Details

analyze80.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
6.2%	43.7%	50%	5
9.4%	28.1%	62.5%	6
12.5%	25%	62.5%	7
15.6%	15.6%	68.8%	8
16.8%	14.4%	68.8%	9
18.5%	8.8%	72.7%	10
19.2%	7.7%	73.1%	11
20.1%	4.6%	75.2%	12
20.5%	4%	75.5%	13
21%	2.4%	76.6%	14

sample23.0ms

Algorithm

intervals

Results

14.0ms	256×	body	80	valid
1.0ms	15×	body	80	invalid
0.0ms	8×	body	80	nan

simplify110.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	1031	21
1	1031	21

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

Merged error: 0.1b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 a 1/3) 9)
0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
0.1b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.2b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
11×	`pow1_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
8×	`associate-*l/_binary64`
7×	`associate-r_binary64`
6×	`flip3--_binary64` `flip--_binary64`
5×	`sqrt-prod_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `insert-posit16` `frac-times_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`cbrt-unprod_binary64` `associate-r/_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `-commutative_binary64`
1×	`pow1/2_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 103

Calls

4 calls:

8.0ms	(*.f64 (-.f64 a 1/3) 9)
17.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
12.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))

series1.3s

Counts

4 → 12

Calls

4 calls:

204.0ms	(*.f64 (-.f64 a 1/3) 9)
543.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
251.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
288.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	419	492
1	419	492
0	64	92
1	64	92
0	419	492
1	419	492
0	64	92
1	64	92
0	12	30
1	12	30
0	348	546
1	348	546
0	56	15
1	56	15
0	348	546
1	348	546
0	56	15
1	56	15
0	5522	48
0	527	738
1	527	738
0	43	9
1	43	9
0	527	738
1	527	738
0	43	9
1	43	9
0	5303	39
0	236	171
1	236	171
0	18	18
1	18	18
0	236	171
1	236	171
0	18	18
1	18	18
0	69	48
1	69	48

simplify106.0ms

Counts

115 → 115

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4943	2067
1	4943	2067

prune141.0ms

Filtered

92 candidates to 115 candidates (-25.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	110	5	115
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	112	5	117

Merged error: 0.0b

Counts

117 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 a 1/3))
0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
0.2b	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
0.2b	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

372×	`times-frac_binary64`
248×	`add-sqr-sqrt_binary64`
247×	`*-un-lft-identity_binary64`
223×	`sqrt-prod_binary64`
191×	`add-cube-cbrt_binary64`
33×	`associate-/l*_binary64`
27×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
18×	`sqrt-div_binary64`
16×	`associate-/r/_binary64`
14×	`associate-/r*_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`flip3--_binary64` `flip--_binary64`
9×	`div-inv_binary64`
7×	`pow1_binary64`
5×	`associate-l_binary64`
4×	`add-log-exp_binary64` `associate-r_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `insert-posit16` `frac-times_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 332

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 a 1/3))
55.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
19.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
8.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))

series1.6s

Counts

4 → 12

Calls

4 calls:

352.0ms	(sqrt.f64 (-.f64 a 1/3))
561.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
389.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
299.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	364	378
1	364	378
0	57	86
1	57	86
0	364	378
1	364	378
0	57	86
1	57	86
0	5463	94
0	487	525
1	487	525
0	82	97
1	82	97
0	487	525
1	487	525
0	82	97
1	82	97
0	5014	95
0	609	777
1	609	777
0	35	9
1	35	9
0	609	777
1	609	777
0	35	9
1	35	9
0	5574	39
0	278	336
1	278	336
0	19	15
1	19	15
0	278	336
1	278	336
0	19	15
1	19	15
0	5014	48

simplify143.0ms

Counts

344 → 344

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5153	8663

prune355.0ms

Filtered

202 candidates to 344 candidates (-70.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	342	2	344
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	342	7	349

Merged error: 0b

Counts

349 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 a 1/3) 9)
0.1b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.2b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
8.0b	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
25×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`pow1_binary64`
10×	`associate-l_binary64` `associate-*l/_binary64`
8×	`sqrt-prod_binary64`
6×	`flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `associate-/r/_binary64` `insert-posit16`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l*_binary64`
2×	`cbrt-undiv_binary64` `sqrt-pow1_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `frac-times_binary64` `*-commutative_binary64`
1×	`pow1/2_binary64` `associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 115

