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)

sample54.0ms (1.6%)

Algorithm

1×

intervals

Results

7.0ms	147×	body	128	valid
7.0ms	50×	body	512	valid
7.0ms	38×	body	1024	valid
2.0ms	21×	body	256	valid

Compiler

Compiled 34 to 28 computations (17.6% saved)

simplify16.0ms (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

8.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	8.4b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 63 to 51 computations (19% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
✓	0.0b	(/.f64 1 (-.f64 x 1))
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	1.9b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series12.0ms (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)))
3.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.0ms	(/.f64 1 (-.f64 x 1))
2.0ms	(/.f64 1 (+.f64 x 1))

rewrite203.0ms (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:

53.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
23.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
10.0ms	(/.f64 1 (-.f64 x 1))
4.0ms	(/.f64 1 (+.f64 x 1))

simplify448.0ms (13%)

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

prune775.0ms (22.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	852	1	853
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	852	2	854

Error

0.2b

Counts

854 → 2

Alt Table

Status	Error	Program
✓	8.4b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
▶	33.7b	(/.f64 2 (pow.f64 x 3))

Compiler

Compiled 33561 to 26113 computations (22.2% 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))

simplify88.0ms (2.6%)

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

prune54.0ms (1.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	62	5	67
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	62	7	69

Error

Counts

69 → 7

Alt Table

Status	Error	Program
	33.6b	(/.f64 (/.f64 2 (*.f64 x x)) x)
	39.4b	(cbrt.f64 (/.f64 (.f64 (.f64 2 2) 2) (.f64 (.f64 (pow.f64 x 3) (pow.f64 x 3)) (pow.f64 x 3))))
✓	33.7b	(/.f64 2 (pow.f64 x 3))
✓	8.4b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
▶	33.6b	(/.f64 (/.f64 2 x) (*.f64 x x))
	38.5b	(*.f64 (sqrt.f64 (/.f64 2 (pow.f64 x 3))) (sqrt.f64 (/.f64 2 (pow.f64 x 3))))
	39.1b	(cbrt.f64 (pow.f64 (/.f64 2 (pow.f64 x 3)) 3))

Compiler

Compiled 950 to 759 computations (20.1% 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))

rewrite9.0ms (0.3%)

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:

5.0ms

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

simplify147.0ms (4.3%)

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

prune50.0ms (1.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	76	7	83

Error

Counts

83 → 7

Alt Table

Status	Error	Program
▶	33.6b	(/.f64 (/.f64 2 (*.f64 x x)) x)
✓	33.7b	(/.f64 2 (pow.f64 x 3))
✓	8.4b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
	39.4b	(cbrt.f64 (/.f64 8 (pow.f64 x 9)))
✓	33.6b	(/.f64 (/.f64 2 x) (*.f64 x x))
	38.5b	(*.f64 (sqrt.f64 (/.f64 2 (pow.f64 x 3))) (sqrt.f64 (/.f64 2 (pow.f64 x 3))))
	39.1b	(cbrt.f64 (pow.f64 (/.f64 2 (pow.f64 x 3)) 3))

Compiler

Compiled 1121 to 708 computations (36.8% 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)
✓	0.5b	(/.f64 2 (*.f64 x x))

series5.0ms (0.2%)

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))

simplify127.0ms (3.7%)

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

prune57.0ms (1.7%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	102	7	109

Error

Counts

109 → 7

Alt Table

Status	Error	Program
✓	33.6b	(/.f64 (/.f64 2 (*.f64 x x)) x)
✓	33.7b	(/.f64 2 (pow.f64 x 3))
✓	8.4b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
	39.4b	(cbrt.f64 (/.f64 8 (pow.f64 x 9)))
✓	33.6b	(/.f64 (/.f64 2 x) (*.f64 x x))
	38.5b	(*.f64 (sqrt.f64 (/.f64 2 (pow.f64 x 3))) (sqrt.f64 (/.f64 2 (pow.f64 x 3))))
	39.1b	(cbrt.f64 (pow.f64 (/.f64 2 (pow.f64 x 3)) 3))

Compiler

Compiled 1377 to 815 computations (40.8% saved)

regimes114.0ms (3.3%)

Accuracy

Total 0.6b remaining (74.7%)

Threshold costs 0.6b (74.7%)

Counts

40 → 3

Compiler

Compiled 1090 to 886 computations (18.7% saved)

bsearch1.0ms (0%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
3×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	88
1	31	88
2	38	88
3	40	88
4	41	88
5	38	88

end1.0ms (0%)

Compiler: Compiled 60 to 48 computations (20% saved)

sample1.2s (35.3%)

Algorithm

1×

intervals

Results

358.0ms	1325×	body	1024	valid
225.0ms	4399×	body	128	valid
219.0ms	1509×	body	512	valid
73.0ms	767×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 146 to 117 computations (19.9% 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%)

sample54.0ms (1.6%)

simplify16.0ms (0.5%)

prune2.0ms (0.1%)

localize10.0ms (0.3%)

series12.0ms (0.3%)

rewrite203.0ms (5.9%)

simplify448.0ms (13%)

prune775.0ms (22.6%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite7.0ms (0.2%)

simplify88.0ms (2.6%)

prune54.0ms (1.6%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite9.0ms (0.3%)

simplify147.0ms (4.3%)

prune50.0ms (1.4%)

localize4.0ms (0.1%)

series5.0ms (0.2%)

rewrite12.0ms (0.3%)

simplify127.0ms (3.7%)

prune57.0ms (1.7%)

regimes114.0ms (3.3%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.2s (35.3%)

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