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)

sample1.7s (34.6%)

Results

579.0ms	1418×	body	1024	valid
504.0ms	4521×	body	128	valid
406.0ms	1546×	body	512	valid
140.0ms	771×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify21.0ms (0.4%)

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

13.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.3b	(+.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))
✓	3.6b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series11.0ms (0.2%)

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))

rewrite183.0ms (3.8%)

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:

47.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
20.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
4.0ms	(/.f64 1 (-.f64 x 1))
4.0ms	(/.f64 1 (+.f64 x 1))

simplify409.0ms (8.5%)

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

prune862.0ms (17.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	850	3	853
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	850	4	854

Error

0.1b

Counts

854 → 4

Alt Table

Status	Error	Program
▶	27.9b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 9)))))
	29.8b	(/.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)))
	35.7b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (-.f64 -1 x))
✓	13.3b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 33689 to 26213 computations (22.2% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 2 (pow.f64 x 7))
✓	0.1b	(/.f64 2 (pow.f64 x 9))
✓	0.1b	(/.f64 2 (pow.f64 x 3))
✓	0.3b	(/.f64 2 (pow.f64 x 5))

series16.0ms (0.3%)

Counts

4 → 0

Calls

4 calls:

6.0ms	(/.f64 2 (pow.f64 x 3))
3.0ms	(/.f64 2 (pow.f64 x 9))
3.0ms	(/.f64 2 (pow.f64 x 7))
3.0ms	(/.f64 2 (pow.f64 x 5))

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`times-frac_binary64`
77×	`*-un-lft-identity_binary64`
77×	`add-sqr-sqrt_binary64`
77×	`add-cube-cbrt_binary64`
48×	`unpow-prod-down_binary64`

Counts

4 → 208

Calls

4 calls:

4.0ms	(/.f64 2 (pow.f64 x 3))
3.0ms	(/.f64 2 (pow.f64 x 9))
3.0ms	(/.f64 2 (pow.f64 x 5))
3.0ms	(/.f64 2 (pow.f64 x 7))

simplify129.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

564×	`times-frac_binary64`
540×	`associate-l_binary64`
390×	`associate-/l/_binary64`
380×	`associate-/l*_binary64`
249×	`fma-def_binary64`

Counts

208 → 235

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	293	3028
1	481	2908
2	1365	2796
3	4199	2796
4	4979	2796
5	5032	2796

prune261.0ms (5.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	232	3	235
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	232	7	239

Error

0.0b

Counts

239 → 7

Alt Table

Status	Error	Program
	28.0b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (/.f64 2 (pow.f64 x 9)))))
✓	27.9b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 9)))))
	29.8b	(/.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)))
	35.7b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (-.f64 -1 x))
✓	13.3b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
	27.8b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 (/.f64 2 x) (*.f64 x x)) (/.f64 2 (pow.f64 x 9)))))
▶	27.8b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 (/.f64 2 (*.f64 x x)) x) (/.f64 2 (pow.f64 x 9)))))

Compiler

Compiled 7436 to 6121 computations (17.7% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 2 (*.f64 x x)) x)
	0.1b	(/.f64 2 (pow.f64 x 9))
✓	0.3b	(/.f64 2 (*.f64 x x))
	0.3b	(/.f64 2 (pow.f64 x 5))

series7.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(/.f64 2 (*.f64 x x))
3.0ms	(/.f64 (/.f64 2 (*.f64 x x)) x)

rewrite11.0ms (0.2%)

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))

simplify115.0ms (2.4%)

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

prune242.0ms (5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	211	1	212
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	211	8	219

Error

Counts

219 → 8

Alt Table

Status	Error	Program
	33.3b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 (cbrt.f64 (.f64 (.f64 (/.f64 2 (.f64 x x)) (/.f64 2 (.f64 x x))) (/.f64 2 (*.f64 x x)))) x) (/.f64 2 (pow.f64 x 9)))))
✓	27.9b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 9)))))
	28.0b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (/.f64 2 (pow.f64 x 9)))))
	29.8b	(/.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)))
	35.7b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (-.f64 -1 x))
✓	13.3b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
▶	27.8b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 (/.f64 2 x) (*.f64 x x)) (/.f64 2 (pow.f64 x 9)))))
✓	27.8b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 (/.f64 2 (*.f64 x x)) x) (/.f64 2 (pow.f64 x 9)))))

Compiler

Compiled 7059 to 5226 computations (26% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 2 (pow.f64 x 7))
	0.1b	(/.f64 2 (pow.f64 x 9))
✓	0.1b	(/.f64 (/.f64 2 x) (*.f64 x x))
	0.3b	(/.f64 2 (pow.f64 x 5))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite12.0ms (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:

9.0ms

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

simplify128.0ms (2.7%)

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

prune271.0ms (5.6%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	241	0	241
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	241	8	249

Error

Counts

249 → 8

Alt Table

Status	Error	Program
	33.3b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 (cbrt.f64 (.f64 (.f64 (/.f64 2 (.f64 x x)) (/.f64 2 (.f64 x x))) (/.f64 2 (*.f64 x x)))) x) (/.f64 2 (pow.f64 x 9)))))
✓	27.9b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 9)))))
	28.0b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (/.f64 2 (pow.f64 x 9)))))
	29.8b	(/.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)))
	35.7b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (-.f64 -1 x))
✓	13.3b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
✓	27.8b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 (/.f64 2 x) (*.f64 x x)) (/.f64 2 (pow.f64 x 9)))))
✓	27.8b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 (/.f64 2 (*.f64 x x)) x) (/.f64 2 (pow.f64 x 9)))))

Compiler

Compiled 7943 to 5927 computations (25.4% saved)

regimes181.0ms (3.8%)

Accuracy

Total 0.2b remaining (95.1%)

Threshold costs 0.2b (95.1%)

Counts

48 → 3

Compiler

Compiled 2222 to 1792 computations (19.4% saved)

bsearch25.0ms (0.5%)

Steps

Iters	Range		Point
9	6.2269265442954204e-15	63222007334.35944	128487391.2932317
3	-437276142.64519256	-20711.948556807893	-10420091.783946034

Compiler

Compiled 2 to 1 computations (50% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
8×	`*-commutative_binary64`
5×	`sub-neg_binary64`
4×	`distribute-rgt-neg-in_binary64`
3×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	123
1	67	123
2	80	123
3	90	123
4	93	123
5	94	123
6	91	123

end174.0ms (3.6%)

Compiler: Compiled 373 to 287 computations (23.1% 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%)

sample1.7s (34.6%)

simplify21.0ms (0.4%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series11.0ms (0.2%)

rewrite183.0ms (3.8%)

simplify409.0ms (8.5%)

prune862.0ms (17.9%)

localize13.0ms (0.3%)

series16.0ms (0.3%)

rewrite22.0ms (0.5%)

simplify129.0ms (2.7%)

prune261.0ms (5.4%)

localize14.0ms (0.3%)

series7.0ms (0.2%)

rewrite11.0ms (0.2%)

simplify115.0ms (2.4%)

prune242.0ms (5%)

localize14.0ms (0.3%)

series3.0ms (0.1%)

rewrite12.0ms (0.2%)

simplify128.0ms (2.7%)

prune271.0ms (5.6%)

regimes181.0ms (3.8%)

bsearch25.0ms (0.5%)

simplify8.0ms (0.2%)

end174.0ms (3.6%)

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