Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

sample25.0ms

Algorithm

intervals

Results

6.0ms	188×	body	80	valid
4.0ms	27×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	28×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	2×	body	160	valid

simplify214.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (199.0ms)

Iter	Nodes	Cost
0	4809	19
1	4809	19

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 16.2b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
0.7b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
19×	`distribute-lft-out_binary64`
14×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
5×	`associate-/r_binary64` `associate-/l_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `pow1_binary64` `associate-/r/_binary64` `div-sub_binary64` `insert-posit16` `flip-+_binary64`
1×	`flip3--_binary64` `cbrt-undiv_binary64` `associate-+l-_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

2 → 67

Calls

2 calls:

13.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
21.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

series3.1s

Counts

2 → 6

Calls

2 calls:

1.2s	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
1.9s	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	18811	9
1	18811	9
0	18811	9
1	18811	9
0	1	3
1	1	3
0	21882	9
1	21882	9
0	21882	9
1	21882	9
0	1	3
1	1	3

simplify106.0ms

Counts

73 → 73

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5231	1437

prune72.0ms

Filtered

48 candidates to 73 candidates (-52.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	62	11	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	11	74

Merged error: 15.5b

Counts

74 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.0b	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
0.7b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity_binary64`
40×	`add-sqr-sqrt_binary64`
34×	`times-frac_binary64`
24×	`distribute-lft-out_binary64` `add-cube-cbrt_binary64`
11×	`add-log-exp_binary64`
10×	`associate-/r*_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64`
4×	`pow1_binary64` `diff-log_binary64` `associate-/r/_binary64` `distribute-lft-out--_binary64` `insert-posit16`
3×	`sub-neg_binary64` `flip3--_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `cbrt-undiv_binary64` `difference-of-sqr-1_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `frac-sub_binary64`
1×	`associate--r+_binary64` `associate--r-_binary64`

Counts

4 → 116

Calls

4 calls:

9.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
9.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
39.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
17.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

series4.1s

Counts

4 → 12

Calls

4 calls:

779.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
784.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
1.7s	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
820.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	28083	9
0	28083	9
0	1	3
1	1	3
0	26304	9
0	26304	9
0	1	3
1	1	3
0	33039	9
0	33039	9
0	1	3
1	1	3
0	33039	9
0	33039	9
0	1	3
1	1	3

simplify127.0ms

Counts

128 → 128

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4961	2525
1	4961	2525

prune138.0ms

Filtered

87 candidates to 128 candidates (-47.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	120	8	128
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	122	17	139

Merged error: 15.5b

Counts

139 → 17

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)
0.1b	(/.f64 (+.f64 (.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))) (-.f64 beta (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 -1 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3))))) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))))
0.7b	(+.f64 -1 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3))
8.5b	(.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
33×	`times-frac_binary64`
26×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
23×	`associate-*r/_binary64`
21×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
19×	`distribute-lft-out_binary64`
16×	`flip3-+_binary64` `flip-+_binary64`
12×	`associate-/l/_binary64` `associate-/r/_binary64`
10×	`pow1_binary64` `frac-add_binary64` `frac-times_binary64`
6×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
5×	`flip3--_binary64` `flip--_binary64` `associate-*l/_binary64`
4×	`cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-exp_binary64` `insert-posit16`
3×	`pow-prod-down_binary64` `pow-unpow_binary64` `associate-l_binary64` `associate-/l*_binary64` `div-inv_binary64`
2×	`rem-cube-cbrt_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `associate-/r_binary64` `associate-+r-_binary64` `associate-r_binary64` `pow-pow_binary64` `sqr-pow_binary64` `cube-div_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `unpow3_binary64` `sum-log_binary64` `-commutative_binary64` `cube-mult_binary64`

Counts

4 → 149

Calls

4 calls:

12.0ms	(pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)
48.0ms	(/.f64 (+.f64 (.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))) (-.f64 beta (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 -1 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3))))) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))))
25.0ms	(+.f64 -1 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3))
30.0ms	(.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))

series3.8s

Counts

4 → 12

Calls

4 calls:

689.0ms	(pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)
1.2s	(/.f64 (+.f64 (.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))) (-.f64 beta (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 -1 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3))))) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))))
683.0ms	(+.f64 -1 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3))
1.2s	(.f64 beta (.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	26941	9
0	26941	9
0	1	3
1	1	3
0	27394	9
0	27394	9
0	1	3
1	1	3
0	28264	9
0	28264	9
0	1	3
1	1	3
0	26714	9
0	26714	9
0	1	3
1	1	3

simplify142.0ms

Counts

161 → 161

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4994	7863
1	4994	7863

prune535.0ms

Filtered

104 candidates to 161 candidates (-54.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	153	8	161
Fresh	9	7	16
Picked	1	0	1
Done	0	0	0
Total	163	15	178

Merged error: 15.2b

Counts

178 → 15

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))
0.6b	(exp.f64 (log.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))))
0.7b	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
10.5b	(log.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
14×	`log-prod_binary64`
11×	`add-log-exp_binary64`
10×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`log-div_binary64`
7×	`flip3--_binary64` `add-cube-cbrt_binary64` `exp-sum_binary64` `flip--_binary64`
6×	`pow1_binary64` `times-frac_binary64` `frac-sub_binary64`
5×	`add-exp-log_binary64`
4×	`diff-log_binary64` `add-cbrt-cube_binary64` `exp-diff_binary64` `insert-posit16` `exp-prod_binary64`
3×	`sub-neg_binary64`
2×	`log-pow_binary64` `difference-of-sqr-1_binary64`
1×	`associate--r+_binary64` `associate--r-_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64`

Counts

4 → 85

Calls

4 calls:

37.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))
39.0ms	(exp.f64 (log.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))))
17.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
35.0ms	(log.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))

series7.6s

Counts

4 → 12

Calls

4 calls:

2.8s	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))
1.9s	(exp.f64 (log.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))))
885.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
2.0s	(log.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	26869	9
0	26869	9
0	1	3
1	1	3
0	28551	9
0	28551	9
0	1	3
1	1	3
0	27155	9
0	27155	9
0	1	3
1	1	3
0	25324	9
0	25324	9
0	1	3
1	1	3

simplify122.0ms

Counts

97 → 97

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	6197	3219

prune111.0ms

Filtered

72 candidates to 97 candidates (-34.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	91	6	97
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	96	16	112

Merged error: 15.2b

Counts

112 → 16

regimes117.0ms

Accuracy

0% (0.6b remaining)

Error of 15.8b against oracle of 15.2b and baseline of 15.8b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	65	37
1	65	37

end0.0ms

sample711.0ms

Algorithm

intervals

Results

179.0ms	5837×	body	80	valid
130.0ms	873×	body	1280	valid
128.0ms	8000×	pre	80	true
78.0ms	676×	body	640	valid
41.0ms	414×	body	320	valid
12.0ms	200×	body	160	valid

Details

analyze2.0ms

sample25.0ms

simplify214.0ms

prune8.0ms

localize9.0ms

rewrite38.0ms

series3.1s

simplify106.0ms

prune72.0ms

localize11.0ms

rewrite79.0ms

series4.1s

simplify127.0ms

prune138.0ms

localize20.0ms

rewrite124.0ms

series3.8s

simplify142.0ms

prune535.0ms

localize12.0ms

rewrite132.0ms

series7.6s

simplify122.0ms

prune111.0ms

regimes117.0ms

bsearch0.0ms

simplify7.0ms

end0.0ms

sample711.0ms

Profiling