Details

analyze406.0ms

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample42.0ms

Algorithm

intervals

Results

11.0ms	165×	body	80	valid
10.0ms	40×	body	2560	valid
5.0ms	24×	body	1280	valid
2.0ms	12×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	22×	body	80	nan
1.0ms	7×	body	320	valid
1.0ms	12×	body	80	invalid
0.0ms	4×	body	160	valid

simplify162.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	310	18
1	310	18

prune13.0ms

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: 31.3b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
21.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite241.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `insert-posit16` `flip--_binary64`
3×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 86

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
14.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
205.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
54.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
59.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
56.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	41	9
1	41	9
0	41	9
1	41	9
0	1	3
1	1	3
0	63	9
1	63	9
0	63	9
1	63	9
0	1	3
1	1	3
0	38	9
1	38	9
0	38	9
1	38	9
0	1	3
1	1	3
0	78	9
1	78	9
0	78	9
1	78	9
0	1	3
1	1	3

simplify113.0ms

Counts

98 → 98

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	5019	2077

prune92.0ms

Filtered

70 candidates to 98 candidates (-40.0%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	85	13	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	85	14	99

Merged error: 20.2b

Counts

99 → 14

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
21.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64`
11×	`times-frac_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
6×	`associate-l_binary64`
5×	`flip3--_binary64` `flip--_binary64` `sqrt-prod_binary64`
4×	`prod-exp_binary64` `difference-of-squares_binary64` `insert-posit16`
3×	`unswap-sqr_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 87

Calls

4 calls:

18.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
54.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
54.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
55.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	41	9
1	41	9
0	41	9
1	41	9
0	1	3
1	1	3
0	63	9
1	63	9
0	63	9
1	63	9
0	1	3
1	1	3
0	38	9
1	38	9
0	38	9
1	38	9
0	1	3
1	1	3
0	71	9
1	71	9
0	71	9
1	71	9
0	1	3
1	1	3

simplify153.0ms

Counts

99 → 99

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	5037	1834

prune68.0ms

Filtered

66 candidates to 99 candidates (-50.0%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	98	15	113

Merged error: 20.2b

Counts

113 → 15

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 a)
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
21.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
6×	`add-cube-cbrt_binary64`
5×	`pow1_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `sqrt-prod_binary64`
3×	`flip3--_binary64` `flip--_binary64` `cbrt-prod_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `difference-of-squares_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `pow1/3_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64`

Counts

4 → 55

Calls

4 calls:

1.0ms	(cbrt.f64 a)
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series212.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(cbrt.f64 a)
53.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
56.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
56.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	41	9
1	41	9
0	41	9
1	41	9
0	1	3
1	1	3
0	63	9
1	63	9
0	63	9
1	63	9
0	1	3
1	1	3
0	38	9
1	38	9
0	38	9
1	38	9
0	1	3
1	1	3
0	18	9
1	18	9
0	18	9
1	18	9
0	1	3
1	1	3

simplify111.0ms

Counts

67 → 67

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4923	880
1	4923	880

prune67.0ms

Filtered

51 candidates to 67 candidates (-31.4%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	61	6	67
Fresh	2	10	12
Picked	1	0	1
Done	0	2	2
Total	64	18	82

Merged error: 20.2b

Counts

82 → 18

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
21.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
21.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_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` `distribute-lft-out--_binary64`

Counts

4 → 62

Calls

4 calls:

10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
56.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
53.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
55.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	41	9
1	41	9
0	41	9
1	41	9
0	1	3
1	1	3
0	41	9
1	41	9
0	41	9
1	41	9
0	1	3
1	1	3
0	63	9
1	63	9
0	63	9
1	63	9
0	1	3
1	1	3
0	63	9
1	63	9
0	63	9
1	63	9
0	1	3
1	1	3

simplify141.0ms

Counts

74 → 74

Iterations

Useful iterations: 0 (116.0ms)

Iter	Nodes	Cost
0	4972	1220
1	4972	1220

prune61.0ms

Filtered

54 candidates to 74 candidates (-37.0%)

Pruning

19 alts after pruning (16 fresh and 3 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	15	15
Picked	0	1	1
Done	0	2	2
Total	73	19	92

Merged error: 20.2b

Counts

92 → 19

regimes186.0ms

Accuracy

94.3% (0.7b remaining)

Error of 21.9b against oracle of 21.2b and baseline of 34.0b

bsearch52.0ms

Steps

Iters	Range		Point
6	3.947951409424808e-92	6.25469584947764e-91	4.0435292778603006e-92
10	-9.016554096635856e+165	-6.078197847532872e+152	-1.3450496563396583e+154

simplify10.0ms

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	138	75
1	138	75

end0.0ms

sample1.0s

Algorithm

intervals

Results

268.0ms	1074×	body	2560	valid
222.0ms	5159×	body	80	valid
170.0ms	860×	body	1280	valid
66.0ms	434×	body	640	valid
33.0ms	115×	body	5120	valid
31.0ms	767×	body	80	nan
28.0ms	241×	body	320	valid
12.0ms	271×	body	80	invalid
9.0ms	117×	body	160	valid

