Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
81.2%	18.7%	0%	5
90.6%	9.4%	0%	6
95.3%	4.7%	0%	7
97.6%	2.3%	0%	8
98.8%	1.2%	0%	9
99.4%	0.6%	0%	10
99.7%	0.3%	0%	11
99.8%	0.1%	0%	12
99.9%	0.1%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample1.1s (30%)

Results

344.0ms	1366×	body	1024	valid
344.0ms	4616×	body	128	valid
297.0ms	1505×	body	512	valid
104.0ms	769×	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

prune2.0ms (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

10.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	10.5b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 63 to 51 computations (19% saved)

localize8.0ms (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))
✓	1.9b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series11.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

4.0ms	(+.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))

rewrite189.0ms (5%)

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 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
18.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
4.0ms	(/.f64 1 (-.f64 x 1))
4.0ms	(/.f64 1 (+.f64 x 1))

simplify428.0ms (11.4%)

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

prune764.0ms (20.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	850	3	853
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	851	3	854

Error

0.2b

Counts

854 → 3

Alt Table

Status	Error	Program
	28.4b	(/.f64 2 (pow.f64 x 3))
	35.3b	(fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x))
▶	28.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (.f64 (*.f64 (+.f64 x 1) x) (-.f64 x 1)))

Compiler

Compiled 33631 to 26164 computations (22.2% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (-.f64 (.f64 1 x) (*.f64 (+.f64 x 1) 2)) (-.f64 x 1))
✓	0.0b	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))
✓	0.0b	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
✓	17.7b	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))

series10.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

3.0ms	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))
3.0ms	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
2.0ms	(.f64 (-.f64 (.f64 1 x) (*.f64 (+.f64 x 1) 2)) (-.f64 x 1))
1.0ms	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))

rewrite51.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-sqr-sqrt_binary64`
55×	`prod-diff_binary64`
55×	`*-un-lft-identity_binary64`
49×	`add-cube-cbrt_binary64`
46×	`associate-*l/_binary64`

Counts

4 → 188

Calls

4 calls:

12.0ms	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))
10.0ms	(.f64 (-.f64 (.f64 1 x) (*.f64 (+.f64 x 1) 2)) (-.f64 x 1))
9.0ms	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
3.0ms	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))

simplify150.0ms (4%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-neg_binary64`
626×	`associate-l_binary64`
459×	`associate-r_binary64`
377×	`distribute-rgt-in_binary64`
359×	`distribute-lft-in_binary64`

Counts

236 → 303

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	272	5247
1	827	4042
2	3405	3411
3	4686	3405
4	5206	3405

prune313.0ms (8.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	303	0	303
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	303	3	306

Error

0.2b

Counts

306 → 3

Alt Table

Status	Error	Program
▶	28.4b	(/.f64 2 (pow.f64 x 3))
	35.3b	(fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x))
✓	28.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (.f64 (*.f64 (+.f64 x 1) x) (-.f64 x 1)))

Compiler

Compiled 14315 to 10641 computations (25.7% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 2 (pow.f64 x 3))

series3.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

3.0ms

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

rewrite7.0ms (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))

simplify87.0ms (2.3%)

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

prune57.0ms (1.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	65	5	70

Error

0.0b

Counts

70 → 5

Alt Table

Status	Error	Program
✓	28.4b	(/.f64 2 (pow.f64 x 3))
	35.3b	(fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x))
▶	28.3b	(/.f64 (/.f64 2 (*.f64 x x)) x)
✓	28.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (.f64 (*.f64 (+.f64 x 1) x) (-.f64 x 1)))
	28.4b	(.f64 (/.f64 (sqrt.f64 2) (.f64 x x)) (/.f64 (sqrt.f64 2) x))

Compiler

Compiled 912 to 722 computations (20.8% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 2 (*.f64 x x)) x)
✓	0.4b	(/.f64 2 (*.f64 x x))

series5.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(/.f64 (/.f64 2 (*.f64 x x)) x)
3.0ms	(/.f64 2 (*.f64 x x))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`

Counts

2 → 73

Calls

2 calls:

5.0ms	(/.f64 (/.f64 2 (*.f64 x x)) x)
3.0ms	(/.f64 2 (*.f64 x x))

simplify117.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

565×	`fma-neg_binary64`
514×	`fma-def_binary64`
311×	`div-sub_binary64`
272×	`*-commutative_binary64`
270×	`cancel-sign-sub-inv_binary64`

Counts

97 → 102

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	121	1258
1	240	1147
2	571	1138
3	1725	1111
4	2300	1099
5	3261	1099
6	4474	1099
7	4981	1099
8	4848	1099

prune56.0ms (1.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	100	7	107

Error

Counts

107 → 7

Alt Table

Status	Error	Program
	28.4b	(.f64 (sqrt.f64 (/.f64 2 (.f64 x x))) (/.f64 (sqrt.f64 (/.f64 2 (*.f64 x x))) x))
✓	28.3b	(/.f64 (/.f64 2 (*.f64 x x)) x)
✓	28.4b	(/.f64 2 (pow.f64 x 3))
	35.3b	(fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x))
	28.6b	(.f64 (.f64 (cbrt.f64 (/.f64 2 (.f64 x x))) (cbrt.f64 (/.f64 2 (.f64 x x)))) (/.f64 (cbrt.f64 (/.f64 2 (*.f64 x x))) x))
✓	28.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (.f64 (*.f64 (+.f64 x 1) x) (-.f64 x 1)))
	28.4b	(.f64 (/.f64 (sqrt.f64 2) (.f64 x x)) (/.f64 (sqrt.f64 2) x))

Compiler

Compiled 1417 to 836 computations (41% saved)

regimes126.0ms (3.3%)

Accuracy

Total 0.2b remaining (93.5%)

Threshold costs 0.2b (93.5%)

Counts

61 → 1

Compiler

Compiled 2714 to 2000 computations (26.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	17	16
2	18	16
3	16	16

end185.0ms (4.9%)

Compiler: Compiled 132 to 93 computations (29.5% 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

analyze5.0ms (0.1%)

sample1.1s (30%)

simplify20.0ms (0.5%)

prune2.0ms (0.1%)

localize8.0ms (0.2%)

series11.0ms (0.3%)

rewrite189.0ms (5%)

simplify428.0ms (11.4%)

prune764.0ms (20.3%)

localize12.0ms (0.3%)

series10.0ms (0.3%)

rewrite51.0ms (1.4%)

simplify150.0ms (4%)

prune313.0ms (8.3%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite7.0ms (0.2%)

simplify87.0ms (2.3%)

prune57.0ms (1.5%)

localize4.0ms (0.1%)

series5.0ms (0.1%)

rewrite12.0ms (0.3%)

simplify117.0ms (3.1%)

prune56.0ms (1.5%)

regimes126.0ms (3.3%)

simplify2.0ms (0.1%)

end185.0ms (4.9%)

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