Calls

4 calls:

9.0ms	(*.f64 (-.f64 a 1/3) 9)
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
9.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
18.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))

series1.0s

Counts

4 → 12

Calls

4 calls:

203.0ms	(*.f64 (-.f64 a 1/3) 9)
253.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
291.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
297.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	477	693
1	477	693
0	89	142
1	89	142
0	477	693
1	477	693
0	89	142
1	89	142
0	14	30
1	14	30
0	419	492
1	419	492
0	64	92
1	64	92
0	419	492
1	419	492
0	64	92
1	64	92
0	12	30
1	12	30
0	348	546
1	348	546
0	56	15
1	56	15
0	348	546
1	348	546
0	56	15
1	56	15
0	5522	48
0	236	171
1	236	171
0	18	18
1	18	18
0	236	171
1	236	171
0	18	18
1	18	18
0	69	48
1	69	48

simplify197.0ms

Counts

127 → 127

Iterations

Useful iterations: 0 (162.0ms)

Iter	Nodes	Cost
0	4915	2112
1	4915	2112

prune135.0ms

Filtered

99 candidates to 127 candidates (-28.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	128	6	134

Merged error: 0b

Counts

134 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 rand)
0.6b	(cbrt.f64 rand)
0.6b	(cbrt.f64 rand)
1.2b	(.f64 (-.f64 a 1/3) (/.f64 (.f64 (cbrt.f64 rand) (cbrt.f64 rand)) (sqrt.f64 (-.f64 a 1/3))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

1.0ms	(cbrt.f64 rand)
1.0ms	(cbrt.f64 rand)
1.0ms	(cbrt.f64 rand)
21.0ms	(.f64 (-.f64 a 1/3) (/.f64 (.f64 (cbrt.f64 rand) (cbrt.f64 rand)) (sqrt.f64 (-.f64 a 1/3))))

series1.2s

Counts

4 → 12

Calls

4 calls:

275.0ms	(cbrt.f64 rand)
276.0ms	(cbrt.f64 rand)
275.0ms	(cbrt.f64 rand)
390.0ms	(.f64 (-.f64 a 1/3) (/.f64 (.f64 (cbrt.f64 rand) (cbrt.f64 rand)) (sqrt.f64 (-.f64 a 1/3))))

Iterations

Useful iterations: 0 (152.0ms)

Iter	Nodes	Cost
0	465	1827
1	465	1827
0	743	1374
1	743	1374
0	465	1827
1	465	1827
0	743	1374
1	743	1374
0	5118	75
0	40	1603
1	40	1603
0	42	1590
1	42	1590
0	40	1603
1	40	1603
0	42	1590
1	42	1590
0	4890	50
1	4890	50
0	40	1603
1	40	1603
0	42	1590
1	42	1590
0	40	1603
1	40	1603
0	42	1590
1	42	1590
0	4890	50
1	4890	50
0	40	1603
1	40	1603
0	42	1590
1	42	1590
0	40	1603
1	40	1603
0	42	1590
1	42	1590
0	4890	50
1	4890	50

simplify137.0ms

Counts

91 → 91

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	4975	1465
1	4975	1465

prune107.0ms

Filtered

73 candidates to 91 candidates (-24.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	91	6	97

Merged error: 0b

Counts

97 → 6

regimes35.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	26	21
1	26	21

end0.0ms

sample625.0ms

Algorithm

intervals

Results

449.0ms	8000×	body	80	valid
16.0ms	288×	body	80	invalid
15.0ms	288×	body	80	nan

Details

analyze80.0ms

sample23.0ms

simplify110.0ms

prune5.0ms

localize10.0ms

rewrite47.0ms

series1.3s

simplify106.0ms

prune141.0ms

localize10.0ms

rewrite117.0ms

series1.6s

simplify143.0ms

prune355.0ms

localize9.0ms

rewrite47.0ms

series1.0s

simplify197.0ms

prune135.0ms

localize14.0ms

rewrite28.0ms

series1.2s

simplify137.0ms

prune107.0ms

regimes35.0ms

bsearch0.0ms

simplify6.0ms

end0.0ms

sample625.0ms

Profiling