Details

analyze8.0ms (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%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample1.5s (34.8%)

Results

486.0ms	1390×	body	1024	valid
463.0ms	4578×	body	128	valid
402.0ms	1551×	body	512	valid
131.0ms	737×	body	256	valid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify20.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

127×	`fma-neg_binary64`
82×	`fma-def_binary64`
41×	`cancel-sign-sub-inv_binary64`
41×	`sub-neg_binary64`
28×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

10.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	10.0b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 63 to 51 computations (19% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 x 1))
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
✓	2.7b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series10.0ms (0.2%)

Counts

4 → 48

Calls

4 calls:

3.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
2.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.0ms	(/.f64 1 (+.f64 x 1))
2.0ms	(/.f64 1 (-.f64 x 1))

rewrite255.0ms (5.9%)

Algorithm

1×	rewrite-expression-head

Rules

757×	`*-un-lft-identity_binary64`
733×	`times-frac_binary64`
558×	`add-sqr-sqrt_binary64`
508×	`add-cube-cbrt_binary64`
468×	`prod-diff_binary64`

Counts

4 → 668

Calls

4 calls:

48.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
46.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
4.0ms	(/.f64 1 (-.f64 x 1))
4.0ms	(/.f64 1 (+.f64 x 1))

simplify444.0ms (10.2%)

Algorithm

1×	egg-herbie

Rules

932×	`fma-neg_binary64`
457×	`times-frac_binary64`
236×	`fma-def_binary64`
186×	`sub-neg_binary64`
176×	`exp-prod_binary64`

Counts

716 → 853

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	419	19278
1	989	13709
2	2519	9843
3	4349	9843
4	4815	9843

prune869.0ms (20%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	851	2	853
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	851	3	854

Error

0.6b

Counts

854 → 3

Alt Table

Status	Error	Program
▶	25.3b	(+.f64 (/.f64 (-.f64 x (+.f64 2 (*.f64 x 2))) (fma.f64 x x x)) (/.f64 1 (-.f64 x 1)))
✓	10.0b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
	32.5b	(/.f64 2 (pow.f64 x 3))

Compiler

Compiled 33599 to 26139 computations (22.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (-.f64 x 1))
✓	0.0b	(-.f64 x (+.f64 2 (*.f64 x 2)))
✓	1.7b	(+.f64 (/.f64 (-.f64 x (+.f64 2 (*.f64 x 2))) (fma.f64 x x x)) (/.f64 1 (-.f64 x 1)))
✓	12.6b	(/.f64 (-.f64 x (+.f64 2 (*.f64 x 2))) (fma.f64 x x x))

series8.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(+.f64 (/.f64 (-.f64 x (+.f64 2 (*.f64 x 2))) (fma.f64 x x x)) (/.f64 1 (-.f64 x 1)))
2.0ms	(/.f64 (-.f64 x (+.f64 2 (*.f64 x 2))) (fma.f64 x x x))
1.0ms	(-.f64 x (+.f64 2 (*.f64 x 2)))

rewrite47.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`*-un-lft-identity_binary64`
48×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
32×	`add-cube-cbrt_binary64`
19×	`fma-def_binary64`

Counts

3 → 120

Calls

3 calls:

25.0ms	(+.f64 (/.f64 (-.f64 x (+.f64 2 (*.f64 x 2))) (fma.f64 x x x)) (/.f64 1 (-.f64 x 1)))
8.0ms	(/.f64 (-.f64 x (+.f64 2 (*.f64 x 2))) (fma.f64 x x x))
5.0ms	(-.f64 x (+.f64 2 (*.f64 x 2)))

simplify95.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

869×	`fma-def_binary64`
541×	`distribute-rgt-in_binary64`
431×	`fma-neg_binary64`
305×	`times-frac_binary64`
228×	`cancel-sign-sub-inv_binary64`

Counts

156 → 198

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	225	2950
1	554	2504
2	1811	2055
3	4832	2055
4	4990	2055

prune200.0ms (4.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	274	0	274
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	274	3	277

Error

0.6b

Counts

277 → 3

Alt Table

Status	Error	Program
✓	25.3b	(+.f64 (/.f64 (-.f64 x (+.f64 2 (*.f64 x 2))) (fma.f64 x x x)) (/.f64 1 (-.f64 x 1)))
✓	10.0b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
▶	32.5b	(/.f64 2 (pow.f64 x 3))

Compiler

Compiled 7303 to 4689 computations (35.8% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.6b	(/.f64 2 (pow.f64 x 3))

series3.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

3.0ms

(/.f64 2 (pow.f64 x 3))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
26×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
26×	`add-cube-cbrt_binary64`
12×	`associate-/r*_binary64`

