mul-1_binary64`
438×	`neg-sub0_binary64`

Counts

72 → 59

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	300
1	41	264
2	92	246
3	253	210
4	693	210
5	1267	210
6	2302	210
7	3410	210
8	4539	210
9	4972	210
10	4803	210

prune68.0ms (3.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	59	5	64

Error

0.0b

Counts

64 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 3 (.f64 x x) (.f64 (pow.f64 x 3) -2))
	12.2b	(-.f64 (sqrt.f64 (.f64 9 (pow.f64 x 4))) (.f64 2 (pow.f64 x 3)))
	0.8b	(.f64 x (pow.f64 (cbrt.f64 (.f64 x (fma.f64 x -2 3))) 3))
✓	0.2b	(.f64 x (.f64 x (fma.f64 x -2 3)))
✓	0.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))

Compiler

Compiled 745 to 518 computations (30.5% saved)

regimes65.0ms (3%)

Accuracy

Total 0.1b remaining (85.1%)

Threshold costs 0.1b (85.1%)

Counts

21 → 1

Compiler

Compiled 426 to 312 computations (26.8% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	9	14
2	9	14

end146.0ms (6.8%)

Compiler: Compiled 79 to 60 computations (24.1% saved)

Details

analyze4.0ms (0.2%)

sample827.0ms (38.2%)

simplify165.0ms (7.6%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series3.0ms (0.1%)

rewrite70.0ms (3.2%)

simplify88.0ms (4%)

prune22.0ms (1%)

localize6.0ms (0.3%)

series9.0ms (0.4%)

rewrite63.0ms (2.9%)

simplify156.0ms (7.2%)

prune65.0ms (3%)

localize5.0ms (0.2%)

series6.0ms (0.3%)

rewrite48.0ms (2.2%)

simplify115.0ms (5.3%)

prune37.0ms (1.7%)

localize4.0ms (0.2%)

series6.0ms (0.3%)

rewrite82.0ms (3.8%)

simplify96.0ms (4.4%)

prune68.0ms (3.1%)

regimes65.0ms (3%)

simplify4.0ms (0.2%)

end146.0ms (6.8%)

Profiling