Iter	Nodes	Cost
0	41	9
1	41	9
0	41	9
1	41	9
0	1	3
1	1	3
0	63	9
1	63	9
0	63	9
1	63	9
0	1	3
1	1	3
0	38	9
1	38	9
0	38	9
1	38	9
0	1	3
1	1	3
0	78	9
1	78	9
0	78	9
1	78	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	41	9
1	41	9
0	41	9
1	41	9
0	1	3
1	1	3
0	63	9
1	63	9
0	63	9
1	63	9
0	1	3
1	1	3
0	38	9
1	38	9
0	38	9
1	38	9
0	1	3
1	1	3
0	71	9
1	71	9
0	71	9
1	71	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	41	9
1	41	9
0	41	9
1	41	9
0	1	3
1	1	3
0	63	9
1	63	9
0	63	9
1	63	9
0	1	3
1	1	3
0	38	9
1	38	9
0	38	9
1	38	9
0	1	3
1	1	3
0	18	9
1	18	9
0	18	9
1	18	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	41	9
1	41	9
0	41	9
1	41	9
0	1	3
1	1	3
0	41	9
1	41	9
0	41	9
1	41	9
0	1	3
1	1	3
0	63	9
1	63	9
0	63	9
1	63	9
0	1	3
1	1	3
0	63	9
1	63	9
0	63	9
1	63	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	41	9
1	41	9
0	41	9
1	41	9
0	1	3
1	1	3
0	63	9
1	63	9
0	63	9
1	63	9
0	1	3
1	1	3
0	38	9
1	38	9
0	38	9
1	38	9
0	1	3
1	1	3
0	78	9
1	78	9
0	78	9
1	78	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	41	9
1	41	9
0	41	9
1	41	9
0	1	3
1	1	3
0	63	9
1	63	9
0	63	9
1	63	9
0	1	3
1	1	3
0	38	9
1	38	9
0	38	9
1	38	9
0	1	3
1	1	3
0	71	9
1	71	9
0	71	9
1	71	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	41	9
1	41	9
0	41	9
1	41	9
0	1	3
1	1	3
0	63	9
1	63	9
0	63	9
1	63	9
0	1	3
1	1	3
0	38	9
1	38	9
0	38	9
1	38	9
0	1	3
1	1	3
0	18	9
1	18	9
0	18	9
1	18	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	41	9
1	41	9
0	41	9
1	41	9
0	1	3
1	1	3
0	41	9
1	41	9
0	41	9
1	41	9
0	1	3
1	1	3
0	63	9
1	63	9
0	63	9
1	63	9
0	1	3
1	1	3
0	63	9
1	63	9
0	63	9
1	63	9
0	1	3
1	1	3

Details

analyze406.0ms

sample42.0ms

simplify162.0ms

prune13.0ms

localize10.0ms

rewrite241.0ms

series225.0ms

simplify113.0ms

prune92.0ms

localize11.0ms

rewrite41.0ms

series220.0ms

simplify153.0ms

prune68.0ms

localize13.0ms

rewrite23.0ms

series212.0ms

simplify111.0ms

prune67.0ms

localize15.0ms

rewrite32.0ms

series221.0ms

simplify141.0ms

prune61.0ms

regimes186.0ms

bsearch52.0ms

simplify10.0ms

end0.0ms

sample1.0s

Profiling

Iter	Nodes	Cost
0	41	9
1	41	9
0	41	9
1	41	9
0	1	3
1	1	3
0	63	9
1	63	9
0	63	9
1	63	9
0	1	3
1	1	3
0	38	9
1	38	9
0	38	9
1	38	9
0	1	3
1	1	3
0	78	9
1	78	9
0	78	9
1	78	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	41	9
1	41	9
0	41	9
1	41	9
0	1	3
1	1	3
0	63	9
1	63	9
0	63	9
1	63	9
0	1	3
1	1	3
0	38	9
1	38	9
0	38	9
1	38	9
0	1	3
1	1	3
0	71	9
1	71	9
0	71	9
1	71	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	41	9
1	41	9
0	41	9
1	41	9
0	1	3
1	1	3
0	63	9
1	63	9
0	63	9
1	63	9
0	1	3
1	1	3
0	38	9
1	38	9
0	38	9
1	38	9
0	1	3
1	1	3
0	18	9
1	18	9
0	18	9
1	18	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	41	9
1	41	9
0	41	9
1	41	9
0	1	3
1	1	3
0	41	9
1	41	9
0	41	9
1	41	9
0	1	3
1	1	3
0	63	9
1	63	9
0	63	9
1	63	9
0	1	3
1	1	3
0	63	9
1	63	9
0	63	9
1	63	9
0	1	3
1	1	3