Details

analyze5.0ms (0.3%)

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)

sample857.0ms (42.5%)

Results

669.0ms	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify160.0ms (7.9%)

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

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

0.2b

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)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite6.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
3×	`associate-r_binary64`
3×	`add-sqr-sqrt_binary64`

Counts

1 → 23

Calls

1 calls:

5.0ms

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

simplify61.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1057×	`fma-def_binary64`
450×	`associate-l_binary64`
439×	`times-frac_binary64`
381×	`exp-prod_binary64`
334×	`associate-r_binary64`

Counts

35 → 37

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	51	539
1	122	424
2	381	424
3	1373	424
4	2370	424
5	3834	424
6	5293	424

prune31.0ms (1.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	33	4	37
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	34	4	38

Error

0.0b

Counts

38 → 4

Alt Table

Status	Error	Program
	24.7b	(*.f64 -2 (pow.f64 x 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)))
	9.6b	(.f64 (sqrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3)))) (sqrt.f64 (.f64 x (*.f64 x (fma.f64 x -2 3)))))

Compiler

Compiled 584 to 379 computations (35.1% 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))

rewrite16.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
20×	`associate-r_binary64`
13×	`add-exp-log_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

3 → 78

Calls

3 calls:

6.0ms	(*.f64 3 (pow.f64 x 2))
4.0ms	(*.f64 2 (pow.f64 x 3))
3.0ms	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))

simplify104.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

796×	`fma-def_binary64`
465×	`fma-neg_binary64`
389×	`exp-prod_binary64`
316×	`distribute-rgt-neg-in_binary64`
308×	`distribute-lft-neg-in_binary64`

Counts

81 → 114

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	131	1015
1	258	861
2	724	817
3	1848	788
4	3852	780
5	4761	780
6	4994	780
7	4715	780

prune97.0ms (4.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	114	4	118

Error

0.0b

Counts

118 → 4

Alt Table

Status	Error	Program
▶	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)))
	42.8b	(/.f64 (fma.f64 9 (pow.f64 x 4) (.f64 (pow.f64 x 6) -4)) (.f64 (*.f64 x x) (fma.f64 x 2 3)))
	9.6b	(.f64 (sqrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3)))) (sqrt.f64 (.f64 x (*.f64 x (fma.f64 x -2 3)))))

Compiler

Compiled 1999 to 1571 computations (21.4% 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))

rewrite11.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`

Counts

2 → 46

Calls

2 calls:

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

simplify73.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

654×	`fma-def_binary64`
444×	`unswap-sqr_binary64`
444×	`times-frac_binary64`
351×	`*-commutative_binary64`
216×	`exp-prod_binary64`

Counts

70 → 70

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	74	970
1	152	752
2	484	752
3	1374	750
4	2163	750
5	4334	750
6	5493	750

prune48.0ms (2.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	69	5	74

Error

Counts

74 → 5

Alt Table

Status	Error	Program
	30.4b	(.f64 (sqrt.f64 x) (.f64 (fma.f64 x -2 3) (pow.f64 x 3/2)))
✓	0.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
✓	0.2b	(.f64 x (.f64 x (fma.f64 x -2 3)))
	42.8b	(/.f64 (fma.f64 9 (pow.f64 x 4) (.f64 (pow.f64 x 6) -4)) (.f64 (*.f64 x x) (fma.f64 x 2 3)))
▶	9.6b	(.f64 (sqrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3)))) (sqrt.f64 (.f64 x (*.f64 x (fma.f64 x -2 3)))))

Compiler

Compiled 1024 to 663 computations (35.3% saved)

localize6.0ms (0.3%)

Local error

Found 4 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)))
✓	0.3b	(.f64 (sqrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3)))) (sqrt.f64 (.f64 x (*.f64 x (fma.f64 x -2 3)))))
✓	20.5b	(sqrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3))))

series16.0ms (0.8%)

Counts

2 → 16

Calls

2 calls:

12.0ms	(sqrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3))))
3.0ms	(.f64 (sqrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3)))) (sqrt.f64 (.f64 x (*.f64 x (fma.f64 x -2 3)))))

rewrite19.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

135×	`pow1_binary64`
74×	`pow-prod-down_binary64`
63×	`sqrt-pow1_binary64`
17×	`pow-prod-up_binary64`
13×	`pow1/2_binary64`

Counts

2 → 82

Calls

2 calls:

8.0ms	(.f64 (sqrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3)))) (sqrt.f64 (.f64 x (*.f64 x (fma.f64 x -2 3)))))
3.0ms	(sqrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3))))

simplify83.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

862×	`times-frac_binary64`
637×	`associate-r_binary64`
582×	`unswap-sqr_binary64`
459×	`fma-def_binary64`
438×	`fma-neg_binary64`

Counts

98 → 79

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	75	1384
1	161	1102
2	563	1040
3	2502	1004
4	4964	1004
5	5140	1004

prune172.0ms (8.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	239	0	239
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	239	5	244

Error

Counts

244 → 5

Alt Table

Status	Error	Program
	30.4b	(.f64 (sqrt.f64 x) (.f64 (fma.f64 x -2 3) (pow.f64 x 3/2)))
✓	0.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
✓	0.2b	(.f64 x (.f64 x (fma.f64 x -2 3)))
	42.8b	(/.f64 (fma.f64 9 (pow.f64 x 4) (.f64 (pow.f64 x 6) -4)) (.f64 (*.f64 x x) (fma.f64 x 2 3)))
✓	9.6b	(.f64 (sqrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3)))) (sqrt.f64 (.f64 x (*.f64 x (fma.f64 x -2 3)))))

Compiler

Compiled 5724 to 3985 computations (30.4% saved)

regimes121.0ms (6%)

Accuracy

Total 0.1b remaining (87.3%)

Threshold costs 0.1b (87.3%)

Counts

69 → 1

Compiler

Compiled 2024 to 1464 computations (27.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	10	14
2	10	14

end92.0ms (4.6%)

Compiler: Compiled 95 to 72 computations (24.2% saved)

Details

analyze5.0ms (0.3%)

sample857.0ms (42.5%)

simplify160.0ms (7.9%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series4.0ms (0.2%)

rewrite6.0ms (0.3%)

simplify61.0ms (3%)

prune31.0ms (1.6%)

localize6.0ms (0.3%)

series9.0ms (0.4%)

rewrite16.0ms (0.8%)

simplify104.0ms (5.1%)

prune97.0ms (4.8%)

localize4.0ms (0.2%)

series6.0ms (0.3%)

rewrite11.0ms (0.6%)

simplify73.0ms (3.6%)

prune48.0ms (2.4%)

localize6.0ms (0.3%)

series16.0ms (0.8%)

rewrite19.0ms (0.9%)

simplify83.0ms (4.1%)

prune172.0ms (8.5%)

regimes121.0ms (6%)

simplify2.0ms (0.1%)

end92.0ms (4.6%)

Profiling