Details

analyze27.0ms (0.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample25.0ms (0.7%)

Algorithm

1×

intervals

Results

8.0ms	62×	body	1024	valid
5.0ms	140×	body	128	valid
3.0ms	35×	body	512	valid
1.0ms	14×	body	256	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify23.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

29.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.5b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.2b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series16.0ms (0.4%)

Counts

1 → 1

Calls

1 calls:

16.0ms

(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`sqrt-prod_binary64`
52×	`*-un-lft-identity_binary64`
42×	`prod-diff_binary64`
39×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`

Counts

1 → 75

Calls

1 calls:

8.0ms

(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

simplify247.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

485×	`sqr-pow_binary64`
481×	`fma-neg_binary64`
455×	`unsub-neg_binary64`
425×	`unswap-sqr_binary64`
380×	`exp-prod_binary64`

Counts

76 → 69

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	87	2325
1	154	1099
2	417	889
3	1547	889
4	3056	889
5	4410	889
6	4523	889
7	4696	853
8	4047	853
9	4796	853
10	4713	853

prune105.0ms (2.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	66	3	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	3	70

Error

0.1b

Counts

70 → 3

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	29.5b	(*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
	29.5b	(+.f64 (fma.f64 (sqrt.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))))) (fma.f64 (neg.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))))

Compiler

Compiled 1630 to 814 computations (50.1% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series22.0ms (0.6%)

Counts

2 → 2

Calls

2 calls:

12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
9.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite21.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64`
24×	`sqrt-prod_binary64`
21×	`distribute-lft-out_binary64`
18×	`times-frac_binary64`
15×	`add-sqr-sqrt_binary64`

Counts

2 → 70

Calls

2 calls:

8.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
7.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify192.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

744×	`div-sub_binary64`
483×	`fma-neg_binary64`
334×	`times-frac_binary64`
317×	`associate-/l*_binary64`
310×	`distribute-rgt-in_binary64`

Counts

72 → 67

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	58	1097
1	123	1012
2	243	1012
3	504	1010
4	1190	1010
5	2283	1010
6	4202	1010
7	4971	1010
8	4998	1010
9	4828	1010

prune102.0ms (2.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	60	7	67
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	63	7	70

Error

0.0b

Counts

70 → 7

Alt Table

Status	Error	Program
	0.3b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	9.0b	(cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	0.4b	(.f64 (.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	0.4b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	9.1b	(.f64 (/.f64 1 (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (+.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	0.5b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
▶	0.2b	(/.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))

Compiler

Compiled 1504 to 1085 computations (27.9% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
✓	0.2b	(/.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))

series22.0ms (0.6%)

Counts

2 → 2

Calls

2 calls:

13.0ms	(/.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
9.0ms	(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64`
23×	`sqrt-prod_binary64`
20×	`distribute-lft-out_binary64`
18×	`times-frac_binary64`
15×	`add-sqr-sqrt_binary64`

Counts

2 → 69

Calls

2 calls:

8.0ms	(/.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
7.0ms	(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

simplify170.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

578×	`fma-neg_binary64`
337×	`sub-neg_binary64`
335×	`associate-/l*_binary64`
331×	`times-frac_binary64`
317×	`distribute-rgt-in_binary64`

Counts

71 → 67

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	58	1097
1	123	1012
2	242	1012
3	510	1010
4	1229	1010
5	2371	1010
6	4345	1010
7	4559	1010
8	4920	1010
9	4820	1010

prune118.0ms (3.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	67	7	74

Error

0.0b

Counts

74 → 7

Alt Table

Status	Error	Program
▶	0.3b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	9.0b	(cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	0.4b	(.f64 (.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	0.4b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	9.1b	(.f64 (/.f64 1 (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (+.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	0.5b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
✓	0.2b	(/.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))

Compiler

Compiled 1484 to 1059 computations (28.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓	0.1b	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
✓	0.3b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

series40.0ms (1.1%)

Counts

2 → 2

Calls

2 calls:

27.0ms

(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

13.0ms

(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

rewrite91.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

258×	`sqrt-prod_binary64`
236×	`*-un-lft-identity_binary64`
148×	`times-frac_binary64`
144×	`add-sqr-sqrt_binary64`
84×	`distribute-lft-out_binary64`

Counts

2 → 204

Calls

2 calls:

37.0ms

(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

7.0ms

(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

simplify282.0ms (7.5%)

Algorithm

1×	egg-herbie

Rules

635×	`unswap-sqr_binary64`
539×	`times-frac_binary64`
411×	`div-sub_binary64`
403×	`fma-def_binary64`
378×	`associate-/l*_binary64`

Counts

206 → 200

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	111	4253
1	186	4015
2	493	3961
3	1230	3833
4	2521	3833
5	4243	3833
6	4256	3829
7	4926	3829
8	4788	3829

prune600.0ms (15.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	371	4	375
Fresh	3	2	5
Picked	1	0	1
Done	1	0	1
Total	376	6	382

Error

Counts

382 → 6

Alt Table

Status	Error	Program
	0.3b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))
	0.3b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))))
	0.4b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	9.1b	(.f64 (/.f64 1 (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (+.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	0.6b	(*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) 4) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	0.1b	(pow.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 -1 2))

Compiler

Compiled 11276 to 8330 computations (26.1% saved)

regimes631.0ms (16.7%)

Accuracy

Total 0.2b remaining (88.6%)

Threshold costs 0.2b (88.6%)

Counts

294 → 1

Compiler

Compiled 14035 to 10828 computations (22.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	27
1	17	27
2	15	27

end1.0ms (0%)

Compiler: Compiled 18 to 13 computations (27.8% saved)

sample974.0ms (25.8%)

Algorithm

1×

intervals

Results

290.0ms	2000×	body	1024	valid
168.0ms	4244×	body	128	valid
114.0ms	1039×	body	512	valid
42.0ms	227×	body	2048	valid
36.0ms	490×	body	256	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 189 to 142 computations (24.9% saved)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

Details

analyze27.0ms (0.7%)

sample25.0ms (0.7%)

simplify23.0ms (0.6%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

series16.0ms (0.4%)

rewrite15.0ms (0.4%)

simplify247.0ms (6.6%)

prune105.0ms (2.8%)

localize6.0ms (0.2%)

series22.0ms (0.6%)

rewrite21.0ms (0.6%)

simplify192.0ms (5.1%)

prune102.0ms (2.7%)

localize6.0ms (0.1%)

series22.0ms (0.6%)

rewrite19.0ms (0.5%)

simplify170.0ms (4.5%)

prune118.0ms (3.1%)

localize8.0ms (0.2%)

series40.0ms (1.1%)

rewrite91.0ms (2.4%)

simplify282.0ms (7.5%)

prune600.0ms (15.9%)

regimes631.0ms (16.7%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample974.0ms (25.8%)

Profiling

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11