Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample28.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 20 to 16 computations (20% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	11	12
2	10	12

prune2.0ms (0%)

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

0.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series58.0ms (0.8%)

Counts

3 → 12

Calls

3 calls:

42.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
8.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
7.0ms	(sqrt.f64 (+.f64 x 1))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
21×	`distribute-lft-out_binary64`
18×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`

Counts

3 → 82

Calls

3 calls:

7.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
4.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
2.0ms	(sqrt.f64 (+.f64 x 1))

simplify94.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

733×	`fma-neg_binary64`
333×	`associate-/r*_binary64`
321×	`associate-/l/_binary64`
303×	`associate-*l/_binary64`
284×	`cancel-sign-sub-inv_binary64`

Counts

94 → 108

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	123	1335
1	263	1239
2	634	1227
3	1878	1212
4	4323	1211
5	4987	1211
6	4875	1211

prune74.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	105	4	109

Error

Counts

109 → 4

Alt Table

Status	Error	Program
▶	22.4b	(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
	41.9b	(cbrt.f64 (/.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
	42.0b	(*.f64 -1 (-.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 1669 to 1284 computations (23.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	0.0b	(sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	0.3b	(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
✓	0.4b	(/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

series245.0ms (3.4%)

Counts

3 → 8

Calls

3 calls:

168.0ms

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

43.0ms

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

34.0ms

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

rewrite162.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

647×	`sqrt-prod_binary64`
499×	`add-sqr-sqrt_binary64`
472×	`*-un-lft-identity_binary64`
442×	`times-frac_binary64`
208×	`distribute-lft-out_binary64`

Counts

3 → 414

Calls

3 calls:

56.0ms

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

8.0ms

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

5.0ms

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

simplify391.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

583×	`times-frac_binary64`
335×	`associate-/r*_binary64`
335×	`fma-neg_binary64`
259×	`associate-/r/_binary64`
233×	`associate-*l/_binary64`

Counts

422 → 345

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	249	16541
1	701	13644
2	2221	12986
3	4564	12930
4	4999	12930
5	4964	12930

prune393.0ms (5.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	513	1	514
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	514	4	518

Error

Counts

518 → 4

Alt Table

Status	Error	Program
✓	22.4b	(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
▶	22.2b	(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 (sqrt.f64 (sqrt.f64 x)) (/.f64 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 (sqrt.f64 x)))))
	42.0b	(*.f64 -1 (-.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 16682 to 12153 computations (27.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (sqrt.f64 (sqrt.f64 x)) (/.f64 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 (sqrt.f64 x))))
✓	0.2b	(/.f64 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 (sqrt.f64 x)))
✓	0.3b	(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 (sqrt.f64 (sqrt.f64 x)) (/.f64 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 (sqrt.f64 x)))))
	0.4b	(/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

series290.0ms (4%)

Counts

3 → 8

Calls

3 calls:

172.0ms

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

70.0ms

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

47.0ms

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

rewrite1.1s (15.5%)

Algorithm

1×	rewrite-expression-head

Rules

5028×	`sqrt-prod_binary64`
3487×	`times-frac_binary64`
2407×	`*-un-lft-identity_binary64`
2385×	`add-sqr-sqrt_binary64`
1472×	`add-cube-cbrt_binary64`

Counts

3 → 1970

Calls

3 calls:

473.0ms

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

30.0ms

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

11.0ms

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

simplify2.3s (31.9%)

Algorithm

1×	egg-herbie

Rules

691×	`associate-/l/_binary64`
682×	`associate-/r/_binary64`
670×	`associate-*l/_binary64`
570×	`associate-/l*_binary64`
218×	`fma-def_binary64`

Counts

1978 → 1232

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	630	91678
1	1736	83373
2	4329	79384
3	4752	79384
4	4993	79384
5	4959	79384

prune1.1s (15.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	1313	0	1313
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	1313	4	1317

Error

Counts

1317 → 4

Alt Table

Status	Error	Program
✓	22.4b	(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
✓	22.2b	(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 (sqrt.f64 (sqrt.f64 x)) (/.f64 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 (sqrt.f64 x)))))
▶	42.0b	(*.f64 -1 (-.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 57632 to 34567 computations (40% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 x 1))
✓	3.4b	(-.f64 1 (sqrt.f64 (+.f64 x 1)))

series10.0ms (0.1%)

Counts

1 → 4

Calls

1 calls:

10.0ms

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

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
21×	`prod-diff_binary64`
20×	`sqrt-prod_binary64`
17×	`add-cube-cbrt_binary64`

Counts

1 → 51

Calls

1 calls:

6.0ms

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

simplify84.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1016×	`fma-neg_binary64`
557×	`unsub-neg_binary64`
351×	`cancel-sign-sub-inv_binary64`
329×	`unswap-sqr_binary64`
299×	`distribute-rgt-in_binary64`

Counts

55 → 52

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	88	978
1	173	803
2	467	629
3	1485	621
4	3213	617
5	4137	617
6	4903	617

prune56.0ms (0.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	81	4	85

Error

Counts

85 → 4

Alt Table

Status	Error	Program
✓	22.4b	(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
✓	22.2b	(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 (sqrt.f64 (sqrt.f64 x)) (/.f64 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 (sqrt.f64 x)))))
✓	42.0b	(*.f64 -1 (-.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 1644 to 1413 computations (14.1% saved)

regimes214.0ms (2.9%)

Accuracy

Total 0.2b remaining (95.9%)

Threshold costs 0.2b (95.9%)

Counts

83 → 1

Compiler

Compiled 2944 to 2260 computations (23.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	13	15
2	12	15

end1.0ms (0%)

Compiler: Compiled 11 to 9 computations (18.2% saved)

sample548.0ms (7.5%)

Algorithm

1×

intervals

Results

305.0ms	7999×	body	128	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 89 to 69 computations (22.5% saved)

Details

analyze4.0ms (0.1%)

sample28.0ms (0.4%)

simplify7.0ms (0.1%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series58.0ms (0.8%)

rewrite17.0ms (0.2%)

simplify94.0ms (1.3%)

prune74.0ms (1%)

localize9.0ms (0.1%)

series245.0ms (3.4%)

rewrite162.0ms (2.2%)

simplify391.0ms (5.3%)

prune393.0ms (5.4%)

localize12.0ms (0.2%)

series290.0ms (4%)

rewrite1.1s (15.5%)

simplify2.3s (31.9%)

prune1.1s (15.4%)

localize5.0ms (0.1%)

series10.0ms (0.1%)

rewrite11.0ms (0.1%)

simplify84.0ms (1.1%)

prune56.0ms (0.8%)

regimes214.0ms (2.9%)

simplify2.0ms (0%)

end1.0ms (0%)

sample548.0ms (7.5%)

Profiling