Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

sample10.0ms

Algorithm

intervals

Results

5.0ms

256×

body

valid

simplify21.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

prune3.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 28.6b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

27.5b

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1_binary64`
2×	`associate-*r/_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1/2_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `insert-posit16` `sqrt-prod_binary64` `flip-+_binary64`

Counts

1 → 14

Calls

1 calls:

10.0ms

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

series987.0ms

Counts

1 → 3

Calls

1 calls:

987.0ms

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

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	38238	9
0	38238	9
0	1	3
1	1	3

simplify106.0ms

Counts

17 → 17

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4732	134
1	4732	134

prune18.0ms

Filtered

13 candidates to 17 candidates (-30.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	11	6	17
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	11	7	18

Merged error: 15.0b

Counts

18 → 7

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
0.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
27.5b	(sqrt.f64 (*.f64 x (+.f64 x x)))
27.5b	(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

84×	`sqrt-pow1_binary64`
71×	`pow1_binary64`
33×	`sqrt-prod_binary64`
32×	`sqrt-div_binary64`
26×	`add-sqr-sqrt_binary64`
25×	`pow-prod-down_binary64`
22×	`pow1/2_binary64`
20×	`associate-*r/_binary64`
14×	`pow-prod-up_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`flip3-+_binary64` `swap-sqr_binary64` `flip-+_binary64`
8×	`pow-sqr_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `insert-posit16` `frac-times_binary64`
2×	`associate-*l/_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 128

Calls

4 calls:

7.0ms	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
21.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
6.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
6.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

series4.3s

Counts

4 → 12

Calls

4 calls:

1.0s	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
1.1s	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
1.1s	(sqrt.f64 (*.f64 x (+.f64 x x)))
1.0s	(sqrt.f64 (*.f64 x (+.f64 x x)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	38238	9
0	38238	9
0	1	3
1	1	3
0	38238	9
0	38238	9
0	1	3
1	1	3
0	23610	9
1	23610	9
0	23610	9
1	23610	9
0	1	3
1	1	3
0	38394	9
0	38394	9
0	1	3
1	1	3

simplify136.0ms

Counts

140 → 140

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4959	1355
1	4959	1355

prune60.0ms

Filtered

69 candidates to 140 candidates (-102.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	136	4	140
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	137	10	147

Merged error: 15.0b

Counts

147 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))) 3)))
19.2b	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))) 3))
27.5b	(sqrt.f64 (*.f64 x (+.f64 x x)))
27.5b	(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

52×	`cbrt-prod_binary64`
43×	`add-sqr-sqrt_binary64`
38×	`sqrt-prod_binary64`
32×	`sqrt-div_binary64`
23×	`associate-r_binary64`
20×	`associate-*r/_binary64`
18×	`unpow-prod-down_binary64` `cube-prod_binary64`
17×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
14×	`unswap-sqr_binary64`
12×	`pow1_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
8×	`cbrt-div_binary64` `cube-div_binary64`
7×	`associate-l_binary64`
6×	`add-exp-log_binary64`
5×	`add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `insert-posit16` `frac-times_binary64`
3×	`pow-prod-down_binary64`
2×	`pow1/2_binary64` `unpow3_binary64` `associate-*l/_binary64` `cube-mult_binary64`
1×	`rem-cbrt-cube_binary64` `cbrt-unprod_binary64` `pow1/3_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 124

Calls

4 calls:

22.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))) 3)))
5.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))) 3))
6.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
6.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

series3.1s

Counts

4 → 12

Calls

4 calls:

1.1s	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))) 3)))
44.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))) 3))
989.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
987.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	38238	9
0	38238	9
0	1	3
1	1	3
0	38238	9
0	38238	9
0	1	3
1	1	3
0	50	9
1	50	9
0	50	9
1	50	9
0	1	3
1	1	3
0	23163	9
1	23163	9
0	23163	9
1	23163	9
0	1	3
1	1	3

simplify140.0ms

Counts

136 → 136

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4931	2119
1	4931	2119

prune74.0ms

Filtered

77 candidates to 136 candidates (-76.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	137	9	146

Merged error: 15.0b

Counts

146 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

19.2b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x))))) 4) (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))) 3))
27.5b	(sqrt.f64 (*.f64 x (+.f64 x x)))
27.5b	(sqrt.f64 (*.f64 x (+.f64 x x)))
27.5b	(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod_binary64`
13×	`pow1_binary64`
10×	`associate-*r/_binary64` `sqrt-div_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`sqrt-pow1_binary64`
5×	`sqrt-prod_binary64`
4×	`cbrt-div_binary64` `flip3-+_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `insert-posit16` `flip-+_binary64`
3×	`pow-prod-down_binary64` `pow1/2_binary64`
2×	`cube-div_binary64`
1×	`rem-cbrt-cube_binary64` `pow1/3_binary64` `sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 68

Calls

4 calls:

8.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x))))) 4) (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))) 3))
6.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
6.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
6.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

series3.1s

Counts

4 → 12

Calls

4 calls:

46.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x))))) 4) (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))) 3))
1.1s	(sqrt.f64 (*.f64 x (+.f64 x x)))
996.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
998.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	38238	9
0	38238	9
0	1	3
1	1	3
0	38238	9
0	38238	9
0	1	3
1	1	3
0	38238	9
0	38238	9
0	1	3
1	1	3
0	66	9
1	66	9
0	66	9
1	66	9
0	1	3
1	1	3

simplify123.0ms

Counts

80 → 80

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4870	1478
1	4870	1478

prune72.0ms

Filtered

57 candidates to 80 candidates (-40.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	80	9	89

Merged error: 15.0b

Counts

89 → 9

regimes26.0ms

Accuracy

98.3% (0.3b remaining)

Error of 15.4b against oracle of 15.1b and baseline of 30.5b

bsearch14.0ms

Steps

Iters	Range		Point
9	-3.7200702278433635e-302	2.1738515532578095e-306	-2.1487218123004e-310

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	14	26
1	14	26

end0.0ms

sample266.0ms

Algorithm

intervals

Results

177.0ms

8000×

body

valid

Details

analyze4.0ms

sample10.0ms

simplify21.0ms

prune3.0ms

localize4.0ms

rewrite11.0ms

series987.0ms

simplify106.0ms

prune18.0ms

localize7.0ms

rewrite47.0ms

series4.3s

simplify136.0ms

prune60.0ms

localize10.0ms

rewrite49.0ms

series3.1s

simplify140.0ms

prune74.0ms

localize17.0ms

rewrite28.0ms

series3.1s

simplify123.0ms

prune72.0ms

regimes26.0ms

bsearch14.0ms

simplify6.0ms

end0.0ms

sample266.0ms

Profiling