Details

analyze517.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
20.3%	73.3%	6.4%	7
27.3%	66.3%	6.4%	8
38.2%	53%	8.7%	9
46%	40.6%	13.4%	10
49.9%	35.1%	15%	11
54.9%	26.9%	18.1%	12
57.4%	22%	20.6%	13
59.7%	18%	22.4%	14

sample37.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
2.0ms	19×	body	80	nan
1.0ms	11×	body	80	invalid

simplify238.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	1225	54
1	1225	54

prune8.0ms

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: 22.9b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
2.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
25.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
25.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
7×	`sqrt-prod_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `flip--_binary64` `sqrt-div_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64`
1×	`distribute-lft-out--_binary64`

Counts

4 → 59

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
208.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series262.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
66.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
62.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
70.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3
0	42	9
1	42	9
0	42	9
1	42	9
0	1	3
1	1	3

simplify106.0ms

Counts

71 → 71

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5014	1301

prune127.0ms

Filtered

53 candidates to 71 candidates (-34.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	62	9	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	9	72

Merged error: 20.4b

Counts

72 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

7.2b	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
25.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
25.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
25.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `sqrt-div_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16`
3×	`pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 60

Calls

4 calls:

4.0ms	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series254.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
63.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
62.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
63.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	68	9
1	68	9
0	68	9
1	68	9
0	1	3
1	1	3

simplify109.0ms

Counts

72 → 72

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	5032	1272

prune147.0ms

Filtered

54 candidates to 72 candidates (-33.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	70	11	81

Merged error: 20.4b

Counts

81 → 11

localize26.0ms

Local error

Found 4 expressions with local error:

5.5b	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
25.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
26.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
26.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `cbrt-prod_binary64`
5×	`pow1_binary64`
4×	`cbrt-div_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16`
3×	`flip3--_binary64` `flip--_binary64` `sqrt-prod_binary64`
2×	`pow1/3_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 56

Calls

4 calls:

4.0ms	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series254.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
63.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
62.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
64.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	68	9
1	68	9
0	68	9
1	68	9
0	1	3
1	1	3

simplify133.0ms

Counts

68 → 68

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	4963	1559
1	4963	1559

prune144.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	68	11	79

Merged error: 20.4b

Counts

79 → 11

localize26.0ms

Local error

Found 4 expressions with local error:

11.1b	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))) b)
25.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
26.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
26.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `cbrt-prod_binary64`
5×	`pow1_binary64`
4×	`cbrt-div_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `flip--_binary64`
3×	`sqrt-prod_binary64`
2×	`pow1/3_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 56

Calls

4 calls:

11.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series256.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))) b)
62.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
64.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
64.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	76	9
1	76	9
0	76	9
1	76	9
0	1	3
1	1	3

simplify168.0ms

Counts

68 → 68

Iterations

Useful iterations: 0 (135.0ms)

Iter	Nodes	Cost
0	4932	1550
1	4932	1550

prune124.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	68	11	79

Merged error: 20.4b

Counts

79 → 11

regimes128.0ms

Accuracy

50.4% (1.3b remaining)

Error of 19.0b against oracle of 17.8b and baseline of 20.3b

bsearch51.0ms

Steps

Iters	Range		Point
10	-4.305234845108821e+161	-4.595700627286232e+149	-1.3316660457403754e+154

simplify9.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	95	120
1	95	120

end0.0ms

sample987.0ms

Algorithm

intervals

Results

683.0ms	8000×	body	80	valid
52.0ms	637×	body	80	nan
33.0ms	389×	body	80	invalid

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3
0	42	9
1	42	9
0	42	9
1	42	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	68	9
1	68	9
0	68	9
1	68	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	68	9
1	68	9
0	68	9
1	68	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	76	9
1	76	9
0	76	9
1	76	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3
0	42	9
1	42	9
0	42	9
1	42	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	68	9
1	68	9
0	68	9
1	68	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	68	9
1	68	9
0	68	9
1	68	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	76	9
1	76	9
0	76	9
1	76	9
0	1	3
1	1	3

Details

analyze517.0ms

sample37.0ms

simplify238.0ms

prune8.0ms

localize23.0ms

rewrite232.0ms

series262.0ms

simplify106.0ms

prune127.0ms

localize24.0ms

rewrite21.0ms

series254.0ms

simplify109.0ms

prune147.0ms

localize26.0ms

rewrite21.0ms

series254.0ms

simplify133.0ms

prune144.0ms

localize26.0ms

rewrite28.0ms

series256.0ms

simplify168.0ms

prune124.0ms

regimes128.0ms

bsearch51.0ms

simplify9.0ms

end0.0ms

sample987.0ms

Profiling

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3
0	42	9
1	42	9
0	42	9
1	42	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	68	9
1	68	9
0	68	9
1	68	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	68	9
1	68	9
0	68	9
1	68	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	76	9
1	76	9
0	76	9
1	76	9
0	1	3
1	1	3