Counts

1 → 67

Calls

1 calls:

4.0ms

(/.f64 2 (pow.f64 x 3))

simplify93.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

625×	`associate-/r*_binary64`
441×	`fma-def_binary64`
393×	`times-frac_binary64`
368×	`associate-l_binary64`
295×	`log-prod_binary64`

Counts

67 → 67

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	886
1	145	856
2	528	856
3	3173	800
4	4256	800
5	4968	800
6	4943	800

prune53.0ms (1.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	62	5	67
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	62	8	70

Error

0.0b

Counts

70 → 8

Alt Table

Status	Error	Program
✓	25.3b	(+.f64 (/.f64 (-.f64 x (+.f64 2 (*.f64 x 2))) (fma.f64 x x x)) (/.f64 1 (-.f64 x 1)))
✓	10.0b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
	47.2b	(*.f64 (/.f64 1 (pow.f64 x 3/2)) (/.f64 2 (pow.f64 x 3/2)))
✓	32.5b	(/.f64 2 (pow.f64 x 3))
	32.6b	(*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 2) (pow.f64 x 3)))
▶	32.0b	(/.f64 (/.f64 2 x) (*.f64 x x))
	32.0b	(/.f64 (/.f64 2 (*.f64 x x)) x)
	32.1b	(/.f64 (/.f64 2 (*.f64 x x)) (pow.f64 (cbrt.f64 x) 3))

Compiler

Compiled 951 to 754 computations (20.7% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 2 x) (*.f64 x x))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(/.f64 (/.f64 2 x) (*.f64 x x))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`times-frac_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
13×	`associate-/l*_binary64`

Counts

1 → 48

Calls

1 calls:

8.0ms

(/.f64 (/.f64 2 x) (*.f64 x x))

simplify127.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

586×	`div-sub_binary64`
337×	`*-commutative_binary64`
333×	`sub-neg_binary64`
305×	`associate-/l/_binary64`
305×	`times-frac_binary64`

Counts

60 → 76

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	105	779
1	227	689
2	591	689
3	1852	689
4	2243	674
5	2845	674
6	3851	647
7	4175	647
8	4804	647
9	4921	647
10	4607	647

prune51.0ms (1.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	1	3	4
Picked	1	0	1
Done	0	3	3
Total	77	7	84

Error

Counts

84 → 7

Alt Table

Status	Error	Program
✓	25.3b	(+.f64 (/.f64 (-.f64 x (+.f64 2 (*.f64 x 2))) (fma.f64 x x x)) (/.f64 1 (-.f64 x 1)))
✓	10.0b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
	47.2b	(*.f64 (/.f64 1 (pow.f64 x 3/2)) (/.f64 2 (pow.f64 x 3/2)))
✓	32.5b	(/.f64 2 (pow.f64 x 3))
	31.9b	(/.f64 (/.f64 (/.f64 2 x) x) x)
	32.0b	(/.f64 (/.f64 2 (*.f64 x x)) x)
	32.1b	(/.f64 (/.f64 2 (*.f64 x x)) (pow.f64 (cbrt.f64 x) 3))

Compiler

Compiled 1095 to 682 computations (37.7% saved)

regimes383.0ms (8.8%)

Accuracy

Total 0.4b remaining (74.1%)

Threshold costs 0.4b (74.1%)

Counts

103 → 3

Compiler

Compiled 3828 to 3020 computations (21.1% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 16 to 13 computations (18.8% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`*-commutative_binary64`
4×	`distribute-rgt-neg-in_binary64`
4×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	116
1	51	116
2	67	116
3	79	116
4	83	116
5	84	116
6	81	116

end110.0ms (2.5%)

Compiler: Compiled 240 to 179 computations (25.4% saved)

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

Details

analyze8.0ms (0.2%)

sample1.5s (34.8%)

simplify20.0ms (0.5%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series10.0ms (0.2%)

rewrite255.0ms (5.9%)

simplify444.0ms (10.2%)

prune869.0ms (20%)

localize9.0ms (0.2%)

series8.0ms (0.2%)

rewrite47.0ms (1.1%)

simplify95.0ms (2.2%)

prune200.0ms (4.6%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite8.0ms (0.2%)

simplify93.0ms (2.1%)

prune53.0ms (1.2%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite11.0ms (0.2%)

simplify127.0ms (2.9%)

prune51.0ms (1.2%)

regimes383.0ms (8.8%)

bsearch3.0ms (0.1%)

simplify5.0ms (0.1%)

end110.0ms (2.5%)

Profiling

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22